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/home/tahkoom/public_html/wp-includes/sodium_compat/src/Core/Curve25519.php
<?php
if (class_exists('ParagonIE_Sodium_Core_Curve25519', false)) {
return;
}
/**
* Class ParagonIE_Sodium_Core_Curve25519
*
* Implements Curve25519 core functions
*
* Based on the ref10 curve25519 code provided by libsodium
*
* @ref https://github.com/jedisct1/libsodium/blob/master/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c
*/
abstract class ParagonIE_Sodium_Core_Curve25519 extends ParagonIE_Sodium_Core_Curve25519_H
{
/**
* Get a field element of size 10 with a value of 0
*
* @internal You should not use this directly from another application
*
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_0()
{
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
);
}
/**
* Get a field element of size 10 with a value of 1
*
* @internal You should not use this directly from another application
*
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_1()
{
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
);
}
/**
* Add two field elements.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @param ParagonIE_Sodium_Core_Curve25519_Fe $g
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @psalm-suppress MixedAssignment
* @psalm-suppress MixedOperand
*/
public static function fe_add(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g
) {
/** @var array<int, int> $arr */
$arr = array();
for ($i = 0; $i < 10; ++$i) {
$arr[$i] = (int) ($f[$i] + $g[$i]);
}
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($arr);
}
/**
* Constant-time conditional move.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @param ParagonIE_Sodium_Core_Curve25519_Fe $g
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @psalm-suppress MixedAssignment
*/
public static function fe_cmov(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g,
$b = 0
) {
/** @var array<int, int> $h */
$h = array();
$b *= -1;
for ($i = 0; $i < 10; ++$i) {
$x = (($f[$i] ^ $g[$i]) & $b);
$h[$i] = ($f[$i]) ^ $x;
}
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($h);
}
/**
* Create a copy of a field element.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_copy(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$h = clone $f;
return $h;
}
/**
* Give: 32-byte string.
* Receive: A field element object to use for internal calculations.
*
* @internal You should not use this directly from another application
*
* @param string $s
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @throws RangeException
* @throws TypeError
*/
public static function fe_frombytes($s)
{
if (self::strlen($s) !== 32) {
throw new RangeException('Expected a 32-byte string.');
}
$h0 = self::load_4($s);
$h1 = self::load_3(self::substr($s, 4, 3)) << 6;
$h2 = self::load_3(self::substr($s, 7, 3)) << 5;
$h3 = self::load_3(self::substr($s, 10, 3)) << 3;
$h4 = self::load_3(self::substr($s, 13, 3)) << 2;
$h5 = self::load_4(self::substr($s, 16, 4));
$h6 = self::load_3(self::substr($s, 20, 3)) << 7;
$h7 = self::load_3(self::substr($s, 23, 3)) << 5;
$h8 = self::load_3(self::substr($s, 26, 3)) << 4;
$h9 = (self::load_3(self::substr($s, 29, 3)) & 8388607) << 2;
$carry9 = ($h9 + (1 << 24)) >> 25;
$h0 += self::mul($carry9, 19, 5);
$h9 -= $carry9 << 25;
$carry1 = ($h1 + (1 << 24)) >> 25;
$h2 += $carry1;
$h1 -= $carry1 << 25;
$carry3 = ($h3 + (1 << 24)) >> 25;
$h4 += $carry3;
$h3 -= $carry3 << 25;
$carry5 = ($h5 + (1 << 24)) >> 25;
$h6 += $carry5;
$h5 -= $carry5 << 25;
$carry7 = ($h7 + (1 << 24)) >> 25;
$h8 += $carry7;
$h7 -= $carry7 << 25;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
$carry2 = ($h2 + (1 << 25)) >> 26;
$h3 += $carry2;
$h2 -= $carry2 << 26;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry6 = ($h6 + (1 << 25)) >> 26;
$h7 += $carry6;
$h6 -= $carry6 << 26;
$carry8 = ($h8 + (1 << 25)) >> 26;
$h9 += $carry8;
$h8 -= $carry8 << 26;
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
(int) $h0,
(int) $h1,
(int) $h2,
(int) $h3,
(int) $h4,
(int) $h5,
(int) $h6,
(int) $h7,
(int) $h8,
(int) $h9
)
);
}
/**
* Convert a field element to a byte string.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $h
* @return string
*/
public static function fe_tobytes(ParagonIE_Sodium_Core_Curve25519_Fe $h)
{
$h0 = (int) $h[0];
$h1 = (int) $h[1];
$h2 = (int) $h[2];
$h3 = (int) $h[3];
$h4 = (int) $h[4];
$h5 = (int) $h[5];
$h6 = (int) $h[6];
$h7 = (int) $h[7];
$h8 = (int) $h[8];
$h9 = (int) $h[9];
$q = (self::mul($h9, 19, 5) + (1 << 24)) >> 25;
$q = ($h0 + $q) >> 26;
$q = ($h1 + $q) >> 25;
$q = ($h2 + $q) >> 26;
$q = ($h3 + $q) >> 25;
$q = ($h4 + $q) >> 26;
$q = ($h5 + $q) >> 25;
$q = ($h6 + $q) >> 26;
$q = ($h7 + $q) >> 25;
$q = ($h8 + $q) >> 26;
$q = ($h9 + $q) >> 25;
$h0 += self::mul($q, 19, 5);
$carry0 = $h0 >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
$carry1 = $h1 >> 25;
$h2 += $carry1;
$h1 -= $carry1 << 25;
$carry2 = $h2 >> 26;
$h3 += $carry2;
$h2 -= $carry2 << 26;
$carry3 = $h3 >> 25;
$h4 += $carry3;
$h3 -= $carry3 << 25;
$carry4 = $h4 >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry5 = $h5 >> 25;
$h6 += $carry5;
$h5 -= $carry5 << 25;
$carry6 = $h6 >> 26;
$h7 += $carry6;
$h6 -= $carry6 << 26;
$carry7 = $h7 >> 25;
$h8 += $carry7;
$h7 -= $carry7 << 25;
$carry8 = $h8 >> 26;
$h9 += $carry8;
$h8 -= $carry8 << 26;
$carry9 = $h9 >> 25;
$h9 -= $carry9 << 25;
/**
* @var array<int, int>
*/
$s = array(
(int) (($h0 >> 0) & 0xff),
(int) (($h0 >> 8) & 0xff),
(int) (($h0 >> 16) & 0xff),
(int) ((($h0 >> 24) | ($h1 << 2)) & 0xff),
(int) (($h1 >> 6) & 0xff),
(int) (($h1 >> 14) & 0xff),
(int) ((($h1 >> 22) | ($h2 << 3)) & 0xff),
(int) (($h2 >> 5) & 0xff),
(int) (($h2 >> 13) & 0xff),
(int) ((($h2 >> 21) | ($h3 << 5)) & 0xff),
(int) (($h3 >> 3) & 0xff),
(int) (($h3 >> 11) & 0xff),
(int) ((($h3 >> 19) | ($h4 << 6)) & 0xff),
(int) (($h4 >> 2) & 0xff),
(int) (($h4 >> 10) & 0xff),
(int) (($h4 >> 18) & 0xff),
(int) (($h5 >> 0) & 0xff),
(int) (($h5 >> 8) & 0xff),
(int) (($h5 >> 16) & 0xff),
(int) ((($h5 >> 24) | ($h6 << 1)) & 0xff),
(int) (($h6 >> 7) & 0xff),
(int) (($h6 >> 15) & 0xff),
(int) ((($h6 >> 23) | ($h7 << 3)) & 0xff),
(int) (($h7 >> 5) & 0xff),
(int) (($h7 >> 13) & 0xff),
(int) ((($h7 >> 21) | ($h8 << 4)) & 0xff),
(int) (($h8 >> 4) & 0xff),
(int) (($h8 >> 12) & 0xff),
(int) ((($h8 >> 20) | ($h9 << 6)) & 0xff),
(int) (($h9 >> 2) & 0xff),
(int) (($h9 >> 10) & 0xff),
(int) (($h9 >> 18) & 0xff)
);
return self::intArrayToString($s);
}
/**
* Is a field element negative? (1 = yes, 0 = no. Used in calculations.)
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return int
* @throws SodiumException
* @throws TypeError
*/
public static function fe_isnegative(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$str = self::fe_tobytes($f);
return (int) (self::chrToInt($str[0]) & 1);
}
/**
* Returns 0 if this field element results in all NUL bytes.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return bool
* @throws SodiumException
* @throws TypeError
*/
public static function fe_isnonzero(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
static $zero;
if ($zero === null) {
$zero = str_repeat("\x00", 32);
}
/** @var string $zero */
/** @var string $str */
$str = self::fe_tobytes($f);
return !self::verify_32($str, (string) $zero);
}
/**
* Multiply two field elements
*
* h = f * g
*
* @internal You should not use this directly from another application
*
* @security Is multiplication a source of timing leaks? If so, can we do
* anything to prevent that from happening?
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @param ParagonIE_Sodium_Core_Curve25519_Fe $g
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_mul(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g
) {
// Ensure limbs aren't oversized.
$f = self::fe_normalize($f);
$g = self::fe_normalize($g);
$f0 = $f[0];
$f1 = $f[1];
$f2 = $f[2];
$f3 = $f[3];
$f4 = $f[4];
$f5 = $f[5];
$f6 = $f[6];
$f7 = $f[7];
$f8 = $f[8];
$f9 = $f[9];
$g0 = $g[0];
$g1 = $g[1];
$g2 = $g[2];
$g3 = $g[3];
$g4 = $g[4];
$g5 = $g[5];
$g6 = $g[6];
$g7 = $g[7];
$g8 = $g[8];
$g9 = $g[9];
$g1_19 = self::mul($g1, 19, 5);
$g2_19 = self::mul($g2, 19, 5);
$g3_19 = self::mul($g3, 19, 5);
$g4_19 = self::mul($g4, 19, 5);
$g5_19 = self::mul($g5, 19, 5);
$g6_19 = self::mul($g6, 19, 5);
$g7_19 = self::mul($g7, 19, 5);
$g8_19 = self::mul($g8, 19, 5);
$g9_19 = self::mul($g9, 19, 5);
$f1_2 = $f1 << 1;
$f3_2 = $f3 << 1;
$f5_2 = $f5 << 1;
$f7_2 = $f7 << 1;
$f9_2 = $f9 << 1;
$f0g0 = self::mul($f0, $g0, 26);
$f0g1 = self::mul($f0, $g1, 25);
$f0g2 = self::mul($f0, $g2, 26);
$f0g3 = self::mul($f0, $g3, 25);
$f0g4 = self::mul($f0, $g4, 26);
$f0g5 = self::mul($f0, $g5, 25);
$f0g6 = self::mul($f0, $g6, 26);
$f0g7 = self::mul($f0, $g7, 25);
$f0g8 = self::mul($f0, $g8, 26);
$f0g9 = self::mul($f0, $g9, 26);
$f1g0 = self::mul($f1, $g0, 26);
$f1g1_2 = self::mul($f1_2, $g1, 25);
$f1g2 = self::mul($f1, $g2, 26);
$f1g3_2 = self::mul($f1_2, $g3, 25);
$f1g4 = self::mul($f1, $g4, 26);
$f1g5_2 = self::mul($f1_2, $g5, 25);
$f1g6 = self::mul($f1, $g6, 26);
$f1g7_2 = self::mul($f1_2, $g7, 25);
$f1g8 = self::mul($f1, $g8, 26);
$f1g9_38 = self::mul($g9_19, $f1_2, 26);
$f2g0 = self::mul($f2, $g0, 26);
$f2g1 = self::mul($f2, $g1, 25);
$f2g2 = self::mul($f2, $g2, 26);
$f2g3 = self::mul($f2, $g3, 25);
$f2g4 = self::mul($f2, $g4, 26);
$f2g5 = self::mul($f2, $g5, 25);
$f2g6 = self::mul($f2, $g6, 26);
$f2g7 = self::mul($f2, $g7, 25);
$f2g8_19 = self::mul($g8_19, $f2, 26);
$f2g9_19 = self::mul($g9_19, $f2, 26);
$f3g0 = self::mul($f3, $g0, 26);
$f3g1_2 = self::mul($f3_2, $g1, 25);
$f3g2 = self::mul($f3, $g2, 26);
$f3g3_2 = self::mul($f3_2, $g3, 25);
$f3g4 = self::mul($f3, $g4, 26);
$f3g5_2 = self::mul($f3_2, $g5, 25);
$f3g6 = self::mul($f3, $g6, 26);
$f3g7_38 = self::mul($g7_19, $f3_2, 26);
$f3g8_19 = self::mul($g8_19, $f3, 25);
$f3g9_38 = self::mul($g9_19, $f3_2, 26);
$f4g0 = self::mul($f4, $g0, 26);
$f4g1 = self::mul($f4, $g1, 25);
$f4g2 = self::mul($f4, $g2, 26);
$f4g3 = self::mul($f4, $g3, 25);
$f4g4 = self::mul($f4, $g4, 26);
$f4g5 = self::mul($f4, $g5, 25);
$f4g6_19 = self::mul($g6_19, $f4, 26);
$f4g7_19 = self::mul($g7_19, $f4, 26);
$f4g8_19 = self::mul($g8_19, $f4, 26);
$f4g9_19 = self::mul($g9_19, $f4, 26);
$f5g0 = self::mul($f5, $g0, 26);
$f5g1_2 = self::mul($f5_2, $g1, 25);
$f5g2 = self::mul($f5, $g2, 26);
$f5g3_2 = self::mul($f5_2, $g3, 25);
$f5g4 = self::mul($f5, $g4, 26);
$f5g5_38 = self::mul($g5_19, $f5_2, 26);
$f5g6_19 = self::mul($g6_19, $f5, 25);
$f5g7_38 = self::mul($g7_19, $f5_2, 26);
$f5g8_19 = self::mul($g8_19, $f5, 25);
$f5g9_38 = self::mul($g9_19, $f5_2, 26);
$f6g0 = self::mul($f6, $g0, 26);
$f6g1 = self::mul($f6, $g1, 25);
$f6g2 = self::mul($f6, $g2, 26);
$f6g3 = self::mul($f6, $g3, 25);
$f6g4_19 = self::mul($g4_19, $f6, 26);
$f6g5_19 = self::mul($g5_19, $f6, 26);
$f6g6_19 = self::mul($g6_19, $f6, 26);
$f6g7_19 = self::mul($g7_19, $f6, 26);
$f6g8_19 = self::mul($g8_19, $f6, 26);
$f6g9_19 = self::mul($g9_19, $f6, 26);
$f7g0 = self::mul($f7, $g0, 26);
$f7g1_2 = self::mul($f7_2, $g1, 25);
$f7g2 = self::mul($f7, $g2, 26);
$f7g3_38 = self::mul($g3_19, $f7_2, 26);
$f7g4_19 = self::mul($g4_19, $f7, 26);
$f7g5_38 = self::mul($g5_19, $f7_2, 26);
$f7g6_19 = self::mul($g6_19, $f7, 25);
$f7g7_38 = self::mul($g7_19, $f7_2, 26);
$f7g8_19 = self::mul($g8_19, $f7, 25);
$f7g9_38 = self::mul($g9_19,$f7_2, 26);
$f8g0 = self::mul($f8, $g0, 26);
$f8g1 = self::mul($f8, $g1, 25);
$f8g2_19 = self::mul($g2_19, $f8, 26);
$f8g3_19 = self::mul($g3_19, $f8, 26);
$f8g4_19 = self::mul($g4_19, $f8, 26);
$f8g5_19 = self::mul($g5_19, $f8, 26);
$f8g6_19 = self::mul($g6_19, $f8, 26);
$f8g7_19 = self::mul($g7_19, $f8, 26);
$f8g8_19 = self::mul($g8_19, $f8, 26);
$f8g9_19 = self::mul($g9_19, $f8, 26);
$f9g0 = self::mul($f9, $g0, 26);
$f9g1_38 = self::mul($g1_19, $f9_2, 26);
$f9g2_19 = self::mul($g2_19, $f9, 25);
$f9g3_38 = self::mul($g3_19, $f9_2, 26);
$f9g4_19 = self::mul($g4_19, $f9, 25);
$f9g5_38 = self::mul($g5_19, $f9_2, 26);
$f9g6_19 = self::mul($g6_19, $f9, 25);
$f9g7_38 = self::mul($g7_19, $f9_2, 26);
$f9g8_19 = self::mul($g8_19, $f9, 25);
$f9g9_38 = self::mul($g9_19, $f9_2, 26);
$h0 = $f0g0 + $f1g9_38 + $f2g8_19 + $f3g7_38 + $f4g6_19 + $f5g5_38 + $f6g4_19 + $f7g3_38 + $f8g2_19 + $f9g1_38;
$h1 = $f0g1 + $f1g0 + $f2g9_19 + $f3g8_19 + $f4g7_19 + $f5g6_19 + $f6g5_19 + $f7g4_19 + $f8g3_19 + $f9g2_19;
$h2 = $f0g2 + $f1g1_2 + $f2g0 + $f3g9_38 + $f4g8_19 + $f5g7_38 + $f6g6_19 + $f7g5_38 + $f8g4_19 + $f9g3_38;
$h3 = $f0g3 + $f1g2 + $f2g1 + $f3g0 + $f4g9_19 + $f5g8_19 + $f6g7_19 + $f7g6_19 + $f8g5_19 + $f9g4_19;
$h4 = $f0g4 + $f1g3_2 + $f2g2 + $f3g1_2 + $f4g0 + $f5g9_38 + $f6g8_19 + $f7g7_38 + $f8g6_19 + $f9g5_38;
$h5 = $f0g5 + $f1g4 + $f2g3 + $f3g2 + $f4g1 + $f5g0 + $f6g9_19 + $f7g8_19 + $f8g7_19 + $f9g6_19;
$h6 = $f0g6 + $f1g5_2 + $f2g4 + $f3g3_2 + $f4g2 + $f5g1_2 + $f6g0 + $f7g9_38 + $f8g8_19 + $f9g7_38;
$h7 = $f0g7 + $f1g6 + $f2g5 + $f3g4 + $f4g3 + $f5g2 + $f6g1 + $f7g0 + $f8g9_19 + $f9g8_19;
$h8 = $f0g8 + $f1g7_2 + $f2g6 + $f3g5_2 + $f4g4 + $f5g3_2 + $f6g2 + $f7g1_2 + $f8g0 + $f9g9_38;
$h9 = $f0g9 + $f1g8 + $f2g7 + $f3g6 + $f4g5 + $f5g4 + $f6g3 + $f7g2 + $f8g1 + $f9g0 ;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry1 = ($h1 + (1 << 24)) >> 25;
$h2 += $carry1;
$h1 -= $carry1 << 25;
$carry5 = ($h5 + (1 << 24)) >> 25;
$h6 += $carry5;
$h5 -= $carry5 << 25;
$carry2 = ($h2 + (1 << 25)) >> 26;
$h3 += $carry2;
$h2 -= $carry2 << 26;
$carry6 = ($h6 + (1 << 25)) >> 26;
$h7 += $carry6;
$h6 -= $carry6 << 26;
$carry3 = ($h3 + (1 << 24)) >> 25;
$h4 += $carry3;
$h3 -= $carry3 << 25;
$carry7 = ($h7 + (1 << 24)) >> 25;
$h8 += $carry7;
$h7 -= $carry7 << 25;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry8 = ($h8 + (1 << 25)) >> 26;
$h9 += $carry8;
$h8 -= $carry8 << 26;
$carry9 = ($h9 + (1 << 24)) >> 25;
$h0 += self::mul($carry9, 19, 5);
$h9 -= $carry9 << 25;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
(int) $h0,
(int) $h1,
(int) $h2,
(int) $h3,
(int) $h4,
(int) $h5,
(int) $h6,
(int) $h7,
(int) $h8,
(int) $h9
)
)
);
}
/**
* Get the negative values for each piece of the field element.
*
* h = -f
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @psalm-suppress MixedAssignment
*/
public static function fe_neg(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$h = new ParagonIE_Sodium_Core_Curve25519_Fe();
for ($i = 0; $i < 10; ++$i) {
$h[$i] = -$f[$i];
}
return self::fe_normalize($h);
}
/**
* Square a field element
*
* h = f * f
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_sq(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$f = self::fe_normalize($f);
$f0 = (int) $f[0];
$f1 = (int) $f[1];
$f2 = (int) $f[2];
$f3 = (int) $f[3];
$f4 = (int) $f[4];
$f5 = (int) $f[5];
$f6 = (int) $f[6];
$f7 = (int) $f[7];
$f8 = (int) $f[8];
$f9 = (int) $f[9];
$f0_2 = $f0 << 1;
$f1_2 = $f1 << 1;
$f2_2 = $f2 << 1;
$f3_2 = $f3 << 1;
$f4_2 = $f4 << 1;
$f5_2 = $f5 << 1;
$f6_2 = $f6 << 1;
$f7_2 = $f7 << 1;
$f5_38 = self::mul($f5, 38, 6);
$f6_19 = self::mul($f6, 19, 5);
$f7_38 = self::mul($f7, 38, 6);
$f8_19 = self::mul($f8, 19, 5);
$f9_38 = self::mul($f9, 38, 6);
$f0f0 = self::mul($f0, $f0, 26);
$f0f1_2 = self::mul($f0_2, $f1, 26);
$f0f2_2 = self::mul($f0_2, $f2, 26);
$f0f3_2 = self::mul($f0_2, $f3, 26);
$f0f4_2 = self::mul($f0_2, $f4, 26);
$f0f5_2 = self::mul($f0_2, $f5, 26);
$f0f6_2 = self::mul($f0_2, $f6, 26);
$f0f7_2 = self::mul($f0_2, $f7, 26);
$f0f8_2 = self::mul($f0_2, $f8, 26);
$f0f9_2 = self::mul($f0_2, $f9, 26);
$f1f1_2 = self::mul($f1_2, $f1, 26);
$f1f2_2 = self::mul($f1_2, $f2, 26);
$f1f3_4 = self::mul($f1_2, $f3_2, 26);
$f1f4_2 = self::mul($f1_2, $f4, 26);
$f1f5_4 = self::mul($f1_2, $f5_2, 26);
$f1f6_2 = self::mul($f1_2, $f6, 26);
$f1f7_4 = self::mul($f1_2, $f7_2, 26);
$f1f8_2 = self::mul($f1_2, $f8, 26);
$f1f9_76 = self::mul($f9_38, $f1_2, 27);
$f2f2 = self::mul($f2, $f2, 27);
$f2f3_2 = self::mul($f2_2, $f3, 27);
$f2f4_2 = self::mul($f2_2, $f4, 27);
$f2f5_2 = self::mul($f2_2, $f5, 27);
$f2f6_2 = self::mul($f2_2, $f6, 27);
$f2f7_2 = self::mul($f2_2, $f7, 27);
$f2f8_38 = self::mul($f8_19, $f2_2, 27);
$f2f9_38 = self::mul($f9_38, $f2, 26);
$f3f3_2 = self::mul($f3_2, $f3, 26);
$f3f4_2 = self::mul($f3_2, $f4, 26);
$f3f5_4 = self::mul($f3_2, $f5_2, 26);
$f3f6_2 = self::mul($f3_2, $f6, 26);
$f3f7_76 = self::mul($f7_38, $f3_2, 26);
$f3f8_38 = self::mul($f8_19, $f3_2, 26);
$f3f9_76 = self::mul($f9_38, $f3_2, 26);
$f4f4 = self::mul($f4, $f4, 26);
$f4f5_2 = self::mul($f4_2, $f5, 26);
$f4f6_38 = self::mul($f6_19, $f4_2, 27);
$f4f7_38 = self::mul($f7_38, $f4, 26);
$f4f8_38 = self::mul($f8_19, $f4_2, 27);
$f4f9_38 = self::mul($f9_38, $f4, 26);
$f5f5_38 = self::mul($f5_38, $f5, 26);
$f5f6_38 = self::mul($f6_19, $f5_2, 26);
$f5f7_76 = self::mul($f7_38, $f5_2, 26);
$f5f8_38 = self::mul($f8_19, $f5_2, 26);
$f5f9_76 = self::mul($f9_38, $f5_2, 26);
$f6f6_19 = self::mul($f6_19, $f6, 26);
$f6f7_38 = self::mul($f7_38, $f6, 26);
$f6f8_38 = self::mul($f8_19, $f6_2, 27);
$f6f9_38 = self::mul($f9_38, $f6, 26);
$f7f7_38 = self::mul($f7_38, $f7, 26);
$f7f8_38 = self::mul($f8_19, $f7_2, 26);
$f7f9_76 = self::mul($f9_38, $f7_2, 26);
$f8f8_19 = self::mul($f8_19, $f8, 26);
$f8f9_38 = self::mul($f9_38, $f8, 26);
$f9f9_38 = self::mul($f9_38, $f9, 26);
$h0 = $f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38;
$h1 = $f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38;
$h2 = $f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19;
$h3 = $f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38;
$h4 = $f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38;
$h5 = $f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38;
$h6 = $f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19;
$h7 = $f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38;
$h8 = $f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38;
$h9 = $f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry1 = ($h1 + (1 << 24)) >> 25;
$h2 += $carry1;
$h1 -= $carry1 << 25;
$carry5 = ($h5 + (1 << 24)) >> 25;
$h6 += $carry5;
$h5 -= $carry5 << 25;
$carry2 = ($h2 + (1 << 25)) >> 26;
$h3 += $carry2;
$h2 -= $carry2 << 26;
$carry6 = ($h6 + (1 << 25)) >> 26;
$h7 += $carry6;
$h6 -= $carry6 << 26;
$carry3 = ($h3 + (1 << 24)) >> 25;
$h4 += $carry3;
$h3 -= $carry3 << 25;
$carry7 = ($h7 + (1 << 24)) >> 25;
$h8 += $carry7;
$h7 -= $carry7 << 25;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry8 = ($h8 + (1 << 25)) >> 26;
$h9 += $carry8;
$h8 -= $carry8 << 26;
$carry9 = ($h9 + (1 << 24)) >> 25;
$h0 += self::mul($carry9, 19, 5);
$h9 -= $carry9 << 25;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
(int) $h0,
(int) $h1,
(int) $h2,
(int) $h3,
(int) $h4,
(int) $h5,
(int) $h6,
(int) $h7,
(int) $h8,
(int) $h9
)
)
);
}
/**
* Square and double a field element
*
* h = 2 * f * f
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_sq2(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$f = self::fe_normalize($f);
$f0 = (int) $f[0];
$f1 = (int) $f[1];
$f2 = (int) $f[2];
$f3 = (int) $f[3];
$f4 = (int) $f[4];
$f5 = (int) $f[5];
$f6 = (int) $f[6];
$f7 = (int) $f[7];
$f8 = (int) $f[8];
$f9 = (int) $f[9];
$f0_2 = $f0 << 1;
$f1_2 = $f1 << 1;
$f2_2 = $f2 << 1;
$f3_2 = $f3 << 1;
$f4_2 = $f4 << 1;
$f5_2 = $f5 << 1;
$f6_2 = $f6 << 1;
$f7_2 = $f7 << 1;
$f5_38 = self::mul($f5, 38, 6); /* 1.959375*2^30 */
$f6_19 = self::mul($f6, 19, 5); /* 1.959375*2^30 */
$f7_38 = self::mul($f7, 38, 6); /* 1.959375*2^30 */
$f8_19 = self::mul($f8, 19, 5); /* 1.959375*2^30 */
$f9_38 = self::mul($f9, 38, 6); /* 1.959375*2^30 */
$f0f0 = self::mul($f0, $f0, 24);
$f0f1_2 = self::mul($f0_2, $f1, 24);
$f0f2_2 = self::mul($f0_2, $f2, 24);
$f0f3_2 = self::mul($f0_2, $f3, 24);
$f0f4_2 = self::mul($f0_2, $f4, 24);
$f0f5_2 = self::mul($f0_2, $f5, 24);
$f0f6_2 = self::mul($f0_2, $f6, 24);
$f0f7_2 = self::mul($f0_2, $f7, 24);
$f0f8_2 = self::mul($f0_2, $f8, 24);
$f0f9_2 = self::mul($f0_2, $f9, 24);
$f1f1_2 = self::mul($f1_2, $f1, 24);
$f1f2_2 = self::mul($f1_2, $f2, 24);
$f1f3_4 = self::mul($f1_2, $f3_2, 24);
$f1f4_2 = self::mul($f1_2, $f4, 24);
$f1f5_4 = self::mul($f1_2, $f5_2, 24);
$f1f6_2 = self::mul($f1_2, $f6, 24);
$f1f7_4 = self::mul($f1_2, $f7_2, 24);
$f1f8_2 = self::mul($f1_2, $f8, 24);
$f1f9_76 = self::mul($f9_38, $f1_2, 24);
$f2f2 = self::mul($f2, $f2, 24);
$f2f3_2 = self::mul($f2_2, $f3, 24);
$f2f4_2 = self::mul($f2_2, $f4, 24);
$f2f5_2 = self::mul($f2_2, $f5, 24);
$f2f6_2 = self::mul($f2_2, $f6, 24);
$f2f7_2 = self::mul($f2_2, $f7, 24);
$f2f8_38 = self::mul($f8_19, $f2_2, 25);
$f2f9_38 = self::mul($f9_38, $f2, 24);
$f3f3_2 = self::mul($f3_2, $f3, 24);
$f3f4_2 = self::mul($f3_2, $f4, 24);
$f3f5_4 = self::mul($f3_2, $f5_2, 24);
$f3f6_2 = self::mul($f3_2, $f6, 24);
$f3f7_76 = self::mul($f7_38, $f3_2, 24);
$f3f8_38 = self::mul($f8_19, $f3_2, 24);
$f3f9_76 = self::mul($f9_38, $f3_2, 24);
$f4f4 = self::mul($f4, $f4, 24);
$f4f5_2 = self::mul($f4_2, $f5, 24);
$f4f6_38 = self::mul($f6_19, $f4_2, 25);
$f4f7_38 = self::mul($f7_38, $f4, 24);
$f4f8_38 = self::mul($f8_19, $f4_2, 25);
$f4f9_38 = self::mul($f9_38, $f4, 24);
$f5f5_38 = self::mul($f5_38, $f5, 24);
$f5f6_38 = self::mul($f6_19, $f5_2, 24);
$f5f7_76 = self::mul($f7_38, $f5_2, 24);
$f5f8_38 = self::mul($f8_19, $f5_2, 24);
$f5f9_76 = self::mul($f9_38, $f5_2, 24);
$f6f6_19 = self::mul($f6_19, $f6, 24);
$f6f7_38 = self::mul($f7_38, $f6, 24);
$f6f8_38 = self::mul($f8_19, $f6_2, 25);
$f6f9_38 = self::mul($f9_38, $f6, 24);
$f7f7_38 = self::mul($f7_38, $f7, 24);
$f7f8_38 = self::mul($f8_19, $f7_2, 24);
$f7f9_76 = self::mul($f9_38, $f7_2, 24);
$f8f8_19 = self::mul($f8_19, $f8, 24);
$f8f9_38 = self::mul($f9_38, $f8, 24);
$f9f9_38 = self::mul($f9_38, $f9, 24);
$h0 = (int) ($f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38) << 1;
$h1 = (int) ($f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38) << 1;
$h2 = (int) ($f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19) << 1;
$h3 = (int) ($f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38) << 1;
$h4 = (int) ($f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38) << 1;
$h5 = (int) ($f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38) << 1;
$h6 = (int) ($f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19) << 1;
$h7 = (int) ($f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38) << 1;
$h8 = (int) ($f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38) << 1;
$h9 = (int) ($f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2) << 1;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry1 = ($h1 + (1 << 24)) >> 25;
$h2 += $carry1;
$h1 -= $carry1 << 25;
$carry5 = ($h5 + (1 << 24)) >> 25;
$h6 += $carry5;
$h5 -= $carry5 << 25;
$carry2 = ($h2 + (1 << 25)) >> 26;
$h3 += $carry2;
$h2 -= $carry2 << 26;
$carry6 = ($h6 + (1 << 25)) >> 26;
$h7 += $carry6;
$h6 -= $carry6 << 26;
$carry3 = ($h3 + (1 << 24)) >> 25;
$h4 += $carry3;
$h3 -= $carry3 << 25;
$carry7 = ($h7 + (1 << 24)) >> 25;
$h8 += $carry7;
$h7 -= $carry7 << 25;
$carry4 = ($h4 + (1 << 25)) >> 26;
$h5 += $carry4;
$h4 -= $carry4 << 26;
$carry8 = ($h8 + (1 << 25)) >> 26;
$h9 += $carry8;
$h8 -= $carry8 << 26;
$carry9 = ($h9 + (1 << 24)) >> 25;
$h0 += self::mul($carry9, 19, 5);
$h9 -= $carry9 << 25;
$carry0 = ($h0 + (1 << 25)) >> 26;
$h1 += $carry0;
$h0 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
(int) $h0,
(int) $h1,
(int) $h2,
(int) $h3,
(int) $h4,
(int) $h5,
(int) $h6,
(int) $h7,
(int) $h8,
(int) $h9
)
)
);
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $Z
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_invert(ParagonIE_Sodium_Core_Curve25519_Fe $Z)
{
$z = clone $Z;
$t0 = self::fe_sq($z);
$t1 = self::fe_sq($t0);
$t1 = self::fe_sq($t1);
$t1 = self::fe_mul($z, $t1);
$t0 = self::fe_mul($t0, $t1);
$t2 = self::fe_sq($t0);
$t1 = self::fe_mul($t1, $t2);
$t2 = self::fe_sq($t1);
for ($i = 1; $i < 5; ++$i) {
$t2 = self::fe_sq($t2);
}
$t1 = self::fe_mul($t2, $t1);
$t2 = self::fe_sq($t1);
for ($i = 1; $i < 10; ++$i) {
$t2 = self::fe_sq($t2);
}
$t2 = self::fe_mul($t2, $t1);
$t3 = self::fe_sq($t2);
for ($i = 1; $i < 20; ++$i) {
$t3 = self::fe_sq($t3);
}
$t2 = self::fe_mul($t3, $t2);
$t2 = self::fe_sq($t2);
for ($i = 1; $i < 10; ++$i) {
$t2 = self::fe_sq($t2);
}
$t1 = self::fe_mul($t2, $t1);
$t2 = self::fe_sq($t1);
for ($i = 1; $i < 50; ++$i) {
$t2 = self::fe_sq($t2);
}
$t2 = self::fe_mul($t2, $t1);
$t3 = self::fe_sq($t2);
for ($i = 1; $i < 100; ++$i) {
$t3 = self::fe_sq($t3);
}
$t2 = self::fe_mul($t3, $t2);
$t2 = self::fe_sq($t2);
for ($i = 1; $i < 50; ++$i) {
$t2 = self::fe_sq($t2);
}
$t1 = self::fe_mul($t2, $t1);
$t1 = self::fe_sq($t1);
for ($i = 1; $i < 5; ++$i) {
$t1 = self::fe_sq($t1);
}
return self::fe_mul($t1, $t0);
}
/**
* @internal You should not use this directly from another application
*
* @ref https://github.com/jedisct1/libsodium/blob/68564326e1e9dc57ef03746f85734232d20ca6fb/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1054-L1106
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $z
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_pow22523(ParagonIE_Sodium_Core_Curve25519_Fe $z)
{
$z = self::fe_normalize($z);
# fe_sq(t0, z);
# fe_sq(t1, t0);
# fe_sq(t1, t1);
# fe_mul(t1, z, t1);
# fe_mul(t0, t0, t1);
# fe_sq(t0, t0);
# fe_mul(t0, t1, t0);
# fe_sq(t1, t0);
$t0 = self::fe_sq($z);
$t1 = self::fe_sq($t0);
$t1 = self::fe_sq($t1);
$t1 = self::fe_mul($z, $t1);
$t0 = self::fe_mul($t0, $t1);
$t0 = self::fe_sq($t0);
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
# for (i = 1; i < 5; ++i) {
# fe_sq(t1, t1);
# }
for ($i = 1; $i < 5; ++$i) {
$t1 = self::fe_sq($t1);
}
# fe_mul(t0, t1, t0);
# fe_sq(t1, t0);
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
# for (i = 1; i < 10; ++i) {
# fe_sq(t1, t1);
# }
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_sq($t1);
}
# fe_mul(t1, t1, t0);
# fe_sq(t2, t1);
$t1 = self::fe_mul($t1, $t0);
$t2 = self::fe_sq($t1);
# for (i = 1; i < 20; ++i) {
# fe_sq(t2, t2);
# }
for ($i = 1; $i < 20; ++$i) {
$t2 = self::fe_sq($t2);
}
# fe_mul(t1, t2, t1);
# fe_sq(t1, t1);
$t1 = self::fe_mul($t2, $t1);
$t1 = self::fe_sq($t1);
# for (i = 1; i < 10; ++i) {
# fe_sq(t1, t1);
# }
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_sq($t1);
}
# fe_mul(t0, t1, t0);
# fe_sq(t1, t0);
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
# for (i = 1; i < 50; ++i) {
# fe_sq(t1, t1);
# }
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_sq($t1);
}
# fe_mul(t1, t1, t0);
# fe_sq(t2, t1);
$t1 = self::fe_mul($t1, $t0);
$t2 = self::fe_sq($t1);
# for (i = 1; i < 100; ++i) {
# fe_sq(t2, t2);
# }
for ($i = 1; $i < 100; ++$i) {
$t2 = self::fe_sq($t2);
}
# fe_mul(t1, t2, t1);
# fe_sq(t1, t1);
$t1 = self::fe_mul($t2, $t1);
$t1 = self::fe_sq($t1);
# for (i = 1; i < 50; ++i) {
# fe_sq(t1, t1);
# }
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_sq($t1);
}
# fe_mul(t0, t1, t0);
# fe_sq(t0, t0);
# fe_sq(t0, t0);
# fe_mul(out, t0, z);
$t0 = self::fe_mul($t1, $t0);
$t0 = self::fe_sq($t0);
$t0 = self::fe_sq($t0);
return self::fe_mul($t0, $z);
}
/**
* Subtract two field elements.
*
* h = f - g
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @param ParagonIE_Sodium_Core_Curve25519_Fe $g
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @psalm-suppress MixedOperand
*/
public static function fe_sub(ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g)
{
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
(int) ($f[0] - $g[0]),
(int) ($f[1] - $g[1]),
(int) ($f[2] - $g[2]),
(int) ($f[3] - $g[3]),
(int) ($f[4] - $g[4]),
(int) ($f[5] - $g[5]),
(int) ($f[6] - $g[6]),
(int) ($f[7] - $g[7]),
(int) ($f[8] - $g[8]),
(int) ($f[9] - $g[9])
)
)
);
}
/**
* Add two group elements.
*
* r = p + q
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_add(
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q
) {
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1();
$r->X = self::fe_add($p->Y, $p->X);
$r->Y = self::fe_sub($p->Y, $p->X);
$r->Z = self::fe_mul($r->X, $q->YplusX);
$r->Y = self::fe_mul($r->Y, $q->YminusX);
$r->T = self::fe_mul($q->T2d, $p->T);
$r->X = self::fe_mul($p->Z, $q->Z);
$t0 = self::fe_add($r->X, $r->X);
$r->X = self::fe_sub($r->Z, $r->Y);
$r->Y = self::fe_add($r->Z, $r->Y);
$r->Z = self::fe_add($t0, $r->T);
$r->T = self::fe_sub($t0, $r->T);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @ref https://github.com/jedisct1/libsodium/blob/157c4a80c13b117608aeae12178b2d38825f9f8f/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1185-L1215
* @param string $a
* @return array<int, mixed>
* @throws SodiumException
* @throws TypeError
*/
public static function slide($a)
{
if (self::strlen($a) < 256) {
if (self::strlen($a) < 16) {
$a = str_pad($a, 256, '0', STR_PAD_RIGHT);
}
}
/** @var array<int, int> $r */
$r = array();
/** @var int $i */
for ($i = 0; $i < 256; ++$i) {
$r[$i] = (int) (
1 & (
self::chrToInt($a[(int) ($i >> 3)])
>>
($i & 7)
)
);
}
for ($i = 0;$i < 256;++$i) {
if ($r[$i]) {
for ($b = 1;$b <= 6 && $i + $b < 256;++$b) {
if ($r[$i + $b]) {
if ($r[$i] + ($r[$i + $b] << $b) <= 15) {
$r[$i] += $r[$i + $b] << $b;
$r[$i + $b] = 0;
} elseif ($r[$i] - ($r[$i + $b] << $b) >= -15) {
$r[$i] -= $r[$i + $b] << $b;
for ($k = $i + $b; $k < 256; ++$k) {
if (!$r[$k]) {
$r[$k] = 1;
break;
}
$r[$k] = 0;
}
} else {
break;
}
}
}
}
}
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param string $s
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
* @throws SodiumException
* @throws TypeError
*/
public static function ge_frombytes_negate_vartime($s)
{
static $d = null;
if (!$d) {
$d = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d);
}
# fe_frombytes(h->Y,s);
# fe_1(h->Z);
$h = new ParagonIE_Sodium_Core_Curve25519_Ge_P3(
self::fe_0(),
self::fe_frombytes($s),
self::fe_1()
);
# fe_sq(u,h->Y);
# fe_mul(v,u,d);
# fe_sub(u,u,h->Z); /* u = y^2-1 */
# fe_add(v,v,h->Z); /* v = dy^2+1 */
$u = self::fe_sq($h->Y);
/** @var ParagonIE_Sodium_Core_Curve25519_Fe $d */
$v = self::fe_mul($u, $d);
$u = self::fe_sub($u, $h->Z); /* u = y^2 - 1 */
$v = self::fe_add($v, $h->Z); /* v = dy^2 + 1 */
# fe_sq(v3,v);
# fe_mul(v3,v3,v); /* v3 = v^3 */
# fe_sq(h->X,v3);
# fe_mul(h->X,h->X,v);
# fe_mul(h->X,h->X,u); /* x = uv^7 */
$v3 = self::fe_sq($v);
$v3 = self::fe_mul($v3, $v); /* v3 = v^3 */
$h->X = self::fe_sq($v3);
$h->X = self::fe_mul($h->X, $v);
$h->X = self::fe_mul($h->X, $u); /* x = uv^7 */
# fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
# fe_mul(h->X,h->X,v3);
# fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */
$h->X = self::fe_pow22523($h->X); /* x = (uv^7)^((q-5)/8) */
$h->X = self::fe_mul($h->X, $v3);
$h->X = self::fe_mul($h->X, $u); /* x = uv^3(uv^7)^((q-5)/8) */
# fe_sq(vxx,h->X);
# fe_mul(vxx,vxx,v);
# fe_sub(check,vxx,u); /* vx^2-u */
$vxx = self::fe_sq($h->X);
$vxx = self::fe_mul($vxx, $v);
$check = self::fe_sub($vxx, $u); /* vx^2 - u */
# if (fe_isnonzero(check)) {
# fe_add(check,vxx,u); /* vx^2+u */
# if (fe_isnonzero(check)) {
# return -1;
# }
# fe_mul(h->X,h->X,sqrtm1);
# }
if (self::fe_isnonzero($check)) {
$check = self::fe_add($vxx, $u); /* vx^2 + u */
if (self::fe_isnonzero($check)) {
throw new RangeException('Internal check failed.');
}
$h->X = self::fe_mul(
$h->X,
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1)
);
}
# if (fe_isnegative(h->X) == (s[31] >> 7)) {
# fe_neg(h->X,h->X);
# }
$i = self::chrToInt($s[31]);
if (self::fe_isnegative($h->X) === ($i >> 7)) {
$h->X = self::fe_neg($h->X);
}
# fe_mul(h->T,h->X,h->Y);
$h->T = self::fe_mul($h->X, $h->Y);
return $h;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_madd(
ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R,
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q
) {
$r = clone $R;
$r->X = self::fe_add($p->Y, $p->X);
$r->Y = self::fe_sub($p->Y, $p->X);
$r->Z = self::fe_mul($r->X, $q->yplusx);
$r->Y = self::fe_mul($r->Y, $q->yminusx);
$r->T = self::fe_mul($q->xy2d, $p->T);
$t0 = self::fe_add(clone $p->Z, clone $p->Z);
$r->X = self::fe_sub($r->Z, $r->Y);
$r->Y = self::fe_add($r->Z, $r->Y);
$r->Z = self::fe_add($t0, $r->T);
$r->T = self::fe_sub($t0, $r->T);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_msub(
ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R,
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q
) {
$r = clone $R;
$r->X = self::fe_add($p->Y, $p->X);
$r->Y = self::fe_sub($p->Y, $p->X);
$r->Z = self::fe_mul($r->X, $q->yminusx);
$r->Y = self::fe_mul($r->Y, $q->yplusx);
$r->T = self::fe_mul($q->xy2d, $p->T);
$t0 = self::fe_add($p->Z, $p->Z);
$r->X = self::fe_sub($r->Z, $r->Y);
$r->Y = self::fe_add($r->Z, $r->Y);
$r->Z = self::fe_sub($t0, $r->T);
$r->T = self::fe_add($t0, $r->T);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P2
*/
public static function ge_p1p1_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p)
{
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P2();
$r->X = self::fe_mul($p->X, $p->T);
$r->Y = self::fe_mul($p->Y, $p->Z);
$r->Z = self::fe_mul($p->Z, $p->T);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
*/
public static function ge_p1p1_to_p3(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p)
{
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P3();
$r->X = self::fe_mul($p->X, $p->T);
$r->Y = self::fe_mul($p->Y, $p->Z);
$r->Z = self::fe_mul($p->Z, $p->T);
$r->T = self::fe_mul($p->X, $p->Y);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P2
*/
public static function ge_p2_0()
{
return new ParagonIE_Sodium_Core_Curve25519_Ge_P2(
self::fe_0(),
self::fe_1(),
self::fe_1()
);
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_p2_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p)
{
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1();
$r->X = self::fe_sq($p->X);
$r->Z = self::fe_sq($p->Y);
$r->T = self::fe_sq2($p->Z);
$r->Y = self::fe_add($p->X, $p->Y);
$t0 = self::fe_sq($r->Y);
$r->Y = self::fe_add($r->Z, $r->X);
$r->Z = self::fe_sub($r->Z, $r->X);
$r->X = self::fe_sub($t0, $r->Y);
$r->T = self::fe_sub($r->T, $r->Z);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
*/
public static function ge_p3_0()
{
return new ParagonIE_Sodium_Core_Curve25519_Ge_P3(
self::fe_0(),
self::fe_1(),
self::fe_1(),
self::fe_0()
);
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached
*/
public static function ge_p3_to_cached(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p)
{
static $d2 = null;
if ($d2 === null) {
$d2 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d2);
}
/** @var ParagonIE_Sodium_Core_Curve25519_Fe $d2 */
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached();
$r->YplusX = self::fe_add($p->Y, $p->X);
$r->YminusX = self::fe_sub($p->Y, $p->X);
$r->Z = self::fe_copy($p->Z);
$r->T2d = self::fe_mul($p->T, $d2);
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P2
*/
public static function ge_p3_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p)
{
return new ParagonIE_Sodium_Core_Curve25519_Ge_P2(
self::fe_copy($p->X),
self::fe_copy($p->Y),
self::fe_copy($p->Z)
);
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h
* @return string
* @throws SodiumException
* @throws TypeError
*/
public static function ge_p3_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h)
{
$recip = self::fe_invert($h->Z);
$x = self::fe_mul($h->X, $recip);
$y = self::fe_mul($h->Y, $recip);
$s = self::fe_tobytes($y);
$s[31] = self::intToChr(
self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7)
);
return $s;
}
/**
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_p3_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p)
{
$q = self::ge_p3_to_p2($p);
return self::ge_p2_dbl($q);
}
/**
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
*/
public static function ge_precomp_0()
{
return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
self::fe_1(),
self::fe_1(),
self::fe_0()
);
}
/**
* @internal You should not use this directly from another application
*
* @param int $b
* @param int $c
* @return int
*/
public static function equal($b, $c)
{
return (int) ((($b ^ $c) - 1) >> 31) & 1;
}
/**
* @internal You should not use this directly from another application
*
* @param int|string $char
* @return int (1 = yes, 0 = no)
* @throws SodiumException
* @throws TypeError
*/
public static function negative($char)
{
if (is_int($char)) {
return ($char >> 63) & 1;
}
$x = self::chrToInt(self::substr($char, 0, 1));
return (int) ($x >> 63);
}
/**
* Conditional move
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
*/
public static function cmov(
ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t,
ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u,
$b
) {
if (!is_int($b)) {
throw new InvalidArgumentException('Expected an integer.');
}
return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
self::fe_cmov($t->yplusx, $u->yplusx, $b),
self::fe_cmov($t->yminusx, $u->yminusx, $b),
self::fe_cmov($t->xy2d, $u->xy2d, $b)
);
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached
*/
public static function ge_cmov_cached(
ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t,
ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u,
$b
) {
$b &= 1;
$ret = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached();
$ret->YplusX = self::fe_cmov($t->YplusX, $u->YplusX, $b);
$ret->YminusX = self::fe_cmov($t->YminusX, $u->YminusX, $b);
$ret->Z = self::fe_cmov($t->Z, $u->Z, $b);
$ret->T2d = self::fe_cmov($t->T2d, $u->T2d, $b);
return $ret;
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $cached
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached
* @throws SodiumException
*/
public static function ge_cmov8_cached(array $cached, $b)
{
// const unsigned char bnegative = negative(b);
// const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1));
$bnegative = self::negative($b);
$babs = $b - (((-$bnegative) & $b) << 1);
// ge25519_cached_0(t);
$t = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(
self::fe_1(),
self::fe_1(),
self::fe_1(),
self::fe_0()
);
// ge25519_cmov_cached(t, &cached[0], equal(babs, 1));
// ge25519_cmov_cached(t, &cached[1], equal(babs, 2));
// ge25519_cmov_cached(t, &cached[2], equal(babs, 3));
// ge25519_cmov_cached(t, &cached[3], equal(babs, 4));
// ge25519_cmov_cached(t, &cached[4], equal(babs, 5));
// ge25519_cmov_cached(t, &cached[5], equal(babs, 6));
// ge25519_cmov_cached(t, &cached[6], equal(babs, 7));
// ge25519_cmov_cached(t, &cached[7], equal(babs, 8));
for ($x = 0; $x < 8; ++$x) {
$t = self::ge_cmov_cached($t, $cached[$x], self::equal($babs, $x + 1));
}
// fe25519_copy(minust.YplusX, t->YminusX);
// fe25519_copy(minust.YminusX, t->YplusX);
// fe25519_copy(minust.Z, t->Z);
// fe25519_neg(minust.T2d, t->T2d);
$minust = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(
self::fe_copy($t->YminusX),
self::fe_copy($t->YplusX),
self::fe_copy($t->Z),
self::fe_neg($t->T2d)
);
return self::ge_cmov_cached($t, $minust, $bnegative);
}
/**
* @internal You should not use this directly from another application
*
* @param int $pos
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
* @throws SodiumException
* @throws TypeError
* @psalm-suppress MixedArgument
* @psalm-suppress MixedArrayAccess
* @psalm-suppress MixedArrayOffset
*/
public static function ge_select($pos = 0, $b = 0)
{
static $base = null;
if ($base === null) {
$base = array();
/** @var int $i */
foreach (self::$base as $i => $bas) {
for ($j = 0; $j < 8; ++$j) {
$base[$i][$j] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][0]),
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][1]),
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][2])
);
}
}
}
/** @var array<int, array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp>> $base */
if (!is_int($pos)) {
throw new InvalidArgumentException('Position must be an integer');
}
if ($pos < 0 || $pos > 31) {
throw new RangeException('Position is out of range [0, 31]');
}
$bnegative = self::negative($b);
$babs = $b - (((-$bnegative) & $b) << 1);
$t = self::ge_precomp_0();
for ($i = 0; $i < 8; ++$i) {
$t = self::cmov(
$t,
$base[$pos][$i],
self::equal($babs, $i + 1)
);
}
$minusT = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
self::fe_copy($t->yminusx),
self::fe_copy($t->yplusx),
self::fe_neg($t->xy2d)
);
return self::cmov($t, $minusT, $bnegative);
}
/**
* Subtract two group elements.
*
* r = p - q
*
* @internal You should not use this directly from another application
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1
*/
public static function ge_sub(
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q
) {
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1();
$r->X = self::fe_add($p->Y, $p->X);
$r->Y = self::fe_sub($p->Y, $p->X);
$r->Z = self::fe_mul($r->X, $q->YminusX);
$r->Y = self::fe_mul($r->Y, $q->YplusX);
$r->T = self::fe_mul($q->T2d, $p->T);
$r->X = self::fe_mul($p->Z, $q->Z);
$t0 = self::fe_add($r->X, $r->X);
$r->X = self::fe_sub($r->Z, $r->Y);
$r->Y = self::fe_add($r->Z, $r->Y);
$r->Z = self::fe_sub($t0, $r->T);
$r->T = self::fe_add($t0, $r->T);
return $r;
}
/**
* Convert a group element to a byte string.
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h
* @return string
* @throws SodiumException
* @throws TypeError
*/
public static function ge_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h)
{
$recip = self::fe_invert($h->Z);
$x = self::fe_mul($h->X, $recip);
$y = self::fe_mul($h->Y, $recip);
$s = self::fe_tobytes($y);
$s[31] = self::intToChr(
self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7)
);
return $s;
}
/**
* @internal You should not use this directly from another application
*
* @param string $a
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A
* @param string $b
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P2
* @throws SodiumException
* @throws TypeError
* @psalm-suppress MixedArgument
* @psalm-suppress MixedArrayAccess
*/
public static function ge_double_scalarmult_vartime(
$a,
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A,
$b
) {
/** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai */
$Ai = array();
/** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp> $Bi */
static $Bi = array();
if (!$Bi) {
for ($i = 0; $i < 8; ++$i) {
$Bi[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][0]),
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][1]),
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][2])
);
}
}
for ($i = 0; $i < 8; ++$i) {
$Ai[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(
self::fe_0(),
self::fe_0(),
self::fe_0(),
self::fe_0()
);
}
# slide(aslide,a);
# slide(bslide,b);
/** @var array<int, int> $aslide */
$aslide = self::slide($a);
/** @var array<int, int> $bslide */
$bslide = self::slide($b);
# ge_p3_to_cached(&Ai[0],A);
# ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
$Ai[0] = self::ge_p3_to_cached($A);
$t = self::ge_p3_dbl($A);
$A2 = self::ge_p1p1_to_p3($t);
# ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
# ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
# ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
# ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
# ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
# ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
# ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
for ($i = 0; $i < 7; ++$i) {
$t = self::ge_add($A2, $Ai[$i]);
$u = self::ge_p1p1_to_p3($t);
$Ai[$i + 1] = self::ge_p3_to_cached($u);
}
# ge_p2_0(r);
$r = self::ge_p2_0();
# for (i = 255;i >= 0;--i) {
# if (aslide[i] || bslide[i]) break;
# }
$i = 255;
for (; $i >= 0; --$i) {
if ($aslide[$i] || $bslide[$i]) {
break;
}
}
# for (;i >= 0;--i) {
for (; $i >= 0; --$i) {
# ge_p2_dbl(&t,r);
$t = self::ge_p2_dbl($r);
# if (aslide[i] > 0) {
if ($aslide[$i] > 0) {
# ge_p1p1_to_p3(&u,&t);
# ge_add(&t,&u,&Ai[aslide[i]/2]);
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_add(
$u,
$Ai[(int) floor($aslide[$i] / 2)]
);
# } else if (aslide[i] < 0) {
} elseif ($aslide[$i] < 0) {
# ge_p1p1_to_p3(&u,&t);
# ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_sub(
$u,
$Ai[(int) floor(-$aslide[$i] / 2)]
);
}
# if (bslide[i] > 0) {
if ($bslide[$i] > 0) {
/** @var int $index */
$index = (int) floor($bslide[$i] / 2);
# ge_p1p1_to_p3(&u,&t);
# ge_madd(&t,&u,&Bi[bslide[i]/2]);
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_madd($t, $u, $Bi[$index]);
# } else if (bslide[i] < 0) {
} elseif ($bslide[$i] < 0) {
/** @var int $index */
$index = (int) floor(-$bslide[$i] / 2);
# ge_p1p1_to_p3(&u,&t);
# ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_msub($t, $u, $Bi[$index]);
}
# ge_p1p1_to_p2(r,&t);
$r = self::ge_p1p1_to_p2($t);
}
return $r;
}
/**
* @internal You should not use this directly from another application
*
* @param string $a
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
* @throws SodiumException
* @throws TypeError
* @psalm-suppress MixedAssignment
* @psalm-suppress MixedOperand
*/
public static function ge_scalarmult($a, $p)
{
$e = array_fill(0, 64, 0);
/** @var ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $pi */
$pi = array();
// ge25519_p3_to_cached(&pi[1 - 1], p); /* p */
$pi[0] = self::ge_p3_to_cached($p);
// ge25519_p3_dbl(&t2, p);
// ge25519_p1p1_to_p3(&p2, &t2);
// ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */
$t2 = self::ge_p3_dbl($p);
$p2 = self::ge_p1p1_to_p3($t2);
$pi[1] = self::ge_p3_to_cached($p2);
// ge25519_add_cached(&t3, p, &pi[2 - 1]);
// ge25519_p1p1_to_p3(&p3, &t3);
// ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */
$t3 = self::ge_add($p, $pi[1]);
$p3 = self::ge_p1p1_to_p3($t3);
$pi[2] = self::ge_p3_to_cached($p3);
// ge25519_p3_dbl(&t4, &p2);
// ge25519_p1p1_to_p3(&p4, &t4);
// ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */
$t4 = self::ge_p3_dbl($p2);
$p4 = self::ge_p1p1_to_p3($t4);
$pi[3] = self::ge_p3_to_cached($p4);
// ge25519_add_cached(&t5, p, &pi[4 - 1]);
// ge25519_p1p1_to_p3(&p5, &t5);
// ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */
$t5 = self::ge_add($p, $pi[3]);
$p5 = self::ge_p1p1_to_p3($t5);
$pi[4] = self::ge_p3_to_cached($p5);
// ge25519_p3_dbl(&t6, &p3);
// ge25519_p1p1_to_p3(&p6, &t6);
// ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */
$t6 = self::ge_p3_dbl($p3);
$p6 = self::ge_p1p1_to_p3($t6);
$pi[5] = self::ge_p3_to_cached($p6);
// ge25519_add_cached(&t7, p, &pi[6 - 1]);
// ge25519_p1p1_to_p3(&p7, &t7);
// ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */
$t7 = self::ge_add($p, $pi[5]);
$p7 = self::ge_p1p1_to_p3($t7);
$pi[6] = self::ge_p3_to_cached($p7);
// ge25519_p3_dbl(&t8, &p4);
// ge25519_p1p1_to_p3(&p8, &t8);
// ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */
$t8 = self::ge_p3_dbl($p4);
$p8 = self::ge_p1p1_to_p3($t8);
$pi[7] = self::ge_p3_to_cached($p8);
// for (i = 0; i < 32; ++i) {
// e[2 * i + 0] = (a[i] >> 0) & 15;
// e[2 * i + 1] = (a[i] >> 4) & 15;
// }
for ($i = 0; $i < 32; ++$i) {
$e[($i << 1) ] = self::chrToInt($a[$i]) & 15;
$e[($i << 1) + 1] = (self::chrToInt($a[$i]) >> 4) & 15;
}
// /* each e[i] is between 0 and 15 */
// /* e[63] is between 0 and 7 */
// carry = 0;
// for (i = 0; i < 63; ++i) {
// e[i] += carry;
// carry = e[i] + 8;
// carry >>= 4;
// e[i] -= carry * ((signed char) 1 << 4);
// }
$carry = 0;
for ($i = 0; $i < 63; ++$i) {
$e[$i] += $carry;
$carry = $e[$i] + 8;
$carry >>= 4;
$e[$i] -= $carry << 4;
}
// e[63] += carry;
// /* each e[i] is between -8 and 8 */
$e[63] += $carry;
// ge25519_p3_0(h);
$h = self::ge_p3_0();
// for (i = 63; i != 0; i--) {
for ($i = 63; $i != 0; --$i) {
// ge25519_cmov8_cached(&t, pi, e[i]);
$t = self::ge_cmov8_cached($pi, $e[$i]);
// ge25519_add_cached(&r, h, &t);
$r = self::ge_add($h, $t);
// ge25519_p1p1_to_p2(&s, &r);
// ge25519_p2_dbl(&r, &s);
// ge25519_p1p1_to_p2(&s, &r);
// ge25519_p2_dbl(&r, &s);
// ge25519_p1p1_to_p2(&s, &r);
// ge25519_p2_dbl(&r, &s);
// ge25519_p1p1_to_p2(&s, &r);
// ge25519_p2_dbl(&r, &s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
// ge25519_p1p1_to_p3(h, &r); /* *16 */
$h = self::ge_p1p1_to_p3($r); /* *16 */
}
// ge25519_cmov8_cached(&t, pi, e[i]);
// ge25519_add_cached(&r, h, &t);
// ge25519_p1p1_to_p3(h, &r);
$t = self::ge_cmov8_cached($pi, $e[0]);
$r = self::ge_add($h, $t);
return self::ge_p1p1_to_p3($r);
}
/**
* @internal You should not use this directly from another application
*
* @param string $a
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
* @throws SodiumException
* @throws TypeError
* @psalm-suppress MixedAssignment
* @psalm-suppress MixedOperand
*/
public static function ge_scalarmult_base($a)
{
/** @var array<int, int> $e */
$e = array();
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1();
for ($i = 0; $i < 32; ++$i) {
$dbl = (int) $i << 1;
$e[$dbl] = (int) self::chrToInt($a[$i]) & 15;
$e[$dbl + 1] = (int) (self::chrToInt($a[$i]) >> 4) & 15;
}
$carry = 0;
for ($i = 0; $i < 63; ++$i) {
$e[$i] += $carry;
$carry = $e[$i] + 8;
$carry >>= 4;
$e[$i] -= $carry << 4;
}
$e[63] += (int) $carry;
$h = self::ge_p3_0();
for ($i = 1; $i < 64; $i += 2) {
$t = self::ge_select((int) floor($i / 2), (int) $e[$i]);
$r = self::ge_madd($r, $h, $t);
$h = self::ge_p1p1_to_p3($r);
}
$r = self::ge_p3_dbl($h);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$s = self::ge_p1p1_to_p2($r);
$r = self::ge_p2_dbl($s);
$h = self::ge_p1p1_to_p3($r);
for ($i = 0; $i < 64; $i += 2) {
$t = self::ge_select($i >> 1, (int) $e[$i]);
$r = self::ge_madd($r, $h, $t);
$h = self::ge_p1p1_to_p3($r);
}
return $h;
}
/**
* Calculates (ab + c) mod l
* where l = 2^252 + 27742317777372353535851937790883648493
*
* @internal You should not use this directly from another application
*
* @param string $a
* @param string $b
* @param string $c
* @return string
* @throws TypeError
*/
public static function sc_muladd($a, $b, $c)
{
$a0 = 2097151 & self::load_3(self::substr($a, 0, 3));
$a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5);
$a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2);
$a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7);
$a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4);
$a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1);
$a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6);
$a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3);
$a8 = 2097151 & self::load_3(self::substr($a, 21, 3));
$a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5);
$a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2);
$a11 = (self::load_4(self::substr($a, 28, 4)) >> 7);
$b0 = 2097151 & self::load_3(self::substr($b, 0, 3));
$b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5);
$b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2);
$b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7);
$b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4);
$b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1);
$b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6);
$b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3);
$b8 = 2097151 & self::load_3(self::substr($b, 21, 3));
$b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5);
$b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2);
$b11 = (self::load_4(self::substr($b, 28, 4)) >> 7);
$c0 = 2097151 & self::load_3(self::substr($c, 0, 3));
$c1 = 2097151 & (self::load_4(self::substr($c, 2, 4)) >> 5);
$c2 = 2097151 & (self::load_3(self::substr($c, 5, 3)) >> 2);
$c3 = 2097151 & (self::load_4(self::substr($c, 7, 4)) >> 7);
$c4 = 2097151 & (self::load_4(self::substr($c, 10, 4)) >> 4);
$c5 = 2097151 & (self::load_3(self::substr($c, 13, 3)) >> 1);
$c6 = 2097151 & (self::load_4(self::substr($c, 15, 4)) >> 6);
$c7 = 2097151 & (self::load_3(self::substr($c, 18, 3)) >> 3);
$c8 = 2097151 & self::load_3(self::substr($c, 21, 3));
$c9 = 2097151 & (self::load_4(self::substr($c, 23, 4)) >> 5);
$c10 = 2097151 & (self::load_3(self::substr($c, 26, 3)) >> 2);
$c11 = (self::load_4(self::substr($c, 28, 4)) >> 7);
/* Can't really avoid the pyramid here: */
$s0 = $c0 + self::mul($a0, $b0, 24);
$s1 = $c1 + self::mul($a0, $b1, 24) + self::mul($a1, $b0, 24);
$s2 = $c2 + self::mul($a0, $b2, 24) + self::mul($a1, $b1, 24) + self::mul($a2, $b0, 24);
$s3 = $c3 + self::mul($a0, $b3, 24) + self::mul($a1, $b2, 24) + self::mul($a2, $b1, 24) + self::mul($a3, $b0, 24);
$s4 = $c4 + self::mul($a0, $b4, 24) + self::mul($a1, $b3, 24) + self::mul($a2, $b2, 24) + self::mul($a3, $b1, 24) +
self::mul($a4, $b0, 24);
$s5 = $c5 + self::mul($a0, $b5, 24) + self::mul($a1, $b4, 24) + self::mul($a2, $b3, 24) + self::mul($a3, $b2, 24) +
self::mul($a4, $b1, 24) + self::mul($a5, $b0, 24);
$s6 = $c6 + self::mul($a0, $b6, 24) + self::mul($a1, $b5, 24) + self::mul($a2, $b4, 24) + self::mul($a3, $b3, 24) +
self::mul($a4, $b2, 24) + self::mul($a5, $b1, 24) + self::mul($a6, $b0, 24);
$s7 = $c7 + self::mul($a0, $b7, 24) + self::mul($a1, $b6, 24) + self::mul($a2, $b5, 24) + self::mul($a3, $b4, 24) +
self::mul($a4, $b3, 24) + self::mul($a5, $b2, 24) + self::mul($a6, $b1, 24) + self::mul($a7, $b0, 24);
$s8 = $c8 + self::mul($a0, $b8, 24) + self::mul($a1, $b7, 24) + self::mul($a2, $b6, 24) + self::mul($a3, $b5, 24) +
self::mul($a4, $b4, 24) + self::mul($a5, $b3, 24) + self::mul($a6, $b2, 24) + self::mul($a7, $b1, 24) +
self::mul($a8, $b0, 24);
$s9 = $c9 + self::mul($a0, $b9, 24) + self::mul($a1, $b8, 24) + self::mul($a2, $b7, 24) + self::mul($a3, $b6, 24) +
self::mul($a4, $b5, 24) + self::mul($a5, $b4, 24) + self::mul($a6, $b3, 24) + self::mul($a7, $b2, 24) +
self::mul($a8, $b1, 24) + self::mul($a9, $b0, 24);
$s10 = $c10 + self::mul($a0, $b10, 24) + self::mul($a1, $b9, 24) + self::mul($a2, $b8, 24) + self::mul($a3, $b7, 24) +
self::mul($a4, $b6, 24) + self::mul($a5, $b5, 24) + self::mul($a6, $b4, 24) + self::mul($a7, $b3, 24) +
self::mul($a8, $b2, 24) + self::mul($a9, $b1, 24) + self::mul($a10, $b0, 24);
$s11 = $c11 + self::mul($a0, $b11, 24) + self::mul($a1, $b10, 24) + self::mul($a2, $b9, 24) + self::mul($a3, $b8, 24) +
self::mul($a4, $b7, 24) + self::mul($a5, $b6, 24) + self::mul($a6, $b5, 24) + self::mul($a7, $b4, 24) +
self::mul($a8, $b3, 24) + self::mul($a9, $b2, 24) + self::mul($a10, $b1, 24) + self::mul($a11, $b0, 24);
$s12 = self::mul($a1, $b11, 24) + self::mul($a2, $b10, 24) + self::mul($a3, $b9, 24) + self::mul($a4, $b8, 24) +
self::mul($a5, $b7, 24) + self::mul($a6, $b6, 24) + self::mul($a7, $b5, 24) + self::mul($a8, $b4, 24) +
self::mul($a9, $b3, 24) + self::mul($a10, $b2, 24) + self::mul($a11, $b1, 24);
$s13 = self::mul($a2, $b11, 24) + self::mul($a3, $b10, 24) + self::mul($a4, $b9, 24) + self::mul($a5, $b8, 24) +
self::mul($a6, $b7, 24) + self::mul($a7, $b6, 24) + self::mul($a8, $b5, 24) + self::mul($a9, $b4, 24) +
self::mul($a10, $b3, 24) + self::mul($a11, $b2, 24);
$s14 = self::mul($a3, $b11, 24) + self::mul($a4, $b10, 24) + self::mul($a5, $b9, 24) + self::mul($a6, $b8, 24) +
self::mul($a7, $b7, 24) + self::mul($a8, $b6, 24) + self::mul($a9, $b5, 24) + self::mul($a10, $b4, 24) +
self::mul($a11, $b3, 24);
$s15 = self::mul($a4, $b11, 24) + self::mul($a5, $b10, 24) + self::mul($a6, $b9, 24) + self::mul($a7, $b8, 24) +
self::mul($a8, $b7, 24) + self::mul($a9, $b6, 24) + self::mul($a10, $b5, 24) + self::mul($a11, $b4, 24);
$s16 = self::mul($a5, $b11, 24) + self::mul($a6, $b10, 24) + self::mul($a7, $b9, 24) + self::mul($a8, $b8, 24) +
self::mul($a9, $b7, 24) + self::mul($a10, $b6, 24) + self::mul($a11, $b5, 24);
$s17 = self::mul($a6, $b11, 24) + self::mul($a7, $b10, 24) + self::mul($a8, $b9, 24) + self::mul($a9, $b8, 24) +
self::mul($a10, $b7, 24) + self::mul($a11, $b6, 24);
$s18 = self::mul($a7, $b11, 24) + self::mul($a8, $b10, 24) + self::mul($a9, $b9, 24) + self::mul($a10, $b8, 24) +
self::mul($a11, $b7, 24);
$s19 = self::mul($a8, $b11, 24) + self::mul($a9, $b10, 24) + self::mul($a10, $b9, 24) + self::mul($a11, $b8, 24);
$s20 = self::mul($a9, $b11, 24) + self::mul($a10, $b10, 24) + self::mul($a11, $b9, 24);
$s21 = self::mul($a10, $b11, 24) + self::mul($a11, $b10, 24);
$s22 = self::mul($a11, $b11, 24);
$s23 = 0;
$carry0 = ($s0 + (1 << 20)) >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry2 = ($s2 + (1 << 20)) >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry4 = ($s4 + (1 << 20)) >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry12 = ($s12 + (1 << 20)) >> 21;
$s13 += $carry12;
$s12 -= $carry12 << 21;
$carry14 = ($s14 + (1 << 20)) >> 21;
$s15 += $carry14;
$s14 -= $carry14 << 21;
$carry16 = ($s16 + (1 << 20)) >> 21;
$s17 += $carry16;
$s16 -= $carry16 << 21;
$carry18 = ($s18 + (1 << 20)) >> 21;
$s19 += $carry18;
$s18 -= $carry18 << 21;
$carry20 = ($s20 + (1 << 20)) >> 21;
$s21 += $carry20;
$s20 -= $carry20 << 21;
$carry22 = ($s22 + (1 << 20)) >> 21;
$s23 += $carry22;
$s22 -= $carry22 << 21;
$carry1 = ($s1 + (1 << 20)) >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry3 = ($s3 + (1 << 20)) >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry5 = ($s5 + (1 << 20)) >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$carry13 = ($s13 + (1 << 20)) >> 21;
$s14 += $carry13;
$s13 -= $carry13 << 21;
$carry15 = ($s15 + (1 << 20)) >> 21;
$s16 += $carry15;
$s15 -= $carry15 << 21;
$carry17 = ($s17 + (1 << 20)) >> 21;
$s18 += $carry17;
$s17 -= $carry17 << 21;
$carry19 = ($s19 + (1 << 20)) >> 21;
$s20 += $carry19;
$s19 -= $carry19 << 21;
$carry21 = ($s21 + (1 << 20)) >> 21;
$s22 += $carry21;
$s21 -= $carry21 << 21;
$s11 += self::mul($s23, 666643, 20);
$s12 += self::mul($s23, 470296, 19);
$s13 += self::mul($s23, 654183, 20);
$s14 -= self::mul($s23, 997805, 20);
$s15 += self::mul($s23, 136657, 18);
$s16 -= self::mul($s23, 683901, 20);
$s10 += self::mul($s22, 666643, 20);
$s11 += self::mul($s22, 470296, 19);
$s12 += self::mul($s22, 654183, 20);
$s13 -= self::mul($s22, 997805, 20);
$s14 += self::mul($s22, 136657, 18);
$s15 -= self::mul($s22, 683901, 20);
$s9 += self::mul($s21, 666643, 20);
$s10 += self::mul($s21, 470296, 19);
$s11 += self::mul($s21, 654183, 20);
$s12 -= self::mul($s21, 997805, 20);
$s13 += self::mul($s21, 136657, 18);
$s14 -= self::mul($s21, 683901, 20);
$s8 += self::mul($s20, 666643, 20);
$s9 += self::mul($s20, 470296, 19);
$s10 += self::mul($s20, 654183, 20);
$s11 -= self::mul($s20, 997805, 20);
$s12 += self::mul($s20, 136657, 18);
$s13 -= self::mul($s20, 683901, 20);
$s7 += self::mul($s19, 666643, 20);
$s8 += self::mul($s19, 470296, 19);
$s9 += self::mul($s19, 654183, 20);
$s10 -= self::mul($s19, 997805, 20);
$s11 += self::mul($s19, 136657, 18);
$s12 -= self::mul($s19, 683901, 20);
$s6 += self::mul($s18, 666643, 20);
$s7 += self::mul($s18, 470296, 19);
$s8 += self::mul($s18, 654183, 20);
$s9 -= self::mul($s18, 997805, 20);
$s10 += self::mul($s18, 136657, 18);
$s11 -= self::mul($s18, 683901, 20);
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry12 = ($s12 + (1 << 20)) >> 21;
$s13 += $carry12;
$s12 -= $carry12 << 21;
$carry14 = ($s14 + (1 << 20)) >> 21;
$s15 += $carry14;
$s14 -= $carry14 << 21;
$carry16 = ($s16 + (1 << 20)) >> 21;
$s17 += $carry16;
$s16 -= $carry16 << 21;
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$carry13 = ($s13 + (1 << 20)) >> 21;
$s14 += $carry13;
$s13 -= $carry13 << 21;
$carry15 = ($s15 + (1 << 20)) >> 21;
$s16 += $carry15;
$s15 -= $carry15 << 21;
$s5 += self::mul($s17, 666643, 20);
$s6 += self::mul($s17, 470296, 19);
$s7 += self::mul($s17, 654183, 20);
$s8 -= self::mul($s17, 997805, 20);
$s9 += self::mul($s17, 136657, 18);
$s10 -= self::mul($s17, 683901, 20);
$s4 += self::mul($s16, 666643, 20);
$s5 += self::mul($s16, 470296, 19);
$s6 += self::mul($s16, 654183, 20);
$s7 -= self::mul($s16, 997805, 20);
$s8 += self::mul($s16, 136657, 18);
$s9 -= self::mul($s16, 683901, 20);
$s3 += self::mul($s15, 666643, 20);
$s4 += self::mul($s15, 470296, 19);
$s5 += self::mul($s15, 654183, 20);
$s6 -= self::mul($s15, 997805, 20);
$s7 += self::mul($s15, 136657, 18);
$s8 -= self::mul($s15, 683901, 20);
$s2 += self::mul($s14, 666643, 20);
$s3 += self::mul($s14, 470296, 19);
$s4 += self::mul($s14, 654183, 20);
$s5 -= self::mul($s14, 997805, 20);
$s6 += self::mul($s14, 136657, 18);
$s7 -= self::mul($s14, 683901, 20);
$s1 += self::mul($s13, 666643, 20);
$s2 += self::mul($s13, 470296, 19);
$s3 += self::mul($s13, 654183, 20);
$s4 -= self::mul($s13, 997805, 20);
$s5 += self::mul($s13, 136657, 18);
$s6 -= self::mul($s13, 683901, 20);
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
$carry0 = ($s0 + (1 << 20)) >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry2 = ($s2 + (1 << 20)) >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry4 = ($s4 + (1 << 20)) >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry1 = ($s1 + (1 << 20)) >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry3 = ($s3 + (1 << 20)) >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry5 = ($s5 + (1 << 20)) >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry11 = $s11 >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
/**
* @var array<int, int>
*/
$arr = array(
(int) (0xff & ($s0 >> 0)),
(int) (0xff & ($s0 >> 8)),
(int) (0xff & (($s0 >> 16) | $s1 << 5)),
(int) (0xff & ($s1 >> 3)),
(int) (0xff & ($s1 >> 11)),
(int) (0xff & (($s1 >> 19) | $s2 << 2)),
(int) (0xff & ($s2 >> 6)),
(int) (0xff & (($s2 >> 14) | $s3 << 7)),
(int) (0xff & ($s3 >> 1)),
(int) (0xff & ($s3 >> 9)),
(int) (0xff & (($s3 >> 17) | $s4 << 4)),
(int) (0xff & ($s4 >> 4)),
(int) (0xff & ($s4 >> 12)),
(int) (0xff & (($s4 >> 20) | $s5 << 1)),
(int) (0xff & ($s5 >> 7)),
(int) (0xff & (($s5 >> 15) | $s6 << 6)),
(int) (0xff & ($s6 >> 2)),
(int) (0xff & ($s6 >> 10)),
(int) (0xff & (($s6 >> 18) | $s7 << 3)),
(int) (0xff & ($s7 >> 5)),
(int) (0xff & ($s7 >> 13)),
(int) (0xff & ($s8 >> 0)),
(int) (0xff & ($s8 >> 8)),
(int) (0xff & (($s8 >> 16) | $s9 << 5)),
(int) (0xff & ($s9 >> 3)),
(int) (0xff & ($s9 >> 11)),
(int) (0xff & (($s9 >> 19) | $s10 << 2)),
(int) (0xff & ($s10 >> 6)),
(int) (0xff & (($s10 >> 14) | $s11 << 7)),
(int) (0xff & ($s11 >> 1)),
(int) (0xff & ($s11 >> 9)),
0xff & ($s11 >> 17)
);
return self::intArrayToString($arr);
}
/**
* @internal You should not use this directly from another application
*
* @param string $s
* @return string
* @throws TypeError
*/
public static function sc_reduce($s)
{
$s0 = 2097151 & self::load_3(self::substr($s, 0, 3));
$s1 = 2097151 & (self::load_4(self::substr($s, 2, 4)) >> 5);
$s2 = 2097151 & (self::load_3(self::substr($s, 5, 3)) >> 2);
$s3 = 2097151 & (self::load_4(self::substr($s, 7, 4)) >> 7);
$s4 = 2097151 & (self::load_4(self::substr($s, 10, 4)) >> 4);
$s5 = 2097151 & (self::load_3(self::substr($s, 13, 3)) >> 1);
$s6 = 2097151 & (self::load_4(self::substr($s, 15, 4)) >> 6);
$s7 = 2097151 & (self::load_3(self::substr($s, 18, 4)) >> 3);
$s8 = 2097151 & self::load_3(self::substr($s, 21, 3));
$s9 = 2097151 & (self::load_4(self::substr($s, 23, 4)) >> 5);
$s10 = 2097151 & (self::load_3(self::substr($s, 26, 3)) >> 2);
$s11 = 2097151 & (self::load_4(self::substr($s, 28, 4)) >> 7);
$s12 = 2097151 & (self::load_4(self::substr($s, 31, 4)) >> 4);
$s13 = 2097151 & (self::load_3(self::substr($s, 34, 3)) >> 1);
$s14 = 2097151 & (self::load_4(self::substr($s, 36, 4)) >> 6);
$s15 = 2097151 & (self::load_3(self::substr($s, 39, 4)) >> 3);
$s16 = 2097151 & self::load_3(self::substr($s, 42, 3));
$s17 = 2097151 & (self::load_4(self::substr($s, 44, 4)) >> 5);
$s18 = 2097151 & (self::load_3(self::substr($s, 47, 3)) >> 2);
$s19 = 2097151 & (self::load_4(self::substr($s, 49, 4)) >> 7);
$s20 = 2097151 & (self::load_4(self::substr($s, 52, 4)) >> 4);
$s21 = 2097151 & (self::load_3(self::substr($s, 55, 3)) >> 1);
$s22 = 2097151 & (self::load_4(self::substr($s, 57, 4)) >> 6);
$s23 = 0x1fffffff & (self::load_4(self::substr($s, 60, 4)) >> 3);
$s11 += self::mul($s23, 666643, 20);
$s12 += self::mul($s23, 470296, 19);
$s13 += self::mul($s23, 654183, 20);
$s14 -= self::mul($s23, 997805, 20);
$s15 += self::mul($s23, 136657, 18);
$s16 -= self::mul($s23, 683901, 20);
$s10 += self::mul($s22, 666643, 20);
$s11 += self::mul($s22, 470296, 19);
$s12 += self::mul($s22, 654183, 20);
$s13 -= self::mul($s22, 997805, 20);
$s14 += self::mul($s22, 136657, 18);
$s15 -= self::mul($s22, 683901, 20);
$s9 += self::mul($s21, 666643, 20);
$s10 += self::mul($s21, 470296, 19);
$s11 += self::mul($s21, 654183, 20);
$s12 -= self::mul($s21, 997805, 20);
$s13 += self::mul($s21, 136657, 18);
$s14 -= self::mul($s21, 683901, 20);
$s8 += self::mul($s20, 666643, 20);
$s9 += self::mul($s20, 470296, 19);
$s10 += self::mul($s20, 654183, 20);
$s11 -= self::mul($s20, 997805, 20);
$s12 += self::mul($s20, 136657, 18);
$s13 -= self::mul($s20, 683901, 20);
$s7 += self::mul($s19, 666643, 20);
$s8 += self::mul($s19, 470296, 19);
$s9 += self::mul($s19, 654183, 20);
$s10 -= self::mul($s19, 997805, 20);
$s11 += self::mul($s19, 136657, 18);
$s12 -= self::mul($s19, 683901, 20);
$s6 += self::mul($s18, 666643, 20);
$s7 += self::mul($s18, 470296, 19);
$s8 += self::mul($s18, 654183, 20);
$s9 -= self::mul($s18, 997805, 20);
$s10 += self::mul($s18, 136657, 18);
$s11 -= self::mul($s18, 683901, 20);
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry12 = ($s12 + (1 << 20)) >> 21;
$s13 += $carry12;
$s12 -= $carry12 << 21;
$carry14 = ($s14 + (1 << 20)) >> 21;
$s15 += $carry14;
$s14 -= $carry14 << 21;
$carry16 = ($s16 + (1 << 20)) >> 21;
$s17 += $carry16;
$s16 -= $carry16 << 21;
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$carry13 = ($s13 + (1 << 20)) >> 21;
$s14 += $carry13;
$s13 -= $carry13 << 21;
$carry15 = ($s15 + (1 << 20)) >> 21;
$s16 += $carry15;
$s15 -= $carry15 << 21;
$s5 += self::mul($s17, 666643, 20);
$s6 += self::mul($s17, 470296, 19);
$s7 += self::mul($s17, 654183, 20);
$s8 -= self::mul($s17, 997805, 20);
$s9 += self::mul($s17, 136657, 18);
$s10 -= self::mul($s17, 683901, 20);
$s4 += self::mul($s16, 666643, 20);
$s5 += self::mul($s16, 470296, 19);
$s6 += self::mul($s16, 654183, 20);
$s7 -= self::mul($s16, 997805, 20);
$s8 += self::mul($s16, 136657, 18);
$s9 -= self::mul($s16, 683901, 20);
$s3 += self::mul($s15, 666643, 20);
$s4 += self::mul($s15, 470296, 19);
$s5 += self::mul($s15, 654183, 20);
$s6 -= self::mul($s15, 997805, 20);
$s7 += self::mul($s15, 136657, 18);
$s8 -= self::mul($s15, 683901, 20);
$s2 += self::mul($s14, 666643, 20);
$s3 += self::mul($s14, 470296, 19);
$s4 += self::mul($s14, 654183, 20);
$s5 -= self::mul($s14, 997805, 20);
$s6 += self::mul($s14, 136657, 18);
$s7 -= self::mul($s14, 683901, 20);
$s1 += self::mul($s13, 666643, 20);
$s2 += self::mul($s13, 470296, 19);
$s3 += self::mul($s13, 654183, 20);
$s4 -= self::mul($s13, 997805, 20);
$s5 += self::mul($s13, 136657, 18);
$s6 -= self::mul($s13, 683901, 20);
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
$carry0 = ($s0 + (1 << 20)) >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry2 = ($s2 + (1 << 20)) >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry4 = ($s4 + (1 << 20)) >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry1 = ($s1 + (1 << 20)) >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry3 = ($s3 + (1 << 20)) >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry5 = ($s5 + (1 << 20)) >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$carry11 = $s11 >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
/**
* @var array<int, int>
*/
$arr = array(
(int) ($s0 >> 0),
(int) ($s0 >> 8),
(int) (($s0 >> 16) | $s1 << 5),
(int) ($s1 >> 3),
(int) ($s1 >> 11),
(int) (($s1 >> 19) | $s2 << 2),
(int) ($s2 >> 6),
(int) (($s2 >> 14) | $s3 << 7),
(int) ($s3 >> 1),
(int) ($s3 >> 9),
(int) (($s3 >> 17) | $s4 << 4),
(int) ($s4 >> 4),
(int) ($s4 >> 12),
(int) (($s4 >> 20) | $s5 << 1),
(int) ($s5 >> 7),
(int) (($s5 >> 15) | $s6 << 6),
(int) ($s6 >> 2),
(int) ($s6 >> 10),
(int) (($s6 >> 18) | $s7 << 3),
(int) ($s7 >> 5),
(int) ($s7 >> 13),
(int) ($s8 >> 0),
(int) ($s8 >> 8),
(int) (($s8 >> 16) | $s9 << 5),
(int) ($s9 >> 3),
(int) ($s9 >> 11),
(int) (($s9 >> 19) | $s10 << 2),
(int) ($s10 >> 6),
(int) (($s10 >> 14) | $s11 << 7),
(int) ($s11 >> 1),
(int) ($s11 >> 9),
(int) $s11 >> 17
);
return self::intArrayToString($arr);
}
/**
* multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493
*
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
*/
public static function ge_mul_l(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A)
{
$aslide = array(
13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0,
0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0,
0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0,
0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1,
0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0,
0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
);
/** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai size 8 */
$Ai = array();
# ge_p3_to_cached(&Ai[0], A);
$Ai[0] = self::ge_p3_to_cached($A);
# ge_p3_dbl(&t, A);
$t = self::ge_p3_dbl($A);
# ge_p1p1_to_p3(&A2, &t);
$A2 = self::ge_p1p1_to_p3($t);
for ($i = 1; $i < 8; ++$i) {
# ge_add(&t, &A2, &Ai[0]);
$t = self::ge_add($A2, $Ai[$i - 1]);
# ge_p1p1_to_p3(&u, &t);
$u = self::ge_p1p1_to_p3($t);
# ge_p3_to_cached(&Ai[i], &u);
$Ai[$i] = self::ge_p3_to_cached($u);
}
$r = self::ge_p3_0();
for ($i = 252; $i >= 0; --$i) {
$t = self::ge_p3_dbl($r);
if ($aslide[$i] > 0) {
# ge_p1p1_to_p3(&u, &t);
$u = self::ge_p1p1_to_p3($t);
# ge_add(&t, &u, &Ai[aslide[i] / 2]);
$t = self::ge_add($u, $Ai[(int)($aslide[$i] / 2)]);
} elseif ($aslide[$i] < 0) {
# ge_p1p1_to_p3(&u, &t);
$u = self::ge_p1p1_to_p3($t);
# ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
$t = self::ge_sub($u, $Ai[(int)(-$aslide[$i] / 2)]);
}
}
# ge_p1p1_to_p3(r, &t);
return self::ge_p1p1_to_p3($t);
}
/**
* @param string $a
* @param string $b
* @return string
*/
public static function sc25519_mul($a, $b)
{
// int64_t a0 = 2097151 & load_3(a);
// int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
// int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
// int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
// int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
// int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
// int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
// int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
// int64_t a8 = 2097151 & load_3(a + 21);
// int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
// int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
// int64_t a11 = (load_4(a + 28) >> 7);
$a0 = 2097151 & self::load_3(self::substr($a, 0, 3));
$a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5);
$a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2);
$a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7);
$a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4);
$a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1);
$a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6);
$a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3);
$a8 = 2097151 & self::load_3(self::substr($a, 21, 3));
$a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5);
$a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2);
$a11 = (self::load_4(self::substr($a, 28, 4)) >> 7);
// int64_t b0 = 2097151 & load_3(b);
// int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
// int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
// int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
// int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
// int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
// int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
// int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
// int64_t b8 = 2097151 & load_3(b + 21);
// int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
// int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
// int64_t b11 = (load_4(b + 28) >> 7);
$b0 = 2097151 & self::load_3(self::substr($b, 0, 3));
$b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5);
$b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2);
$b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7);
$b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4);
$b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1);
$b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6);
$b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3);
$b8 = 2097151 & self::load_3(self::substr($b, 21, 3));
$b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5);
$b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2);
$b11 = (self::load_4(self::substr($b, 28, 4)) >> 7);
// s0 = a0 * b0;
// s1 = a0 * b1 + a1 * b0;
// s2 = a0 * b2 + a1 * b1 + a2 * b0;
// s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
// s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
// s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
// s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
// s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
// a6 * b1 + a7 * b0;
// s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
// a6 * b2 + a7 * b1 + a8 * b0;
// s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
// a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
// s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
// a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
// s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
// a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
// s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 +
// a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
// s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 +
// a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
// s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 +
// a9 * b5 + a10 * b4 + a11 * b3;
// s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 +
// a10 * b5 + a11 * b4;
// s16 =
// a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
// s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
// s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
// s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
// s20 = a9 * b11 + a10 * b10 + a11 * b9;
// s21 = a10 * b11 + a11 * b10;
// s22 = a11 * b11;
// s23 = 0;
$s0 = self::mul($a0, $b0, 22);
$s1 = self::mul($a0, $b1, 22) + self::mul($a1, $b0, 22);
$s2 = self::mul($a0, $b2, 22) + self::mul($a1, $b1, 22) + self::mul($a2, $b0, 22);
$s3 = self::mul($a0, $b3, 22) + self::mul($a1, $b2, 22) + self::mul($a2, $b1, 22) + self::mul($a3, $b0, 22);
$s4 = self::mul($a0, $b4, 22) + self::mul($a1, $b3, 22) + self::mul($a2, $b2, 22) + self::mul($a3, $b1, 22) +
self::mul($a4, $b0, 22);
$s5 = self::mul($a0, $b5, 22) + self::mul($a1, $b4, 22) + self::mul($a2, $b3, 22) + self::mul($a3, $b2, 22) +
self::mul($a4, $b1, 22) + self::mul($a5, $b0, 22);
$s6 = self::mul($a0, $b6, 22) + self::mul($a1, $b5, 22) + self::mul($a2, $b4, 22) + self::mul($a3, $b3, 22) +
self::mul($a4, $b2, 22) + self::mul($a5, $b1, 22) + self::mul($a6, $b0, 22);
$s7 = self::mul($a0, $b7, 22) + self::mul($a1, $b6, 22) + self::mul($a2, $b5, 22) + self::mul($a3, $b4, 22) +
self::mul($a4, $b3, 22) + self::mul($a5, $b2, 22) + self::mul($a6, $b1, 22) + self::mul($a7, $b0, 22);
$s8 = self::mul($a0, $b8, 22) + self::mul($a1, $b7, 22) + self::mul($a2, $b6, 22) + self::mul($a3, $b5, 22) +
self::mul($a4, $b4, 22) + self::mul($a5, $b3, 22) + self::mul($a6, $b2, 22) + self::mul($a7, $b1, 22) +
self::mul($a8, $b0, 22);
$s9 = self::mul($a0, $b9, 22) + self::mul($a1, $b8, 22) + self::mul($a2, $b7, 22) + self::mul($a3, $b6, 22) +
self::mul($a4, $b5, 22) + self::mul($a5, $b4, 22) + self::mul($a6, $b3, 22) + self::mul($a7, $b2, 22) +
self::mul($a8, $b1, 22) + self::mul($a9, $b0, 22);
$s10 = self::mul($a0, $b10, 22) + self::mul($a1, $b9, 22) + self::mul($a2, $b8, 22) + self::mul($a3, $b7, 22) +
self::mul($a4, $b6, 22) + self::mul($a5, $b5, 22) + self::mul($a6, $b4, 22) + self::mul($a7, $b3, 22) +
self::mul($a8, $b2, 22) + self::mul($a9, $b1, 22) + self::mul($a10, $b0, 22);
$s11 = self::mul($a0, $b11, 22) + self::mul($a1, $b10, 22) + self::mul($a2, $b9, 22) + self::mul($a3, $b8, 22) +
self::mul($a4, $b7, 22) + self::mul($a5, $b6, 22) + self::mul($a6, $b5, 22) + self::mul($a7, $b4, 22) +
self::mul($a8, $b3, 22) + self::mul($a9, $b2, 22) + self::mul($a10, $b1, 22) + self::mul($a11, $b0, 22);
$s12 = self::mul($a1, $b11, 22) + self::mul($a2, $b10, 22) + self::mul($a3, $b9, 22) + self::mul($a4, $b8, 22) +
self::mul($a5, $b7, 22) + self::mul($a6, $b6, 22) + self::mul($a7, $b5, 22) + self::mul($a8, $b4, 22) +
self::mul($a9, $b3, 22) + self::mul($a10, $b2, 22) + self::mul($a11, $b1, 22);
$s13 = self::mul($a2, $b11, 22) + self::mul($a3, $b10, 22) + self::mul($a4, $b9, 22) + self::mul($a5, $b8, 22) +
self::mul($a6, $b7, 22) + self::mul($a7, $b6, 22) + self::mul($a8, $b5, 22) + self::mul($a9, $b4, 22) +
self::mul($a10, $b3, 22) + self::mul($a11, $b2, 22);
$s14 = self::mul($a3, $b11, 22) + self::mul($a4, $b10, 22) + self::mul($a5, $b9, 22) + self::mul($a6, $b8, 22) +
self::mul($a7, $b7, 22) + self::mul($a8, $b6, 22) + self::mul($a9, $b5, 22) + self::mul($a10, $b4, 22) +
self::mul($a11, $b3, 22);
$s15 = self::mul($a4, $b11, 22) + self::mul($a5, $b10, 22) + self::mul($a6, $b9, 22) + self::mul($a7, $b8, 22) +
self::mul($a8, $b7, 22) + self::mul($a9, $b6, 22) + self::mul($a10, $b5, 22) + self::mul($a11, $b4, 22);
$s16 =
self::mul($a5, $b11, 22) + self::mul($a6, $b10, 22) + self::mul($a7, $b9, 22) + self::mul($a8, $b8, 22) +
self::mul($a9, $b7, 22) + self::mul($a10, $b6, 22) + self::mul($a11, $b5, 22);
$s17 = self::mul($a6, $b11, 22) + self::mul($a7, $b10, 22) + self::mul($a8, $b9, 22) + self::mul($a9, $b8, 22) +
self::mul($a10, $b7, 22) + self::mul($a11, $b6, 22);
$s18 = self::mul($a7, $b11, 22) + self::mul($a8, $b10, 22) + self::mul($a9, $b9, 22) + self::mul($a10, $b8, 22)
+ self::mul($a11, $b7, 22);
$s19 = self::mul($a8, $b11, 22) + self::mul($a9, $b10, 22) + self::mul($a10, $b9, 22) +
self::mul($a11, $b8, 22);
$s20 = self::mul($a9, $b11, 22) + self::mul($a10, $b10, 22) + self::mul($a11, $b9, 22);
$s21 = self::mul($a10, $b11, 22) + self::mul($a11, $b10, 22);
$s22 = self::mul($a11, $b11, 22);
$s23 = 0;
// carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
// s1 += carry0;
// s0 -= carry0 * ((uint64_t) 1L << 21);
$carry0 = ($s0 + (1 << 20)) >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
// carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
// s3 += carry2;
// s2 -= carry2 * ((uint64_t) 1L << 21);
$carry2 = ($s2 + (1 << 20)) >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
// carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
// s5 += carry4;
// s4 -= carry4 * ((uint64_t) 1L << 21);
$carry4 = ($s4 + (1 << 20)) >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
// carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
// s7 += carry6;
// s6 -= carry6 * ((uint64_t) 1L << 21);
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
// carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
// s9 += carry8;
// s8 -= carry8 * ((uint64_t) 1L << 21);
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
// carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
// s11 += carry10;
// s10 -= carry10 * ((uint64_t) 1L << 21);
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
// carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
// s13 += carry12;
// s12 -= carry12 * ((uint64_t) 1L << 21);
$carry12 = ($s12 + (1 << 20)) >> 21;
$s13 += $carry12;
$s12 -= $carry12 << 21;
// carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
// s15 += carry14;
// s14 -= carry14 * ((uint64_t) 1L << 21);
$carry14 = ($s14 + (1 << 20)) >> 21;
$s15 += $carry14;
$s14 -= $carry14 << 21;
// carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
// s17 += carry16;
// s16 -= carry16 * ((uint64_t) 1L << 21);
$carry16 = ($s16 + (1 << 20)) >> 21;
$s17 += $carry16;
$s16 -= $carry16 << 21;
// carry18 = (s18 + (int64_t) (1L << 20)) >> 21;
// s19 += carry18;
// s18 -= carry18 * ((uint64_t) 1L << 21);
$carry18 = ($s18 + (1 << 20)) >> 21;
$s19 += $carry18;
$s18 -= $carry18 << 21;
// carry20 = (s20 + (int64_t) (1L << 20)) >> 21;
// s21 += carry20;
// s20 -= carry20 * ((uint64_t) 1L << 21);
$carry20 = ($s20 + (1 << 20)) >> 21;
$s21 += $carry20;
$s20 -= $carry20 << 21;
// carry22 = (s22 + (int64_t) (1L << 20)) >> 21;
// s23 += carry22;
// s22 -= carry22 * ((uint64_t) 1L << 21);
$carry22 = ($s22 + (1 << 20)) >> 21;
$s23 += $carry22;
$s22 -= $carry22 << 21;
// carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
// s2 += carry1;
// s1 -= carry1 * ((uint64_t) 1L << 21);
$carry1 = ($s1 + (1 << 20)) >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
// carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
// s4 += carry3;
// s3 -= carry3 * ((uint64_t) 1L << 21);
$carry3 = ($s3 + (1 << 20)) >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
// carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
// s6 += carry5;
// s5 -= carry5 * ((uint64_t) 1L << 21);
$carry5 = ($s5 + (1 << 20)) >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
// carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
// s8 += carry7;
// s7 -= carry7 * ((uint64_t) 1L << 21);
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
// carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
// s10 += carry9;
// s9 -= carry9 * ((uint64_t) 1L << 21);
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
// carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
// s12 += carry11;
// s11 -= carry11 * ((uint64_t) 1L << 21);
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
// carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
// s14 += carry13;
// s13 -= carry13 * ((uint64_t) 1L << 21);
$carry13 = ($s13 + (1 << 20)) >> 21;
$s14 += $carry13;
$s13 -= $carry13 << 21;
// carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
// s16 += carry15;
// s15 -= carry15 * ((uint64_t) 1L << 21);
$carry15 = ($s15 + (1 << 20)) >> 21;
$s16 += $carry15;
$s15 -= $carry15 << 21;
// carry17 = (s17 + (int64_t) (1L << 20)) >> 21;
// s18 += carry17;
// s17 -= carry17 * ((uint64_t) 1L << 21);
$carry17 = ($s17 + (1 << 20)) >> 21;
$s18 += $carry17;
$s17 -= $carry17 << 21;
// carry19 = (s19 + (int64_t) (1L << 20)) >> 21;
// s20 += carry19;
// s19 -= carry19 * ((uint64_t) 1L << 21);
$carry19 = ($s19 + (1 << 20)) >> 21;
$s20 += $carry19;
$s19 -= $carry19 << 21;
// carry21 = (s21 + (int64_t) (1L << 20)) >> 21;
// s22 += carry21;
// s21 -= carry21 * ((uint64_t) 1L << 21);
$carry21 = ($s21 + (1 << 20)) >> 21;
$s22 += $carry21;
$s21 -= $carry21 << 21;
// s11 += s23 * 666643;
// s12 += s23 * 470296;
// s13 += s23 * 654183;
// s14 -= s23 * 997805;
// s15 += s23 * 136657;
// s16 -= s23 * 683901;
$s11 += self::mul($s23, 666643, 20);
$s12 += self::mul($s23, 470296, 19);
$s13 += self::mul($s23, 654183, 20);
$s14 -= self::mul($s23, 997805, 20);
$s15 += self::mul($s23, 136657, 18);
$s16 -= self::mul($s23, 683901, 20);
// s10 += s22 * 666643;
// s11 += s22 * 470296;
// s12 += s22 * 654183;
// s13 -= s22 * 997805;
// s14 += s22 * 136657;
// s15 -= s22 * 683901;
$s10 += self::mul($s22, 666643, 20);
$s11 += self::mul($s22, 470296, 19);
$s12 += self::mul($s22, 654183, 20);
$s13 -= self::mul($s22, 997805, 20);
$s14 += self::mul($s22, 136657, 18);
$s15 -= self::mul($s22, 683901, 20);
// s9 += s21 * 666643;
// s10 += s21 * 470296;
// s11 += s21 * 654183;
// s12 -= s21 * 997805;
// s13 += s21 * 136657;
// s14 -= s21 * 683901;
$s9 += self::mul($s21, 666643, 20);
$s10 += self::mul($s21, 470296, 19);
$s11 += self::mul($s21, 654183, 20);
$s12 -= self::mul($s21, 997805, 20);
$s13 += self::mul($s21, 136657, 18);
$s14 -= self::mul($s21, 683901, 20);
// s8 += s20 * 666643;
// s9 += s20 * 470296;
// s10 += s20 * 654183;
// s11 -= s20 * 997805;
// s12 += s20 * 136657;
// s13 -= s20 * 683901;
$s8 += self::mul($s20, 666643, 20);
$s9 += self::mul($s20, 470296, 19);
$s10 += self::mul($s20, 654183, 20);
$s11 -= self::mul($s20, 997805, 20);
$s12 += self::mul($s20, 136657, 18);
$s13 -= self::mul($s20, 683901, 20);
// s7 += s19 * 666643;
// s8 += s19 * 470296;
// s9 += s19 * 654183;
// s10 -= s19 * 997805;
// s11 += s19 * 136657;
// s12 -= s19 * 683901;
$s7 += self::mul($s19, 666643, 20);
$s8 += self::mul($s19, 470296, 19);
$s9 += self::mul($s19, 654183, 20);
$s10 -= self::mul($s19, 997805, 20);
$s11 += self::mul($s19, 136657, 18);
$s12 -= self::mul($s19, 683901, 20);
// s6 += s18 * 666643;
// s7 += s18 * 470296;
// s8 += s18 * 654183;
// s9 -= s18 * 997805;
// s10 += s18 * 136657;
// s11 -= s18 * 683901;
$s6 += self::mul($s18, 666643, 20);
$s7 += self::mul($s18, 470296, 19);
$s8 += self::mul($s18, 654183, 20);
$s9 -= self::mul($s18, 997805, 20);
$s10 += self::mul($s18, 136657, 18);
$s11 -= self::mul($s18, 683901, 20);
// carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
// s7 += carry6;
// s6 -= carry6 * ((uint64_t) 1L << 21);
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
// carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
// s9 += carry8;
// s8 -= carry8 * ((uint64_t) 1L << 21);
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
// carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
// s11 += carry10;
// s10 -= carry10 * ((uint64_t) 1L << 21);
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
// carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
// s13 += carry12;
// s12 -= carry12 * ((uint64_t) 1L << 21);
$carry12 = ($s12 + (1 << 20)) >> 21;
$s13 += $carry12;
$s12 -= $carry12 << 21;
// carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
// s15 += carry14;
// s14 -= carry14 * ((uint64_t) 1L << 21);
$carry14 = ($s14 + (1 << 20)) >> 21;
$s15 += $carry14;
$s14 -= $carry14 << 21;
// carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
// s17 += carry16;
// s16 -= carry16 * ((uint64_t) 1L << 21);
$carry16 = ($s16 + (1 << 20)) >> 21;
$s17 += $carry16;
$s16 -= $carry16 << 21;
// carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
// s8 += carry7;
// s7 -= carry7 * ((uint64_t) 1L << 21);
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
// carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
// s10 += carry9;
// s9 -= carry9 * ((uint64_t) 1L << 21);
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
// carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
// s12 += carry11;
// s11 -= carry11 * ((uint64_t) 1L << 21);
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
// carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
// s14 += carry13;
// s13 -= carry13 * ((uint64_t) 1L << 21);
$carry13 = ($s13 + (1 << 20)) >> 21;
$s14 += $carry13;
$s13 -= $carry13 << 21;
// carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
// s16 += carry15;
// s15 -= carry15 * ((uint64_t) 1L << 21);
$carry15 = ($s15 + (1 << 20)) >> 21;
$s16 += $carry15;
$s15 -= $carry15 << 21;
// s5 += s17 * 666643;
// s6 += s17 * 470296;
// s7 += s17 * 654183;
// s8 -= s17 * 997805;
// s9 += s17 * 136657;
// s10 -= s17 * 683901;
$s5 += self::mul($s17, 666643, 20);
$s6 += self::mul($s17, 470296, 19);
$s7 += self::mul($s17, 654183, 20);
$s8 -= self::mul($s17, 997805, 20);
$s9 += self::mul($s17, 136657, 18);
$s10 -= self::mul($s17, 683901, 20);
// s4 += s16 * 666643;
// s5 += s16 * 470296;
// s6 += s16 * 654183;
// s7 -= s16 * 997805;
// s8 += s16 * 136657;
// s9 -= s16 * 683901;
$s4 += self::mul($s16, 666643, 20);
$s5 += self::mul($s16, 470296, 19);
$s6 += self::mul($s16, 654183, 20);
$s7 -= self::mul($s16, 997805, 20);
$s8 += self::mul($s16, 136657, 18);
$s9 -= self::mul($s16, 683901, 20);
// s3 += s15 * 666643;
// s4 += s15 * 470296;
// s5 += s15 * 654183;
// s6 -= s15 * 997805;
// s7 += s15 * 136657;
// s8 -= s15 * 683901;
$s3 += self::mul($s15, 666643, 20);
$s4 += self::mul($s15, 470296, 19);
$s5 += self::mul($s15, 654183, 20);
$s6 -= self::mul($s15, 997805, 20);
$s7 += self::mul($s15, 136657, 18);
$s8 -= self::mul($s15, 683901, 20);
// s2 += s14 * 666643;
// s3 += s14 * 470296;
// s4 += s14 * 654183;
// s5 -= s14 * 997805;
// s6 += s14 * 136657;
// s7 -= s14 * 683901;
$s2 += self::mul($s14, 666643, 20);
$s3 += self::mul($s14, 470296, 19);
$s4 += self::mul($s14, 654183, 20);
$s5 -= self::mul($s14, 997805, 20);
$s6 += self::mul($s14, 136657, 18);
$s7 -= self::mul($s14, 683901, 20);
// s1 += s13 * 666643;
// s2 += s13 * 470296;
// s3 += s13 * 654183;
// s4 -= s13 * 997805;
// s5 += s13 * 136657;
// s6 -= s13 * 683901;
$s1 += self::mul($s13, 666643, 20);
$s2 += self::mul($s13, 470296, 19);
$s3 += self::mul($s13, 654183, 20);
$s4 -= self::mul($s13, 997805, 20);
$s5 += self::mul($s13, 136657, 18);
$s6 -= self::mul($s13, 683901, 20);
// s0 += s12 * 666643;
// s1 += s12 * 470296;
// s2 += s12 * 654183;
// s3 -= s12 * 997805;
// s4 += s12 * 136657;
// s5 -= s12 * 683901;
// s12 = 0;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
// carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
// s1 += carry0;
// s0 -= carry0 * ((uint64_t) 1L << 21);
$carry0 = ($s0 + (1 << 20)) >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
// carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
// s3 += carry2;
// s2 -= carry2 * ((uint64_t) 1L << 21);
$carry2 = ($s2 + (1 << 20)) >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
// carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
// s5 += carry4;
// s4 -= carry4 * ((uint64_t) 1L << 21);
$carry4 = ($s4 + (1 << 20)) >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
// carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
// s7 += carry6;
// s6 -= carry6 * ((uint64_t) 1L << 21);
$carry6 = ($s6 + (1 << 20)) >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
// carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
// s9 += carry8;
// s8 -= carry8 * ((uint64_t) 1L << 21);
$carry8 = ($s8 + (1 << 20)) >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
// carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
// s11 += carry10;
// s10 -= carry10 * ((uint64_t) 1L << 21);
$carry10 = ($s10 + (1 << 20)) >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
// carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
// s2 += carry1;
// s1 -= carry1 * ((uint64_t) 1L << 21);
$carry1 = ($s1 + (1 << 20)) >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
// carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
// s4 += carry3;
// s3 -= carry3 * ((uint64_t) 1L << 21);
$carry3 = ($s3 + (1 << 20)) >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
// carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
// s6 += carry5;
// s5 -= carry5 * ((uint64_t) 1L << 21);
$carry5 = ($s5 + (1 << 20)) >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
// carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
// s8 += carry7;
// s7 -= carry7 * ((uint64_t) 1L << 21);
$carry7 = ($s7 + (1 << 20)) >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
// carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
// s10 += carry9;
// s9 -= carry9 * ((uint64_t) 1L << 21);
$carry9 = ($s9 + (1 << 20)) >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
// carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
// s12 += carry11;
// s11 -= carry11 * ((uint64_t) 1L << 21);
$carry11 = ($s11 + (1 << 20)) >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
// s0 += s12 * 666643;
// s1 += s12 * 470296;
// s2 += s12 * 654183;
// s3 -= s12 * 997805;
// s4 += s12 * 136657;
// s5 -= s12 * 683901;
// s12 = 0;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
$s12 = 0;
// carry0 = s0 >> 21;
// s1 += carry0;
// s0 -= carry0 * ((uint64_t) 1L << 21);
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
// carry1 = s1 >> 21;
// s2 += carry1;
// s1 -= carry1 * ((uint64_t) 1L << 21);
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
// carry2 = s2 >> 21;
// s3 += carry2;
// s2 -= carry2 * ((uint64_t) 1L << 21);
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
// carry3 = s3 >> 21;
// s4 += carry3;
// s3 -= carry3 * ((uint64_t) 1L << 21);
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
// carry4 = s4 >> 21;
// s5 += carry4;
// s4 -= carry4 * ((uint64_t) 1L << 21);
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
// carry5 = s5 >> 21;
// s6 += carry5;
// s5 -= carry5 * ((uint64_t) 1L << 21);
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
// carry6 = s6 >> 21;
// s7 += carry6;
// s6 -= carry6 * ((uint64_t) 1L << 21);
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
// carry7 = s7 >> 21;
// s8 += carry7;
// s7 -= carry7 * ((uint64_t) 1L << 21);
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
// carry8 = s8 >> 21;
// s9 += carry8;
// s8 -= carry8 * ((uint64_t) 1L << 21);
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
// carry9 = s9 >> 21;
// s10 += carry9;
// s9 -= carry9 * ((uint64_t) 1L << 21);
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
// carry10 = s10 >> 21;
// s11 += carry10;
// s10 -= carry10 * ((uint64_t) 1L << 21);
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
// carry11 = s11 >> 21;
// s12 += carry11;
// s11 -= carry11 * ((uint64_t) 1L << 21);
$carry11 = $s11 >> 21;
$s12 += $carry11;
$s11 -= $carry11 << 21;
// s0 += s12 * 666643;
// s1 += s12 * 470296;
// s2 += s12 * 654183;
// s3 -= s12 * 997805;
// s4 += s12 * 136657;
// s5 -= s12 * 683901;
$s0 += self::mul($s12, 666643, 20);
$s1 += self::mul($s12, 470296, 19);
$s2 += self::mul($s12, 654183, 20);
$s3 -= self::mul($s12, 997805, 20);
$s4 += self::mul($s12, 136657, 18);
$s5 -= self::mul($s12, 683901, 20);
// carry0 = s0 >> 21;
// s1 += carry0;
// s0 -= carry0 * ((uint64_t) 1L << 21);
$carry0 = $s0 >> 21;
$s1 += $carry0;
$s0 -= $carry0 << 21;
// carry1 = s1 >> 21;
// s2 += carry1;
// s1 -= carry1 * ((uint64_t) 1L << 21);
$carry1 = $s1 >> 21;
$s2 += $carry1;
$s1 -= $carry1 << 21;
// carry2 = s2 >> 21;
// s3 += carry2;
// s2 -= carry2 * ((uint64_t) 1L << 21);
$carry2 = $s2 >> 21;
$s3 += $carry2;
$s2 -= $carry2 << 21;
// carry3 = s3 >> 21;
// s4 += carry3;
// s3 -= carry3 * ((uint64_t) 1L << 21);
$carry3 = $s3 >> 21;
$s4 += $carry3;
$s3 -= $carry3 << 21;
// carry4 = s4 >> 21;
// s5 += carry4;
// s4 -= carry4 * ((uint64_t) 1L << 21);
$carry4 = $s4 >> 21;
$s5 += $carry4;
$s4 -= $carry4 << 21;
// carry5 = s5 >> 21;
// s6 += carry5;
// s5 -= carry5 * ((uint64_t) 1L << 21);
$carry5 = $s5 >> 21;
$s6 += $carry5;
$s5 -= $carry5 << 21;
// carry6 = s6 >> 21;
// s7 += carry6;
// s6 -= carry6 * ((uint64_t) 1L << 21);
$carry6 = $s6 >> 21;
$s7 += $carry6;
$s6 -= $carry6 << 21;
// carry7 = s7 >> 21;
// s8 += carry7;
// s7 -= carry7 * ((uint64_t) 1L << 21);
$carry7 = $s7 >> 21;
$s8 += $carry7;
$s7 -= $carry7 << 21;
// carry8 = s8 >> 21;
// s9 += carry8;
// s8 -= carry8 * ((uint64_t) 1L << 21);
$carry8 = $s8 >> 21;
$s9 += $carry8;
$s8 -= $carry8 << 21;
// carry9 = s9 >> 21;
// s10 += carry9;
// s9 -= carry9 * ((uint64_t) 1L << 21);
$carry9 = $s9 >> 21;
$s10 += $carry9;
$s9 -= $carry9 << 21;
// carry10 = s10 >> 21;
// s11 += carry10;
// s10 -= carry10 * ((uint64_t) 1L << 21);
$carry10 = $s10 >> 21;
$s11 += $carry10;
$s10 -= $carry10 << 21;
$s = array_fill(0, 32, 0);
// s[0] = s0 >> 0;
$s[0] = $s0 >> 0;
// s[1] = s0 >> 8;
$s[1] = $s0 >> 8;
// s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
$s[2] = ($s0 >> 16) | ($s1 << 5);
// s[3] = s1 >> 3;
$s[3] = $s1 >> 3;
// s[4] = s1 >> 11;
$s[4] = $s1 >> 11;
// s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
$s[5] = ($s1 >> 19) | ($s2 << 2);
// s[6] = s2 >> 6;
$s[6] = $s2 >> 6;
// s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
$s[7] = ($s2 >> 14) | ($s3 << 7);
// s[8] = s3 >> 1;
$s[8] = $s3 >> 1;
// s[9] = s3 >> 9;
$s[9] = $s3 >> 9;
// s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
$s[10] = ($s3 >> 17) | ($s4 << 4);
// s[11] = s4 >> 4;
$s[11] = $s4 >> 4;
// s[12] = s4 >> 12;
$s[12] = $s4 >> 12;
// s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
$s[13] = ($s4 >> 20) | ($s5 << 1);
// s[14] = s5 >> 7;
$s[14] = $s5 >> 7;
// s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
$s[15] = ($s5 >> 15) | ($s6 << 6);
// s[16] = s6 >> 2;
$s[16] = $s6 >> 2;
// s[17] = s6 >> 10;
$s[17] = $s6 >> 10;
// s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
$s[18] = ($s6 >> 18) | ($s7 << 3);
// s[19] = s7 >> 5;
$s[19] = $s7 >> 5;
// s[20] = s7 >> 13;
$s[20] = $s7 >> 13;
// s[21] = s8 >> 0;
$s[21] = $s8 >> 0;
// s[22] = s8 >> 8;
$s[22] = $s8 >> 8;
// s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
$s[23] = ($s8 >> 16) | ($s9 << 5);
// s[24] = s9 >> 3;
$s[24] = $s9 >> 3;
// s[25] = s9 >> 11;
$s[25] = $s9 >> 11;
// s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
$s[26] = ($s9 >> 19) | ($s10 << 2);
// s[27] = s10 >> 6;
$s[27] = $s10 >> 6;
// s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
$s[28] = ($s10 >> 14) | ($s11 << 7);
// s[29] = s11 >> 1;
$s[29] = $s11 >> 1;
// s[30] = s11 >> 9;
$s[30] = $s11 >> 9;
// s[31] = s11 >> 17;
$s[31] = $s11 >> 17;
return self::intArrayToString($s);
}
/**
* @param string $s
* @return string
*/
public static function sc25519_sq($s)
{
return self::sc25519_mul($s, $s);
}
/**
* @param string $s
* @param int $n
* @param string $a
* @return string
*/
public static function sc25519_sqmul($s, $n, $a)
{
for ($i = 0; $i < $n; ++$i) {
$s = self::sc25519_sq($s);
}
return self::sc25519_mul($s, $a);
}
/**
* @param string $s
* @return string
*/
public static function sc25519_invert($s)
{
$_10 = self::sc25519_sq($s);
$_11 = self::sc25519_mul($s, $_10);
$_100 = self::sc25519_mul($s, $_11);
$_1000 = self::sc25519_sq($_100);
$_1010 = self::sc25519_mul($_10, $_1000);
$_1011 = self::sc25519_mul($s, $_1010);
$_10000 = self::sc25519_sq($_1000);
$_10110 = self::sc25519_sq($_1011);
$_100000 = self::sc25519_mul($_1010, $_10110);
$_100110 = self::sc25519_mul($_10000, $_10110);
$_1000000 = self::sc25519_sq($_100000);
$_1010000 = self::sc25519_mul($_10000, $_1000000);
$_1010011 = self::sc25519_mul($_11, $_1010000);
$_1100011 = self::sc25519_mul($_10000, $_1010011);
$_1100111 = self::sc25519_mul($_100, $_1100011);
$_1101011 = self::sc25519_mul($_100, $_1100111);
$_10010011 = self::sc25519_mul($_1000000, $_1010011);
$_10010111 = self::sc25519_mul($_100, $_10010011);
$_10111101 = self::sc25519_mul($_100110, $_10010111);
$_11010011 = self::sc25519_mul($_10110, $_10111101);
$_11100111 = self::sc25519_mul($_1010000, $_10010111);
$_11101011 = self::sc25519_mul($_100, $_11100111);
$_11110101 = self::sc25519_mul($_1010, $_11101011);
$recip = self::sc25519_mul($_1011, $_11110101);
$recip = self::sc25519_sqmul($recip, 126, $_1010011);
$recip = self::sc25519_sqmul($recip, 9, $_10);
$recip = self::sc25519_mul($recip, $_11110101);
$recip = self::sc25519_sqmul($recip, 7, $_1100111);
$recip = self::sc25519_sqmul($recip, 9, $_11110101);
$recip = self::sc25519_sqmul($recip, 11, $_10111101);
$recip = self::sc25519_sqmul($recip, 8, $_11100111);
$recip = self::sc25519_sqmul($recip, 9, $_1101011);
$recip = self::sc25519_sqmul($recip, 6, $_1011);
$recip = self::sc25519_sqmul($recip, 14, $_10010011);
$recip = self::sc25519_sqmul($recip, 10, $_1100011);
$recip = self::sc25519_sqmul($recip, 9, $_10010111);
$recip = self::sc25519_sqmul($recip, 10, $_11110101);
$recip = self::sc25519_sqmul($recip, 8, $_11010011);
return self::sc25519_sqmul($recip, 8, $_11101011);
}
/**
* @param string $s
* @return string
*/
public static function clamp($s)
{
$s_ = self::stringToIntArray($s);
$s_[0] &= 248;
$s_[31] |= 64;
$s_[31] &= 128;
return self::intArrayToString($s_);
}
/**
* Ensure limbs are less than 28 bits long to prevent float promotion.
*
* This uses a constant-time conditional swap under the hood.
*
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_normalize(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
$x = (PHP_INT_SIZE << 3) - 1; // 31 or 63
$g = self::fe_copy($f);
for ($i = 0; $i < 10; ++$i) {
$mask = -(($g[$i] >> $x) & 1);
/*
* Get two candidate normalized values for $g[$i], depending on the sign of $g[$i]:
*/
$a = $g[$i] & 0x7ffffff;
$b = -((-$g[$i]) & 0x7ffffff);
/*
* Return the appropriate candidate value, based on the sign of the original input:
*
* The following is equivalent to this ternary:
*
* $g[$i] = (($g[$i] >> $x) & 1) ? $a : $b;
*
* Except what's written doesn't contain timing leaks.
*/
$g[$i] = ($a ^ (($a ^ $b) & $mask));
}
return $g;
}
}
الذكاء الاصطناعي في مصر تطور بلا تشريع فمن يتحمل المسؤولية؟ – tahkoom.com
كتبت شروق عارف يشهد العالم تطورا غير مسبوق في التكنولوجيا، حيث أصبح الذكاء الاصطناعي قوة مؤثرة تعيد تشكيل حياتنا وتغيّر قواعد العديد من المجالات. ورغم ما يتيحه هذا التقدم من فرص واسعة، إلا أنه يثير تحديات ومخاوف، خاصة في ظل غياب تشريعات واضحة تنظم استخدامه في مجالات حساسة كالجراحة، والسيارات ذاتية القيادة، والمجال القانوني. هذا الواقع يطرح تساؤلات مهمة، أبرزها: من يتحمل المسؤولية عند حدوث خطأ؟ وتواجه مصر اليوم تحديا في سن قوانين تحمي حقوق الناس وتواكب في الوقت نفسه التقدم التكنولوجي
لا قانون للذكاء الاصطناعي حتى الان
صرح المحامي محمد عاطف بأن الذكاء الاصطناعي لا يخضع حتى الآن لإطار قانوني واضح ومحدد.
وأوضح أنه لا يجوز قانونًا للذكاء الاصطناعي تقديم استشارات قانونية، حيث إن هذه المهام يجب أن تكون من اختصاص محامي مرخص أو جهة قانونية معترف بها، لضمان صحة المعلومات .
وفي ما يتعلق بالمسؤولية الطبية، أشار إلى أن الطبيب هو المسؤول الأول عن الخطأ الطبي، باعتباره صاحب القرار والمتخصص في تقديم الرعاية الصحية، وبالتالي فهو الذي يُسأل قانونًا عند وقوع أي تقصير أو إهمال.
أما في حالات حوادث السير، فقد بين أن السائق هو المسؤول قانونيًا عن أي خطأ يقع أثناء القيادة، لأنه هو المتحكم .
من جانبه، أوضح المحامي الجنائي محمد علي أن الذكاء الاصطناعي لديه القدرة على تقديم استشارات أو خدمات قانونية.
كما أن الذكاء الاصطناعي يمكنه المساعدة في الوصول إلى مواد قانونية أو شرح بعض المفاهيم، لكنه لا يقدم حلولًا قانونية كاملة، ولا يستطيع التعامل مع تفاصيل كل حالة على حدة كما يفعل المحامي البشري.
وأشار إلى أن مصر لا تمتلك حتى الآن قانونًا خاصًا ينظم الذكاء الاصطناعي.
وفي المجال الطبي، أوضح أن القانون المصري لا يميز بوضوح بين الخطأ الناتج عن الإنسان والخطأ الناتج عن الذكاء الاصطناعي.
أما فيما يخص السيارات ذاتية القيادة، فأكد أن مصر لا تملك إطارًا قانونيًا ينظمها حتى الآن.
من جانبه، أكد المحامي المدني رامي أبو رية بأن مصطلح الذكاء الاصطناعي يعد تعبيرا فضفاضا، مما يجعل من السهل القول بأنه لا يوجد قانون محدد ينظم استخدامه.
وأكد على أهمية تحديد نوع المسؤولية القانونية عند مناقشة الأطر التنظيمية للذكاء الاصطناعي، موضحًا أن الحديث هنا ينصب على المسؤولية المدنية، التي تنقسم بدورها إلى نوعين: المسؤولية العقدية والمسؤولية التقصيرية، التي تُعد الأقرب لتطبيقات الذكاء الاصطناعي في الوقت الراهن.
وأوضح أن المسؤولية التقصيرية تقوم على ثلاثة عناصر: الخطأ، والضرر، وعلاقة السببية، وهو ما تنظمه المادة 163 من القانون المدني المصري.
وفيما يتعلق باستخدام الذكاء الاصطناعي في تقديم الاستشارات القانونية، أشار أبو رية إلى أن هذه التقنية يمكنها حاليًا توليد نصوص قانونية تُقدَّم على هيئة استشارات، لكنها لا تستطيع تطبيقها فعليًا.
صرّحت الأستاذة هند توفيق، المحامية المتخصصة بالإستئناف العالي بأن استخدام الذكاء الاصطناعي في مصر يخضع لإطار قانوني واضح، حيث ينظمه قانون حماية البيانات الشخصية الصادر عام 2020، بالإضافة إلى قانون مكافحة جرائم تقنية المعلومات لسنة 2018، ما يضع استخدام هذه التكنولوجيا تحت الرقابة القانونية.
وأوضحت أن الذكاء الاصطناعي يمكن الاستفادة منه في تقديم استشارات وآراء قانونية أو خدمات مساعدة، مؤكدة على استخدامه بشكل فعلي في الأبحاث القانونية وصياغة المذكرات، إلا أن هذه الأدوات لا تحمل طابعًا رسميًا، ويمكن الاعتماد عليها كمصدر تمهيدي أو مساعد، لا أكثر.
وفيما يتعلق بالمسؤولية القانونية في حالة الأخطاء الطبية الناتجة عن استخدام الروبوتات، أكدت أن هناك شقين للمساءلة: جنائي ومدني. ففي الشق الجنائي، يُعد الروبوت بمثابة أداة جراحية، وأي خلل ناتج عنه يؤدي إلى مساءلة الطبيب جنائيًا بتهمة القتل أو الإصابة الخطأ، وفقًا للضرر الواقع. أما في الشق المدني، فالمسؤولية تقع على الطبيب كذلك، باعتبارها مسؤولية تقصيرية، مضيفة أن القانون المدني المصري يتضمن مفهوم “مسؤولية حارس الأشياء”، والتي يمكن تطبيقها على الروبوت باعتباره شيئًا ماديًا، مما يرتب تعويضًا مدنيًا عن الضرر.
وبالنسبة للحوادث الناجمة عن السيارات ذاتية القيادة، أوضحت أن المبدأ نفسه ينطبق؛ حيث يُسأل مالك السيارة مدنيًا، ما لم يثبت أن العطل ناتج عن خلل تقني أو عيب مصنعي، مع تأكيده على اتخاذه الاحتياطات اللازمة. أما من الناحية الجنائية، فلا يوجد حتى الآن نص قانوني واضح يعالج هذه الحالة.
وفي تقييمها للتأثير الاقتصادي للذكاء الاصطناعي، شددت الأستاذة هند على أن هذه التكنولوجيا باتت تمثل خطرًا حقيقيًا على العديد من المهن، خصوصًا تلك التي تعتمد على المهارات الذهنية، مثل مهنة المحاماة والقضاء. لكنها أوضحت أن الوضع في مصر يختلف، إذ لا يمكن الاعتماد كليًا على الذكاء الاصطناعي في تحقيق العدالة، بسبب الطبيعة البشرية لتكوين قناعة القاضي واستنباط القرائن، وهو ما لا تستطيع الخوارزميات محاكاته حتى الآن.
واختتمت حديثها قائلة: “من يعلم؟! ربما نشهد بعد سنوات قليلة طفرة جديدة تجعل الذكاء الاصطناعي قادراً على أداء مهام لم نكن نتخيل أن يفعلها. منذ أربعين عامًا، لو قال لنا أحد أننا سنتحدث اليوم عبر جهاز يسمى الموبايل ونتبادل الرسائل الإلكترونية، لكنا اتهمناه بالجنون”.
لم يعد الذكاء الاصطناعي مجرد فكرة مستقبلية، بل أصبح واقع نعيشه ، ودخل مجالات حساسة تمس حياة الناس بشكل مباشر.
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