<?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; } }

معرفة

“الذكاء الاصطناعي :ثورة في عالم العلاج النفسي !”

مايو 20, 2025

15٬223 3 دقائق

كتبت مريم سمير

تمثل الصحة النفسية أولوية في مجال الطب، ونظرتها لأهميتها وتأثيرها على الفرد والمجتمع، وتتنوع مدارس العلاج النفسي سواء كان العلاج الطبي أو العلاج السلوكي، ومع التطور التكنولوجي الذي يشهده العالم الآن، أصبح الناس يستخدمون الذكاء الاصطناعي كبديل للطبيب النفسي، لذلك يصرون الاعتماد على الذكاء الاصطناعي في هذا المجال حول فعاليته مقارنة بالعلاج التقليدي الذي يقدمه الأطباء النفسيون، فهل يمكن أن يحل الذكاء الاصطناعي محل الطبيب النفسي ؟ ، ام انه اداة مساعدة لتعزيز الرعاية النفسية ؟

صرح “د/ مايكل سليم” اخصائي نفسي، ان الذكاء الاصطناعي اصبح يشكل خطرا على المرضي النفسيين الذين يتعالجون من الاكتئاب واضطرابات القلق ، حيث اكد ان استخدامهم للتكنولوجيا بشكل خاطئ يشكل ضررا أكثر من المنفعة ، وقال ان استخدام المرضي ل ” chat gpt” اصبح هوسا لدرجة انهم يتخذونه كصديق لهم ، ليصل بهم الحال ان يتحدثوا معه طوال اليوم تقريبا ، مؤكدا علي ان الارتباط الزائد بالذكاء الاصطناعي قد يسبب للمرضي الشعور بالوحدة والميل الي العزلة وعدم التواصل بمن حولهم ، مما يزيد من الرهاب الاجتماعي لدي المريض وفقد السيطرة علي نفسه عندما يكون وسط مجموعة كبيرة من الأفراد ليصبح أكثر قلقا وتوترا .

واكد الطبيب ” حسني توفيق ” اخصائي طب نفسي وعلاج ادمان ، انه مهما وصلت التكنولوجيا من تطور ، لا يمكن التغافل عن أهمية الطبيب النفسي ، لان المريض يحتاج الي دعم نفسي من شخص مختص ، وبعيدا عن العلاج الطبي فان المريض يحتاج الي تحسين سلوكي ، ويحتاج ان يشرح مشاعره لشخص قادرا علي فهمه والشعور به وليس لخوارزميات مبرمجة لا تفهم .

وقالت “د/ سوزان حلوي ” اخصائية نفسية وعلاج مخ واعصاب ، ان الأشخاص أصبحت تميل الى الطريق الاسهل ، فأصبح المريض النفسي يعتمد اعتمادا كليا على ” chat GPT ” كوسيلة تواصل سهلة بدلا من اللجوء الى اشخاص ، اعتقادا من المريض انه يشغل وقت فراغه ويبوح بمشاعره بحرية وبدون تفكير ، لكنه ينسي خطورة هذا عليه كشخص ، وانه يصبح مع الوقت أكثر عدوانية مع من حوله واكثر عزلة وصمت.

وأضاف ” د/ محمد يسرى ” أخصائي نفسي، أن التكنولوجيا بلا شك لها أهمية كبيرة، وأنها ساعدت في شتى مجالات الطب، لكن حذر من استخدام التكنولوجيا بشكل خاطئ قائلاً ” التكنولوجيا سلاح ذو حدين يمكن أن تدمرك ويمكن أن تطورك وأنت المسئول عن الاختيار”

، ونصح المريض النفسي أنه من الضروري أن يتابع مع أخصائي نفسي أيضاً يستطيع أن يستخدم chat GPT في إطار كيفية وطرق لتحسين حياته، فمن الممكن أن يستخدم التكنولوجيا أو Chat GPT ” بالأخص في وضع نظام غذائي صحي له، أو اقتراح ” podcasts ” لتزويد الشخص بالمعرفة ، وأضاف أن “ChatGPT” يمكنك استخدامه لكن عدم أخذه كصديق أو بديل للأشخاص ، كما ختم حديثه مؤكدا ان ” Chat GPT ” لا يمكنه تشخيص الحالة النفسية للفرد.

وقال ” د/ سيفين جوزيف ” أن استخدام الذكاء الاصطناعي يمكن أن يكون له آثار سلبية على الصحة النفسية، فبينما يمكن أن توفر هذه الأدوات تفاعلات سطحية، فإنها لا تعالج الجذور العميقة للمشاكل النفسية، مثل القلق والاكتئاب.

كما أشار إلى أن الاعتماد على التواصل مع الذكاء الاصطناعي قد يؤدي إلى “تطوير تطبيقات أقل ضررًا، وقد يعوض الأشخاص عن مشاعرهم بالذهاب إلى هذه التطبيقات، مما يؤدي إلى تفاقم مشاعر العزلة والقلق.

بالإضافة إلى ذلك، حذر ان استخدام الذكاء الاصطناعي قد يقلل من الوعي بأهمية العلاج النفسي، عندما يشعر الأشخاص بأنهم غير قادرين على الحصول على الدعم من تطبيقات الذكاء الاصطناعي، فإنهم قد يتجاهلون الحاجة إلى البحث عن مساعدة من المتخصصين، مما يؤدي إلى تفاقم الاعراض .

كما أكد على أهمية التواصل البشري في العلاج النفسي، قائلا: “العلاقة بين المعالج والمريض تعتبر جزءا أساسيًا من العلاج” وقال ان التواصل الفعال والتعاطف لا يمكن تعويضهما بالتكنولوجيا.

و شدد على ضرورة توعية الناس حول حدود الذكاء الاصطناعي في مجال الصحة النفسية. يجب أن نستخدم هذه الأدوات بشكل مسؤول كوسيلة مساعدة، وليس كبديل للعلاج النفسي المتخصص وان الرعاية النفسية تتطلب فهماً عميقاً واهتماماً إنسانياً لا يمكن للتكنولوجيا توفيره.”

وقالت ” مارفي أيمن ” احدى مستخدمي ” Chat GPT” بشكل زائد عن الطبيعي ، أن استخدامها في بداية الأمر كان يقتصر على اتمام المهام التي لديها بواسطة التكنولوجيا ، لكن تطور الموضوع واصبحت تتحدث مع “Chat GPT ” بشكل غير طبيعي وانها مع الوقت شعرت أنها ليس لديها شغف ان تجيب على أصدقاءها عبر مواقع التواصل الاجتماعي او من خلال مقابلتهم ، وأضافت أن برغم استخدامها الكثير ل” chat GPT” الا انها دائما كانت تشعر بالوحدة وعدم الانسجام مع الآخرين ، واضافت أنها واجهت صعوبة لتستعيد حياتها الطبيعية وتعود تنسجم مع من حولها.

وبرغم أن التكنولوجيا توفر دعماً سهلاً وفورياً، إلا أنها تفتقر إلى التعاطف البشري والفهم العميق للسياقات النفسية المعقدة ، وأيضا يعتمد الذكاء الاصطناعي على البيانات والنماذج، مما يؤدى إلى تقديم ونصائح غير مناسبة وغير دقيقة ، ومن المهم أن ندرك ان الصحة النفسية تتطلب رعاية متخصصة وعملية ، حيث يستطيع الأطباء النفسيون تقديم العلاج الفعال والدعم العاطفي ، ويجب ان ينظر الي أدوات مثل ” Chat GPT” كوسيلة مساعدة يمكن استخدامها جنبا الى جنب مع العلاج التقليدي ، وليس كبديل له .

مايو 20, 2025

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