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/home/tahkoom/public_html/wp-includes/sodium_compat/src/Core/Ristretto255.php
<?php
/**
* Class ParagonIE_Sodium_Core_Ristretto255
*/
class ParagonIE_Sodium_Core_Ristretto255 extends ParagonIE_Sodium_Core_Ed25519
{
const crypto_core_ristretto255_HASHBYTES = 64;
const HASH_SC_L = 48;
const CORE_H2C_SHA256 = 1;
const CORE_H2C_SHA512 = 2;
/**
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @param int $b
* @return ParagonIE_Sodium_Core_Curve25519_Fe
*/
public static function fe_cneg(ParagonIE_Sodium_Core_Curve25519_Fe $f, $b)
{
$negf = self::fe_neg($f);
return self::fe_cmov($f, $negf, $b);
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Fe $f
* @return ParagonIE_Sodium_Core_Curve25519_Fe
* @throws SodiumException
*/
public static function fe_abs(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
return self::fe_cneg($f, self::fe_isnegative($f));
}
/**
* 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 int
* @throws SodiumException
*/
public static function fe_iszero(ParagonIE_Sodium_Core_Curve25519_Fe $f)
{
static $zero;
if ($zero === null) {
$zero = str_repeat("\x00", 32);
}
/** @var string $zero */
$str = self::fe_tobytes($f);
$d = 0;
for ($i = 0; $i < 32; ++$i) {
$d |= self::chrToInt($str[$i]);
}
return (($d - 1) >> 31) & 1;
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Fe $u
* @param ParagonIE_Sodium_Core_Curve25519_Fe $v
* @return array{x: ParagonIE_Sodium_Core_Curve25519_Fe, nonsquare: int}
*
* @throws SodiumException
*/
public static function ristretto255_sqrt_ratio_m1(
ParagonIE_Sodium_Core_Curve25519_Fe $u,
ParagonIE_Sodium_Core_Curve25519_Fe $v
) {
$sqrtm1 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1);
$v3 = self::fe_mul(
self::fe_sq($v),
$v
); /* v3 = v^3 */
$x = self::fe_mul(
self::fe_mul(
self::fe_sq($v3),
$u
),
$v
); /* x = uv^7 */
$x = self::fe_mul(
self::fe_mul(
self::fe_pow22523($x), /* x = (uv^7)^((q-5)/8) */
$v3
),
$u
); /* x = uv^3(uv^7)^((q-5)/8) */
$vxx = self::fe_mul(
self::fe_sq($x),
$v
); /* vx^2 */
$m_root_check = self::fe_sub($vxx, $u); /* vx^2-u */
$p_root_check = self::fe_add($vxx, $u); /* vx^2+u */
$f_root_check = self::fe_mul($u, $sqrtm1); /* u*sqrt(-1) */
$f_root_check = self::fe_add($vxx, $f_root_check); /* vx^2+u*sqrt(-1) */
$has_m_root = self::fe_iszero($m_root_check);
$has_p_root = self::fe_iszero($p_root_check);
$has_f_root = self::fe_iszero($f_root_check);
$x_sqrtm1 = self::fe_mul($x, $sqrtm1); /* x*sqrt(-1) */
$x = self::fe_abs(
self::fe_cmov($x, $x_sqrtm1, $has_p_root | $has_f_root)
);
return array(
'x' => $x,
'nonsquare' => $has_m_root | $has_p_root
);
}
/**
* @param string $s
* @return int
* @throws SodiumException
*/
public static function ristretto255_point_is_canonical($s)
{
$c = (self::chrToInt($s[31]) & 0x7f) ^ 0x7f;
for ($i = 30; $i > 0; --$i) {
$c |= self::chrToInt($s[$i]) ^ 0xff;
}
$c = ($c - 1) >> 8;
$d = (0xed - 1 - self::chrToInt($s[0])) >> 8;
$e = self::chrToInt($s[31]) >> 7;
return 1 - ((($c & $d) | $e | self::chrToInt($s[0])) & 1);
}
/**
* @param string $s
* @param bool $skipCanonicalCheck
* @return array{h: ParagonIE_Sodium_Core_Curve25519_Ge_P3, res: int}
* @throws SodiumException
*/
public static function ristretto255_frombytes($s, $skipCanonicalCheck = false)
{
if (!$skipCanonicalCheck) {
if (!self::ristretto255_point_is_canonical($s)) {
throw new SodiumException('S is not canonical');
}
}
$s_ = self::fe_frombytes($s);
$ss = self::fe_sq($s_); /* ss = s^2 */
$u1 = self::fe_sub(self::fe_1(), $ss); /* u1 = 1-ss */
$u1u1 = self::fe_sq($u1); /* u1u1 = u1^2 */
$u2 = self::fe_add(self::fe_1(), $ss); /* u2 = 1+ss */
$u2u2 = self::fe_sq($u2); /* u2u2 = u2^2 */
$v = self::fe_mul(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d),
$u1u1
); /* v = d*u1^2 */
$v = self::fe_neg($v); /* v = -d*u1^2 */
$v = self::fe_sub($v, $u2u2); /* v = -(d*u1^2)-u2^2 */
$v_u2u2 = self::fe_mul($v, $u2u2); /* v_u2u2 = v*u2^2 */
// fe25519_1(one);
// notsquare = ristretto255_sqrt_ratio_m1(inv_sqrt, one, v_u2u2);
$one = self::fe_1();
$result = self::ristretto255_sqrt_ratio_m1($one, $v_u2u2);
$inv_sqrt = $result['x'];
$notsquare = $result['nonsquare'];
$h = new ParagonIE_Sodium_Core_Curve25519_Ge_P3();
$h->X = self::fe_mul($inv_sqrt, $u2);
$h->Y = self::fe_mul(self::fe_mul($inv_sqrt, $h->X), $v);
$h->X = self::fe_mul($h->X, $s_);
$h->X = self::fe_abs(
self::fe_add($h->X, $h->X)
);
$h->Y = self::fe_mul($u1, $h->Y);
$h->Z = self::fe_1();
$h->T = self::fe_mul($h->X, $h->Y);
$res = - ((1 - $notsquare) | self::fe_isnegative($h->T) | self::fe_iszero($h->Y));
return array('h' => $h, 'res' => $res);
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h
* @return string
* @throws SodiumException
*/
public static function ristretto255_p3_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h)
{
$sqrtm1 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1);
$invsqrtamd = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$invsqrtamd);
$u1 = self::fe_add($h->Z, $h->Y); /* u1 = Z+Y */
$zmy = self::fe_sub($h->Z, $h->Y); /* zmy = Z-Y */
$u1 = self::fe_mul($u1, $zmy); /* u1 = (Z+Y)*(Z-Y) */
$u2 = self::fe_mul($h->X, $h->Y); /* u2 = X*Y */
$u1_u2u2 = self::fe_mul(self::fe_sq($u2), $u1); /* u1_u2u2 = u1*u2^2 */
$one = self::fe_1();
// fe25519_1(one);
// (void) ristretto255_sqrt_ratio_m1(inv_sqrt, one, u1_u2u2);
$result = self::ristretto255_sqrt_ratio_m1($one, $u1_u2u2);
$inv_sqrt = $result['x'];
$den1 = self::fe_mul($inv_sqrt, $u1); /* den1 = inv_sqrt*u1 */
$den2 = self::fe_mul($inv_sqrt, $u2); /* den2 = inv_sqrt*u2 */
$z_inv = self::fe_mul($h->T, self::fe_mul($den1, $den2)); /* z_inv = den1*den2*T */
$ix = self::fe_mul($h->X, $sqrtm1); /* ix = X*sqrt(-1) */
$iy = self::fe_mul($h->Y, $sqrtm1); /* iy = Y*sqrt(-1) */
$eden = self::fe_mul($den1, $invsqrtamd);
$t_z_inv = self::fe_mul($h->T, $z_inv); /* t_z_inv = T*z_inv */
$rotate = self::fe_isnegative($t_z_inv);
$x_ = self::fe_copy($h->X);
$y_ = self::fe_copy($h->Y);
$den_inv = self::fe_copy($den2);
$x_ = self::fe_cmov($x_, $iy, $rotate);
$y_ = self::fe_cmov($y_, $ix, $rotate);
$den_inv = self::fe_cmov($den_inv, $eden, $rotate);
$x_z_inv = self::fe_mul($x_, $z_inv);
$y_ = self::fe_cneg($y_, self::fe_isnegative($x_z_inv));
// fe25519_sub(s_, h->Z, y_);
// fe25519_mul(s_, den_inv, s_);
// fe25519_abs(s_, s_);
// fe25519_tobytes(s, s_);
return self::fe_tobytes(
self::fe_abs(
self::fe_mul(
$den_inv,
self::fe_sub($h->Z, $y_)
)
)
);
}
/**
* @param ParagonIE_Sodium_Core_Curve25519_Fe $t
* @return ParagonIE_Sodium_Core_Curve25519_Ge_P3
*
* @throws SodiumException
*/
public static function ristretto255_elligator(ParagonIE_Sodium_Core_Curve25519_Fe $t)
{
$sqrtm1 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1);
$onemsqd = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$onemsqd);
$d = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d);
$sqdmone = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqdmone);
$sqrtadm1 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtadm1);
$one = self::fe_1();
$r = self::fe_mul($sqrtm1, self::fe_sq($t)); /* r = sqrt(-1)*t^2 */
$u = self::fe_mul(self::fe_add($r, $one), $onemsqd); /* u = (r+1)*(1-d^2) */
$c = self::fe_neg(self::fe_1()); /* c = -1 */
$rpd = self::fe_add($r, $d); /* rpd = r+d */
$v = self::fe_mul(
self::fe_sub(
$c,
self::fe_mul($r, $d)
),
$rpd
); /* v = (c-r*d)*(r+d) */
$result = self::ristretto255_sqrt_ratio_m1($u, $v);
$s = $result['x'];
$wasnt_square = 1 - $result['nonsquare'];
$s_prime = self::fe_neg(
self::fe_abs(
self::fe_mul($s, $t)
)
); /* s_prime = -|s*t| */
$s = self::fe_cmov($s, $s_prime, $wasnt_square);
$c = self::fe_cmov($c, $r, $wasnt_square);
// fe25519_sub(n, r, one); /* n = r-1 */
// fe25519_mul(n, n, c); /* n = c*(r-1) */
// fe25519_mul(n, n, ed25519_sqdmone); /* n = c*(r-1)*(d-1)^2 */
// fe25519_sub(n, n, v); /* n = c*(r-1)*(d-1)^2-v */
$n = self::fe_sub(
self::fe_mul(
self::fe_mul(
self::fe_sub($r, $one),
$c
),
$sqdmone
),
$v
); /* n = c*(r-1)*(d-1)^2-v */
$w0 = self::fe_mul(
self::fe_add($s, $s),
$v
); /* w0 = 2s*v */
$w1 = self::fe_mul($n, $sqrtadm1); /* w1 = n*sqrt(ad-1) */
$ss = self::fe_sq($s); /* ss = s^2 */
$w2 = self::fe_sub($one, $ss); /* w2 = 1-s^2 */
$w3 = self::fe_add($one, $ss); /* w3 = 1+s^2 */
return new ParagonIE_Sodium_Core_Curve25519_Ge_P3(
self::fe_mul($w0, $w3),
self::fe_mul($w2, $w1),
self::fe_mul($w1, $w3),
self::fe_mul($w0, $w2)
);
}
/**
* @param string $h
* @return string
* @throws SodiumException
*/
public static function ristretto255_from_hash($h)
{
if (self::strlen($h) !== 64) {
throw new SodiumException('Hash must be 64 bytes');
}
//fe25519_frombytes(r0, h);
//fe25519_frombytes(r1, h + 32);
$r0 = self::fe_frombytes(self::substr($h, 0, 32));
$r1 = self::fe_frombytes(self::substr($h, 32, 32));
//ristretto255_elligator(&p0, r0);
//ristretto255_elligator(&p1, r1);
$p0 = self::ristretto255_elligator($r0);
$p1 = self::ristretto255_elligator($r1);
//ge25519_p3_to_cached(&p1_cached, &p1);
//ge25519_add_cached(&p_p1p1, &p0, &p1_cached);
$p_p1p1 = self::ge_add(
$p0,
self::ge_p3_to_cached($p1)
);
//ge25519_p1p1_to_p3(&p, &p_p1p1);
//ristretto255_p3_tobytes(s, &p);
return self::ristretto255_p3_tobytes(
self::ge_p1p1_to_p3($p_p1p1)
);
}
/**
* @param string $p
* @return int
* @throws SodiumException
*/
public static function is_valid_point($p)
{
$result = self::ristretto255_frombytes($p);
if ($result['res'] !== 0) {
return 0;
}
return 1;
}
/**
* @param string $p
* @param string $q
* @return string
* @throws SodiumException
*/
public static function ristretto255_add($p, $q)
{
$p_res = self::ristretto255_frombytes($p);
$q_res = self::ristretto255_frombytes($q);
if ($p_res['res'] !== 0 || $q_res['res'] !== 0) {
throw new SodiumException('Could not add points');
}
$p_p3 = $p_res['h'];
$q_p3 = $q_res['h'];
$q_cached = self::ge_p3_to_cached($q_p3);
$r_p1p1 = self::ge_add($p_p3, $q_cached);
$r_p3 = self::ge_p1p1_to_p3($r_p1p1);
return self::ristretto255_p3_tobytes($r_p3);
}
/**
* @param string $p
* @param string $q
* @return string
* @throws SodiumException
*/
public static function ristretto255_sub($p, $q)
{
$p_res = self::ristretto255_frombytes($p);
$q_res = self::ristretto255_frombytes($q);
if ($p_res['res'] !== 0 || $q_res['res'] !== 0) {
throw new SodiumException('Could not add points');
}
$p_p3 = $p_res['h'];
$q_p3 = $q_res['h'];
$q_cached = self::ge_p3_to_cached($q_p3);
$r_p1p1 = self::ge_sub($p_p3, $q_cached);
$r_p3 = self::ge_p1p1_to_p3($r_p1p1);
return self::ristretto255_p3_tobytes($r_p3);
}
/**
* @param int $hLen
* @param ?string $ctx
* @param string $msg
* @return string
* @throws SodiumException
* @psalm-suppress PossiblyInvalidArgument hash API
*/
protected static function h2c_string_to_hash_sha256($hLen, $ctx, $msg)
{
$h = array_fill(0, $hLen, 0);
$ctx_len = !is_null($ctx) ? self::strlen($ctx) : 0;
if ($hLen > 0xff) {
throw new SodiumException('Hash must be less than 256 bytes');
}
if ($ctx_len > 0xff) {
$st = hash_init('sha256');
self::hash_update($st, "H2C-OVERSIZE-DST-");
self::hash_update($st, $ctx);
$ctx = hash_final($st, true);
$ctx_len = 32;
}
$t = array(0, $hLen, 0);
$ux = str_repeat("\0", 64);
$st = hash_init('sha256');
self::hash_update($st, $ux);
self::hash_update($st, $msg);
self::hash_update($st, self::intArrayToString($t));
self::hash_update($st, $ctx);
self::hash_update($st, self::intToChr($ctx_len));
$u0 = hash_final($st, true);
for ($i = 0; $i < $hLen; $i += 64) {
$ux = self::xorStrings($ux, $u0);
++$t[2];
$st = hash_init('sha256');
self::hash_update($st, $ux);
self::hash_update($st, self::intToChr($t[2]));
self::hash_update($st, $ctx);
self::hash_update($st, self::intToChr($ctx_len));
$ux = hash_final($st, true);
$amount = min($hLen - $i, 64);
for ($j = 0; $j < $amount; ++$j) {
$h[$i + $j] = self::chrToInt($ux[$i]);
}
}
return self::intArrayToString(array_slice($h, 0, $hLen));
}
/**
* @param int $hLen
* @param ?string $ctx
* @param string $msg
* @return string
* @throws SodiumException
* @psalm-suppress PossiblyInvalidArgument hash API
*/
protected static function h2c_string_to_hash_sha512($hLen, $ctx, $msg)
{
$h = array_fill(0, $hLen, 0);
$ctx_len = !is_null($ctx) ? self::strlen($ctx) : 0;
if ($hLen > 0xff) {
throw new SodiumException('Hash must be less than 256 bytes');
}
if ($ctx_len > 0xff) {
$st = hash_init('sha256');
self::hash_update($st, "H2C-OVERSIZE-DST-");
self::hash_update($st, $ctx);
$ctx = hash_final($st, true);
$ctx_len = 32;
}
$t = array(0, $hLen, 0);
$ux = str_repeat("\0", 128);
$st = hash_init('sha512');
self::hash_update($st, $ux);
self::hash_update($st, $msg);
self::hash_update($st, self::intArrayToString($t));
self::hash_update($st, $ctx);
self::hash_update($st, self::intToChr($ctx_len));
$u0 = hash_final($st, true);
for ($i = 0; $i < $hLen; $i += 128) {
$ux = self::xorStrings($ux, $u0);
++$t[2];
$st = hash_init('sha512');
self::hash_update($st, $ux);
self::hash_update($st, self::intToChr($t[2]));
self::hash_update($st, $ctx);
self::hash_update($st, self::intToChr($ctx_len));
$ux = hash_final($st, true);
$amount = min($hLen - $i, 128);
for ($j = 0; $j < $amount; ++$j) {
$h[$i + $j] = self::chrToInt($ux[$i]);
}
}
return self::intArrayToString(array_slice($h, 0, $hLen));
}
/**
* @param int $hLen
* @param ?string $ctx
* @param string $msg
* @param int $hash_alg
* @return string
* @throws SodiumException
*/
public static function h2c_string_to_hash($hLen, $ctx, $msg, $hash_alg)
{
switch ($hash_alg) {
case self::CORE_H2C_SHA256:
return self::h2c_string_to_hash_sha256($hLen, $ctx, $msg);
case self::CORE_H2C_SHA512:
return self::h2c_string_to_hash_sha512($hLen, $ctx, $msg);
default:
throw new SodiumException('Invalid H2C hash algorithm');
}
}
/**
* @param ?string $ctx
* @param string $msg
* @param int $hash_alg
* @return string
* @throws SodiumException
*/
protected static function _string_to_element($ctx, $msg, $hash_alg)
{
return self::ristretto255_from_hash(
self::h2c_string_to_hash(self::crypto_core_ristretto255_HASHBYTES, $ctx, $msg, $hash_alg)
);
}
/**
* @return string
* @throws SodiumException
* @throws Exception
*/
public static function ristretto255_random()
{
return self::ristretto255_from_hash(
ParagonIE_Sodium_Compat::randombytes_buf(self::crypto_core_ristretto255_HASHBYTES)
);
}
/**
* @return string
* @throws SodiumException
*/
public static function ristretto255_scalar_random()
{
return self::scalar_random();
}
/**
* @param string $s
* @return string
* @throws SodiumException
*/
public static function ristretto255_scalar_complement($s)
{
return self::scalar_complement($s);
}
/**
* @param string $s
* @return string
*/
public static function ristretto255_scalar_invert($s)
{
return self::sc25519_invert($s);
}
/**
* @param string $s
* @return string
* @throws SodiumException
*/
public static function ristretto255_scalar_negate($s)
{
return self::scalar_negate($s);
}
/**
* @param string $x
* @param string $y
* @return string
*/
public static function ristretto255_scalar_add($x, $y)
{
return self::scalar_add($x, $y);
}
/**
* @param string $x
* @param string $y
* @return string
*/
public static function ristretto255_scalar_sub($x, $y)
{
return self::scalar_sub($x, $y);
}
/**
* @param string $x
* @param string $y
* @return string
*/
public static function ristretto255_scalar_mul($x, $y)
{
return self::sc25519_mul($x, $y);
}
/**
* @param string $ctx
* @param string $msg
* @param int $hash_alg
* @return string
* @throws SodiumException
*/
public static function ristretto255_scalar_from_string($ctx, $msg, $hash_alg)
{
$h = array_fill(0, 64, 0);
$h_be = self::stringToIntArray(
self::h2c_string_to_hash(
self::HASH_SC_L, $ctx, $msg, $hash_alg
)
);
for ($i = 0; $i < self::HASH_SC_L; ++$i) {
$h[$i] = $h_be[self::HASH_SC_L - 1 - $i];
}
return self::ristretto255_scalar_reduce(self::intArrayToString($h));
}
/**
* @param string $s
* @return string
*/
public static function ristretto255_scalar_reduce($s)
{
return self::sc_reduce($s);
}
/**
* @param string $n
* @param string $p
* @return string
* @throws SodiumException
*/
public static function scalarmult_ristretto255($n, $p)
{
if (self::strlen($n) !== 32) {
throw new SodiumException('Scalar must be 32 bytes, ' . self::strlen($p) . ' given.');
}
if (self::strlen($p) !== 32) {
throw new SodiumException('Point must be 32 bytes, ' . self::strlen($p) . ' given.');
}
$result = self::ristretto255_frombytes($p);
if ($result['res'] !== 0) {
throw new SodiumException('Could not multiply points');
}
$P = $result['h'];
$t = self::stringToIntArray($n);
$t[31] &= 0x7f;
$Q = self::ge_scalarmult(self::intArrayToString($t), $P);
$q = self::ristretto255_p3_tobytes($Q);
if (ParagonIE_Sodium_Compat::is_zero($q)) {
throw new SodiumException('An unknown error has occurred');
}
return $q;
}
/**
* @param string $n
* @return string
* @throws SodiumException
*/
public static function scalarmult_ristretto255_base($n)
{
$t = self::stringToIntArray($n);
$t[31] &= 0x7f;
$Q = self::ge_scalarmult_base(self::intArrayToString($t));
$q = self::ristretto255_p3_tobytes($Q);
if (ParagonIE_Sodium_Compat::is_zero($q)) {
throw new SodiumException('An unknown error has occurred');
}
return $q;
}
}
بين التربية والتقنية هل ينتج العالم الافتراضي جيلاً مثقفًا أم معزولًا؟ – tahkoom.com
كتبت شروق عارف
في ظل التطور التكنولوجي الحادث والابتكارات الجديدة ظهر العالم الافتراضي الذي أحدث ثورة في كافة المجالات مما جعلنا نطرح سؤال مهم ماذا لو أصبح التعليم مرتبط بالعالم الافتراضي؟ وكيف سيؤثر هذا الربط على الطلاب وتحصيلهم الأكاديمي ؟ ما هو العالم الافتراضي والميتافيرس؟ مزايا وتحديات ربط التعليم بالعالم الافتراضي
آراء متباينة حول فاعلية العالم الافتراضي
يمكن القول إن ربط التعليم بالعالم الافتراضي قد يسهم بشكل كبير في توسيع أفاقنا الفكرية وسوف يجعل التجربة التعليمية أكثر متعة ولكن مع ذلك يجب التعامل مع هذه التقنية بحذر حتى نتجنب الأثار السلبية وعلينا التأكد أن العالم الافتراضي لا يمكن أن يحلل محل المعلم
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