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<?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;
}
}
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