: str_replace(): Passing null to parameter #2 ($replace) of type array|string is deprecated in
$f2f5_2 = $f2_2->mulInt64($f5, 28);
$f2f6_2 = $f2_2->mulInt64($f6, 28);
$f2f7_2 = $f2_2->mulInt64($f7, 28);
$f2f8_38 = $f8_19->mulInt64($f2_2, 29);
$f2f9_38 = $f9_38->mulInt64($f2, 29);
$f3f3_2 = $f3_2->mulInt64($f3, 28);
$f3f4_2 = $f3_2->mulInt64($f4, 28);
$f3f5_4 = $f3_2->mulInt64($f5_2, 28);
$f3f6_2 = $f3_2->mulInt64($f6, 28);
$f3f7_76 = $f7_38->mulInt64($f3_2, 29);
$f3f8_38 = $f8_19->mulInt64($f3_2, 29);
$f3f9_76 = $f9_38->mulInt64($f3_2, 29);
$f4f4 = $f4->mulInt64($f4, 28);
$f4f5_2 = $f4_2->mulInt64($f5, 28);
$f4f6_38 = $f6_19->mulInt64($f4_2, 29);
$f4f7_38 = $f7_38->mulInt64($f4, 29);
$f4f8_38 = $f8_19->mulInt64($f4_2, 29);
$f4f9_38 = $f9_38->mulInt64($f4, 29);
$f5f5_38 = $f5_38->mulInt64($f5, 29);
$f5f6_38 = $f6_19->mulInt64($f5_2, 29);
$f5f7_76 = $f7_38->mulInt64($f5_2, 29);
$f5f8_38 = $f8_19->mulInt64($f5_2, 29);
$f5f9_76 = $f9_38->mulInt64($f5_2, 29);
$f6f6_19 = $f6_19->mulInt64($f6, 29);
$f6f7_38 = $f7_38->mulInt64($f6, 29);
$f6f8_38 = $f8_19->mulInt64($f6_2, 29);
$f6f9_38 = $f9_38->mulInt64($f6, 29);
$f7f7_38 = $f7_38->mulInt64($f7, 29);
$f7f8_38 = $f8_19->mulInt64($f7_2, 29);
$f7f9_76 = $f9_38->mulInt64($f7_2, 29);
$f8f8_19 = $f8_19->mulInt64($f8, 29);
$f8f9_38 = $f9_38->mulInt64($f8, 29);
$f9f9_38 = $f9_38->mulInt64($f9, 29);
$h0 = $f0f0->addInt64($f1f9_76)->addInt64($f2f8_38)->addInt64($f3f7_76)->addInt64($f4f6_38)->addInt64($f5f5_38);
$h1 = $f0f1_2->addInt64($f2f9_38)->addInt64($f3f8_38)->addInt64($f4f7_38)->addInt64($f5f6_38);
$h2 = $f0f2_2->addInt64($f1f1_2)->addInt64($f3f9_76)->addInt64($f4f8_38)->addInt64($f5f7_76)->addInt64($f6f6_19);
$h3 = $f0f3_2->addInt64($f1f2_2)->addInt64($f4f9_38)->addInt64($f5f8_38)->addInt64($f6f7_38);
$h4 = $f0f4_2->addInt64($f1f3_4)->addInt64($f2f2)->addInt64($f5f9_76)->addInt64($f6f8_38)->addInt64($f7f7_38);
$h5 = $f0f5_2->addInt64($f1f4_2)->addInt64($f2f3_2)->addInt64($f6f9_38)->addInt64($f7f8_38);
$h6 = $f0f6_2->addInt64($f1f5_4)->addInt64($f2f4_2)->addInt64($f3f3_2)->addInt64($f7f9_76)->addInt64($f8f8_19);
$h7 = $f0f7_2->addInt64($f1f6_2)->addInt64($f2f5_2)->addInt64($f3f4_2)->addInt64($f8f9_38);
$h8 = $f0f8_2->addInt64($f1f7_4)->addInt64($f2f6_2)->addInt64($f3f5_4)->addInt64($f4f4)->addInt64($f9f9_38);
$h9 = $f0f9_2->addInt64($f1f8_2)->addInt64($f2f7_2)->addInt64($f3f6_2)->addInt64($f4f5_2);
* @var ParagonIE_Sodium_Core32_Int64 $h0
* @var ParagonIE_Sodium_Core32_Int64 $h1
* @var ParagonIE_Sodium_Core32_Int64 $h2
* @var ParagonIE_Sodium_Core32_Int64 $h3
* @var ParagonIE_Sodium_Core32_Int64 $h4
* @var ParagonIE_Sodium_Core32_Int64 $h5
* @var ParagonIE_Sodium_Core32_Int64 $h6
* @var ParagonIE_Sodium_Core32_Int64 $h7
* @var ParagonIE_Sodium_Core32_Int64 $h8
* @var ParagonIE_Sodium_Core32_Int64 $h9
$carry0 = $h0->addInt(1 << 25)->shiftRight(26);
$h1 = $h1->addInt64($carry0);
$h0 = $h0->subInt64($carry0->shiftLeft(26));
$carry4 = $h4->addInt(1 << 25)->shiftRight(26);
$h5 = $h5->addInt64($carry4);
$h4 = $h4->subInt64($carry4->shiftLeft(26));
$carry1 = $h1->addInt(1 << 24)->shiftRight(25);
$h2 = $h2->addInt64($carry1);
$h1 = $h1->subInt64($carry1->shiftLeft(25));
$carry5 = $h5->addInt(1 << 24)->shiftRight(25);
$h6 = $h6->addInt64($carry5);
$h5 = $h5->subInt64($carry5->shiftLeft(25));
$carry2 = $h2->addInt(1 << 25)->shiftRight(26);
$h3 = $h3->addInt64($carry2);
$h2 = $h2->subInt64($carry2->shiftLeft(26));
$carry6 = $h6->addInt(1 << 25)->shiftRight(26);
$h7 = $h7->addInt64($carry6);
$h6 = $h6->subInt64($carry6->shiftLeft(26));
$carry3 = $h3->addInt(1 << 24)->shiftRight(25);
$h4 = $h4->addInt64($carry3);
$h3 = $h3->subInt64($carry3->shiftLeft(25));
$carry7 = $h7->addInt(1 << 24)->shiftRight(25);
$h8 = $h8->addInt64($carry7);
$h7 = $h7->subInt64($carry7->shiftLeft(25));
$carry4 = $h4->addInt(1 << 25)->shiftRight(26);
$h5 = $h5->addInt64($carry4);
$h4 = $h4->subInt64($carry4->shiftLeft(26));
$carry8 = $h8->addInt(1 << 25)->shiftRight(26);
$h9 = $h9->addInt64($carry8);
$h8 = $h8->subInt64($carry8->shiftLeft(26));
$carry9 = $h9->addInt(1 << 24)->shiftRight(25);
$h0 = $h0->addInt64($carry9->mulInt(19, 5));
$h9 = $h9->subInt64($carry9->shiftLeft(25));
$carry0 = $h0->addInt(1 << 25)->shiftRight(26);
$h1 = $h1->addInt64($carry0);
$h0 = $h0->subInt64($carry0->shiftLeft(26));
return ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Fe $Z
* @return ParagonIE_Sodium_Core32_Curve25519_Fe
* @throws SodiumException
public static function fe_invert(ParagonIE_Sodium_Core32_Curve25519_Fe $Z)
$t1 = self::fe_mul($z, $t1);
$t0 = self::fe_mul($t0, $t1);
$t1 = self::fe_mul($t1, $t2);
for ($i = 1; $i < 5; ++$i) {
$t1 = self::fe_mul($t2, $t1);
for ($i = 1; $i < 10; ++$i) {
$t2 = self::fe_mul($t2, $t1);
for ($i = 1; $i < 20; ++$i) {
$t2 = self::fe_mul($t3, $t2);
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_mul($t2, $t1);
for ($i = 1; $i < 50; ++$i) {
$t2 = self::fe_mul($t2, $t1);
for ($i = 1; $i < 100; ++$i) {
$t2 = self::fe_mul($t3, $t2);
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_mul($t2, $t1);
for ($i = 1; $i < 5; ++$i) {
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_Core32_Curve25519_Fe $z
* @return ParagonIE_Sodium_Core32_Curve25519_Fe
* @throws SodiumException
public static function fe_pow22523(ParagonIE_Sodium_Core32_Curve25519_Fe $z)
$t1 = self::fe_mul($z, $t1);
$t0 = self::fe_mul($t0, $t1);
$t0 = self::fe_mul($t1, $t0);
# for (i = 1; i < 5; ++i) {
for ($i = 1; $i < 5; ++$i) {
$t0 = self::fe_mul($t1, $t0);
# for (i = 1; i < 10; ++i) {
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_mul($t1, $t0);
# for (i = 1; i < 20; ++i) {
for ($i = 1; $i < 20; ++$i) {
$t1 = self::fe_mul($t2, $t1);
# for (i = 1; i < 10; ++i) {
for ($i = 1; $i < 10; ++$i) {
$t0 = self::fe_mul($t1, $t0);
# for (i = 1; i < 50; ++i) {
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_mul($t1, $t0);
# for (i = 1; i < 100; ++i) {
for ($i = 1; $i < 100; ++$i) {
$t1 = self::fe_mul($t2, $t1);
# for (i = 1; i < 50; ++i) {
for ($i = 1; $i < 50; ++$i) {
$t0 = self::fe_mul($t1, $t0);
return self::fe_mul($t0, $z);
* Subtract two field elements.
* |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.
* |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_Core32_Curve25519_Fe $f
* @param ParagonIE_Sodium_Core32_Curve25519_Fe $g
* @return ParagonIE_Sodium_Core32_Curve25519_Fe
* @throws SodiumException
* @psalm-suppress MixedMethodCall
* @psalm-suppress MixedTypeCoercion
public static function fe_sub(ParagonIE_Sodium_Core32_Curve25519_Fe $f, ParagonIE_Sodium_Core32_Curve25519_Fe $g)
return ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
* Add two group elements.
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_Cached $q
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1
* @throws SodiumException
public static function ge_add(
ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core32_Curve25519_Ge_Cached $q
$r = new ParagonIE_Sodium_Core32_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, $r->T);
* @internal You should not use this directly from another application
* @ref https://github.com/jedisct1/libsodium/blob/157c4a80c13b117608aeae12178b2d38825f9f8f/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1185-L1215
* @return array<int, mixed>
* @throws SodiumException
* @psalm-suppress MixedArrayOffset
public static function slide($a)
if (self::strlen($a) < 256) {
if (self::strlen($a) < 16) {
$a = str_pad($a, 256, '0', STR_PAD_RIGHT);
/** @var array<int, int> $r */
for ($i = 0; $i < 256; ++$i) {
self::chrToInt($a[$i >> 3])
for ($i = 0;$i < 256;++$i) {
for ($b = 1;$b <= 6 && $i + $b < 256;++$b) {
if ($r[$i] + ($r[$i + $b] << $b) <= 15) {
$r[$i] += $r[$i + $b] << $b;
} elseif ($r[$i] - ($r[$i + $b] << $b) >= -15) {
$r[$i] -= $r[$i + $b] << $b;
for ($k = $i + $b; $k < 256; ++$k) {
* @internal You should not use this directly from another application
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P3
* @throws SodiumException
public static function ge_frombytes_negate_vartime($s)
$d = ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[0]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[1]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[2]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[3]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[4]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[5]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[6]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[7]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[8]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d[9])
/** @var ParagonIE_Sodium_Core32_Curve25519_Fe $d */
$h = new ParagonIE_Sodium_Core32_Curve25519_Ge_P3(
# fe_sub(u,u,h->Z); /* u = y^2-1 */
# fe_add(v,v,h->Z); /* v = dy^2+1 */
/** @var ParagonIE_Sodium_Core32_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_mul(v3,v3,v); /* v3 = v^3 */
# fe_mul(h->X,h->X,u); /* x = uv^7 */
$v3 = self::fe_mul($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,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_sub(check,vxx,u); /* vx^2-u */