: str_replace(): Passing null to parameter #2 ($replace) of type array|string is deprecated in
$vxx = self::fe_sq($h->X);
$vxx = self::fe_mul($vxx, $v);
$check = self::fe_sub($vxx, $u); /* vx^2 - u */
# if (fe_isnonzero(check)) {
# fe_add(check,vxx,u); /* vx^2+u */
# if (fe_isnonzero(check)) {
# fe_mul(h->X,h->X,sqrtm1);
if (self::fe_isnonzero($check)) {
$check = self::fe_add($vxx, $u); /* vx^2 + u */
if (self::fe_isnonzero($check)) {
throw new RangeException('Internal check failed.');
ParagonIE_Sodium_Core32_Curve25519_Fe::fromIntArray(self::$sqrtm1)
# if (fe_isnegative(h->X) == (s[31] >> 7)) {
$i = self::chrToInt($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);
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $R
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $q
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1
* @throws SodiumException
public static function ge_madd(
ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $R,
ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $q
$r->X = self::fe_add($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);
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $R
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $q
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1
* @throws SodiumException
public static function ge_msub(
ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $R,
ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p,
ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $q
$r->X = self::fe_add($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);
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P2
* @throws SodiumException
public static function ge_p1p1_to_p2(ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $p)
$r = new ParagonIE_Sodium_Core32_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);
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P3
* @throws SodiumException
public static function ge_p1p1_to_p3(ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1 $p)
$r = new ParagonIE_Sodium_Core32_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);
* @internal You should not use this directly from another application
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P2
* @throws SodiumException
public static function ge_p2_0()
return new ParagonIE_Sodium_Core32_Curve25519_Ge_P2(
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P2 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1
* @throws SodiumException
public static function ge_p2_dbl(ParagonIE_Sodium_Core32_Curve25519_Ge_P2 $p)
$r = new ParagonIE_Sodium_Core32_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);
* @internal You should not use this directly from another application
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P3
* @throws SodiumException
public static function ge_p3_0()
return new ParagonIE_Sodium_Core32_Curve25519_Ge_P3(
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_Cached
* @throws SodiumException
public static function ge_p3_to_cached(ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p)
$d2 = ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[0]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[1]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[2]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[3]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[4]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[5]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[6]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[7]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[8]),
ParagonIE_Sodium_Core32_Int32::fromInt(self::$d2[9])
/** @var ParagonIE_Sodium_Core32_Curve25519_Fe $d2 */
$r = new ParagonIE_Sodium_Core32_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);
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P2
public static function ge_p3_to_p2(ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p)
return new ParagonIE_Sodium_Core32_Curve25519_Ge_P2(
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $h
* @throws SodiumException
public static function ge_p3_tobytes(ParagonIE_Sodium_Core32_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);
self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7)
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_P1p1
* @throws SodiumException
public static function ge_p3_dbl(ParagonIE_Sodium_Core32_Curve25519_Ge_P3 $p)
$q = self::ge_p3_to_p2($p);
return self::ge_p2_dbl($q);
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp
* @throws SodiumException
public static function ge_precomp_0()
return new ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp(
* @internal You should not use this directly from another application
* @psalm-suppress MixedReturnStatement
public static function equal($b, $c)
$b1 = ($b >> 16) & 0xffff;
$c1 = ($c >> 16) & 0xffff;
$d0 = (($b0 ^ $c0) - 1) >> 31;
$d1 = (($b1 ^ $c1) - 1) >> 31;
* @internal You should not use this directly from another application
* @param string|int $char
* @return int (1 = yes, 0 = no)
* @throws SodiumException
public static function negative($char)
return $char < 0 ? 1 : 0;
$x = self::chrToInt(self::substr($char, 0, 1));
* @internal You should not use this directly from another application
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $t
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $u
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp
* @throws SodiumException
public static function cmov(
ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $t,
ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp $u,
throw new InvalidArgumentException('Expected an integer.');
return new ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp(
self::fe_cmov($t->yplusx, $u->yplusx, $b),
self::fe_cmov($t->yminusx, $u->yminusx, $b),
self::fe_cmov($t->xy2d, $u->xy2d, $b)
* @internal You should not use this directly from another application
* @return ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp
* @throws SodiumException
* @psalm-suppress MixedArrayAccess
* @psalm-suppress MixedArrayOffset
* @psalm-suppress MixedArgument
public static function ge_select($pos = 0, $b = 0)
foreach (self::$base as $i => $bas) {
for ($j = 0; $j < 8; ++$j) {
$base[$i][$j] = new ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp(
ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][0]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][1]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][2]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][3]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][4]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][5]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][6]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][7]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][8]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][0][9])
ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][0]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][1]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][2]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][3]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][4]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][5]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][6]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][7]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][8]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][1][9])
ParagonIE_Sodium_Core32_Curve25519_Fe::fromArray(
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][0]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][1]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][2]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][3]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][4]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][5]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][6]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][7]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][8]),
ParagonIE_Sodium_Core32_Int32::fromInt($bas[$j][2][9])
throw new InvalidArgumentException('Position must be an integer');
if ($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) {
-self::equal($babs, $i + 1)
$minusT = new ParagonIE_Sodium_Core32_Curve25519_Ge_Precomp(
self::fe_copy($t->yminusx),
self::fe_copy($t->yplusx),
return self::cmov($t, $minusT, -$bnegative);
* Subtract 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_sub(
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->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);
* Convert a group element to a byte string.
* @param ParagonIE_Sodium_Core32_Curve25519_Ge_P2 $h
* @throws SodiumException
public static function ge_tobytes(ParagonIE_Sodium_Core32_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);
self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7)