ParagonIE_Sodium_Core_Ed25519::verify_detached

    public static function verify_detached($sig, $message, $pk)
    {
        if (self::strlen($sig) < 64) {
            throw new SodiumException('Signature is too short');
        }
        if ((self::chrToInt($sig[63]) & 240) && self::check_S_lt_L(self::substr($sig, 32, 32))) {
            throw new SodiumException('S < L - Invalid signature');
        }
        if (self::small_order($sig)) {
            throw new SodiumException('Signature is on too small of an order');
        }
        if ((self::chrToInt($sig[63]) & 224) !== 0) {
            throw new SodiumException('Invalid signature');
        }
        $d = 0;
        for ($i = 0; $i < 32; ++$i) {
            $d |= self::chrToInt($pk[$i]);
        }
        if ($d === 0) {
            throw new SodiumException('All zero public key');
        }

        /** @var bool The original value of ParagonIE_Sodium_Compat::$fastMult */
        $orig = ParagonIE_Sodium_Compat::$fastMult;

        // Set ParagonIE_Sodium_Compat::$fastMult to true to speed up verification.
        ParagonIE_Sodium_Compat::$fastMult = true;

        /** @var ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A */
        $A = self::ge_frombytes_negate_vartime($pk);

        /** @var string $hDigest */
        $hDigest = hash(
            'sha512',
            self::substr($sig, 0, 32) .
                self::substr($pk, 0, 32) .
                $message,
            true
        );

        /** @var string $h */
        $h = self::sc_reduce($hDigest) . self::substr($hDigest, 32);

        /** @var ParagonIE_Sodium_Core_Curve25519_Ge_P2 $R */
        $R = self::ge_double_scalarmult_vartime(
            $h,
            $A,
            self::substr($sig, 32)
        );

        /** @var string $rcheck */
        $rcheck = self::ge_tobytes($R);

        // Reset ParagonIE_Sodium_Compat::$fastMult to what it was before.
        ParagonIE_Sodium_Compat::$fastMult = $orig;

        return self::verify_32($rcheck, self::substr($sig, 0, 32));
    }