// MakePublicKey makes a publicKey from the first half of privateKey.
func MakePublicKey(privateKey *[PrivateKeySize]byte) (publicKey *[PublicKeySize]byte) {
	publicKey = new([32]byte)

	h := sha512.New()
	h.Write(privateKey[:32])
	digest := h.Sum(nil)

	digest[0] &= 248
	digest[31] &= 127
	digest[31] |= 64

	var A edwards25519.ExtendedGroupElement
	var hBytes [32]byte
	copy(hBytes[:], digest)
	edwards25519.GeScalarMultBase(&A, &hBytes)
	A.ToBytes(publicKey)

	copy(privateKey[32:], publicKey[:])
	return
}
// Sign signs the message with privateKey and returns a signature.
func Sign(privateKey *[PrivateKeySize]byte, message []byte) *[SignatureSize]byte {
	h := sha512.New()
	h.Write(privateKey[:32])

	var digest1, messageDigest, hramDigest [64]byte
	var expandedSecretKey [32]byte
	h.Sum(digest1[:0])
	copy(expandedSecretKey[:], digest1[:])
	expandedSecretKey[0] &= 248
	expandedSecretKey[31] &= 63
	expandedSecretKey[31] |= 64

	h.Reset()
	h.Write(digest1[32:])
	h.Write(message)
	h.Sum(messageDigest[:0])

	var messageDigestReduced [32]byte
	edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
	var R edwards25519.ExtendedGroupElement
	edwards25519.GeScalarMultBase(&R, &messageDigestReduced)

	var encodedR [32]byte
	R.ToBytes(&encodedR)

	h.Reset()
	h.Write(encodedR[:])
	h.Write(privateKey[32:])
	h.Write(message)
	h.Sum(hramDigest[:0])
	var hramDigestReduced [32]byte
	edwards25519.ScReduce(&hramDigestReduced, &hramDigest)

	var s [32]byte
	edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced)

	signature := new([64]byte)
	copy(signature[:], encodedR[:])
	copy(signature[32:], s[:])
	return signature
}
// ScalarBaseMult computes a curve25519 public key from a private key and also
// a uniform representative for that public key. Note that this function will
// fail and return false for about half of private keys.
// See http://elligator.cr.yp.to/elligator-20130828.pdf.
func ScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool {
	var maskedPrivateKey [32]byte
	copy(maskedPrivateKey[:], privateKey[:])

	maskedPrivateKey[0] &= 248
	maskedPrivateKey[31] &= 127
	maskedPrivateKey[31] |= 64

	var A edwards25519.ExtendedGroupElement
	edwards25519.GeScalarMultBase(&A, &maskedPrivateKey)

	var inv1 edwards25519.FieldElement
	edwards25519.FeSub(&inv1, &A.Z, &A.Y)
	edwards25519.FeMul(&inv1, &inv1, &A.X)
	edwards25519.FeInvert(&inv1, &inv1)

	var t0, u edwards25519.FieldElement
	edwards25519.FeMul(&u, &inv1, &A.X)
	edwards25519.FeAdd(&t0, &A.Y, &A.Z)
	edwards25519.FeMul(&u, &u, &t0)

	var v edwards25519.FieldElement
	edwards25519.FeMul(&v, &t0, &inv1)
	edwards25519.FeMul(&v, &v, &A.Z)
	edwards25519.FeMul(&v, &v, &sqrtMinusA)

	var b edwards25519.FieldElement
	edwards25519.FeAdd(&b, &u, &edwards25519.A)

	var c, b3, b8 edwards25519.FieldElement
	edwards25519.FeSquare(&b3, &b)   // 2
	edwards25519.FeMul(&b3, &b3, &b) // 3
	edwards25519.FeSquare(&c, &b3)   // 6
	edwards25519.FeMul(&c, &c, &b)   // 7
	edwards25519.FeMul(&b8, &c, &b)  // 8
	edwards25519.FeMul(&c, &c, &u)
	q58(&c, &c)

	var chi edwards25519.FieldElement
	edwards25519.FeSquare(&chi, &c)
	edwards25519.FeSquare(&chi, &chi)

	edwards25519.FeSquare(&t0, &u)
	edwards25519.FeMul(&chi, &chi, &t0)

	edwards25519.FeSquare(&t0, &b)   // 2
	edwards25519.FeMul(&t0, &t0, &b) // 3
	edwards25519.FeSquare(&t0, &t0)  // 6
	edwards25519.FeMul(&t0, &t0, &b) // 7
	edwards25519.FeSquare(&t0, &t0)  // 14
	edwards25519.FeMul(&chi, &chi, &t0)
	edwards25519.FeNeg(&chi, &chi)

	var chiBytes [32]byte
	edwards25519.FeToBytes(&chiBytes, &chi)
	// chi[1] is either 0 or 0xff
	if chiBytes[1] == 0xff {
		return false
	}

	// Calculate r1 = sqrt(-u/(2*(u+A)))
	var r1 edwards25519.FieldElement
	edwards25519.FeMul(&r1, &c, &u)
	edwards25519.FeMul(&r1, &r1, &b3)
	edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf)

	var maybeSqrtM1 edwards25519.FieldElement
	edwards25519.FeSquare(&t0, &r1)
	edwards25519.FeMul(&t0, &t0, &b)
	edwards25519.FeAdd(&t0, &t0, &t0)
	edwards25519.FeAdd(&t0, &t0, &u)

	edwards25519.FeOne(&maybeSqrtM1)
	edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
	edwards25519.FeMul(&r1, &r1, &maybeSqrtM1)

	// Calculate r = sqrt(-(u+A)/(2u))
	var r edwards25519.FieldElement
	edwards25519.FeSquare(&t0, &c)   // 2
	edwards25519.FeMul(&t0, &t0, &c) // 3
	edwards25519.FeSquare(&t0, &t0)  // 6
	edwards25519.FeMul(&r, &t0, &c)  // 7

	edwards25519.FeSquare(&t0, &u)   // 2
	edwards25519.FeMul(&t0, &t0, &u) // 3
	edwards25519.FeMul(&r, &r, &t0)

	edwards25519.FeSquare(&t0, &b8)   // 16
	edwards25519.FeMul(&t0, &t0, &b8) // 24
	edwards25519.FeMul(&t0, &t0, &b)  // 25
	edwards25519.FeMul(&r, &r, &t0)
	edwards25519.FeMul(&r, &r, &sqrtMinusHalf)

	edwards25519.FeSquare(&t0, &r)
	edwards25519.FeMul(&t0, &t0, &u)
	edwards25519.FeAdd(&t0, &t0, &t0)
	edwards25519.FeAdd(&t0, &t0, &b)
	edwards25519.FeOne(&maybeSqrtM1)
	edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
	edwards25519.FeMul(&r, &r, &maybeSqrtM1)

	var vBytes [32]byte
	edwards25519.FeToBytes(&vBytes, &v)
	vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes)
	edwards25519.FeCMove(&r, &r1, vInSquareRootImage)

	edwards25519.FeToBytes(publicKey, &u)
	edwards25519.FeToBytes(representative, &r)
	return true
}