constants_32.go

package ed448

const (
	lmask    = 0xffffffff
	zeroMask = 0x80
	allZeros = word(0x00)
	allOnes  = word(0xffffffff)

	decafTrue  = word(0xffffffff)
	decafFalse = word(0x00)

	nLimbs      = 16
	scalarLimbs = 14
	radix       = 28
	radixMask   = word(0xfffffff)

	// The size of the Goldilocks field, in bits.
	fieldBits = 448
	edwardsD  = -39081
	twistedD  = (edwardsD) - 1
	effD      = 39082

	// The size of the Goldilocks field, in bytes.
	fieldBytes     = fieldBits / 8 // 56
	scalarSerBytes = 56
	dsaFieldBytes  = 57
	x448FieldBytes = 56
	x448FieldBits  = 448

	// The size of the Goldilocks scalars, in bits.
	scalarBits = fieldBits - 2 // 446
	// The size of the Goldilocks field, in bytes.
	scalarBytes = (scalarBits + 7) / 8 // 56

	wordBits = 32 // 32-bits

	// The number of words in the Goldilocks field.
	// 14 for 32-bit and 7 for 64-bits
	scalarWords = (scalarBits + wordBits - 1) / wordBits

	bitSize  = scalarBits
	byteSize = fieldBytes

	symKeyBytes  = 32
	pubKeyBytes  = fieldBytes
	privKeyBytes = 2*fieldBytes + symKeyBytes // 144

	signatureBytes = 2 * fieldBytes // 112

	// Comb configuration
	combNumber  = uint(0x08)
	combTeeth   = uint(0x04)
	combSpacing = uint(0x0e)

	// DecafComb configuration
	decafCombNumber  = uint(0x05)
	decafCombTeeth   = uint(0x05)
	decafCombSpacing = uint(0x12)

	decafWindowBits = int(0x05)

	uintZero = uint(0)

	montgomeryFactor = word(0xae918bc5)
)

var (
	// Cofactor is the ratio between the order of the group (p) and the one
	// from the subgroup (q).
	Cofactor = byte(4)
	byteOne  = byte(1)

	bigZero = &bigNumber{0x00}
	bigOne  = &bigNumber{0x01}
	bigTwo  = &bigNumber{0x02}

	scalarZero = &scalar{0x00}

	identity = &twExtendedPoint{
		&bigNumber{0x00},
		&bigNumber{0x01},
		&bigNumber{0x01},
		&bigNumber{0x00},
	}

	sqrtDminus1 = mustDeserialize(serialized{
		0x46, 0x9f, 0x74, 0x36, 0x18, 0xe2, 0xd2, 0x79,
		0x01, 0x4f, 0x2b, 0xb4, 0x8d, 0x88, 0x38, 0xea,
		0xde, 0xab, 0x9a, 0x18, 0x5a, 0x06, 0x4c, 0xf1,
		0xa6, 0x5c, 0xe6, 0x51, 0x70, 0x97, 0x4d, 0x42,
		0x7b, 0x9f, 0xa4, 0x56, 0xf6, 0xc5, 0x28, 0x46,
		0xac, 0xdc, 0x4a, 0x73, 0x48, 0x87, 0x3b, 0x44,
		0x49, 0x7a, 0x5b, 0xb2, 0xc0, 0xc0, 0xfe, 0x12,
	})

	//ScalarQ is the prime order of the curve (q).
	ScalarQ = &scalar{
		0xab5844f3, 0x2378c292, 0x8dc58f55, 0x216cc272,
		0xaed63690, 0xc44edb49, 0x7cca23e9, 0xffffffff,
		0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
		0xffffffff, 0x3fffffff,
	}

	scalarR2 = &scalar{
		0x049b9b60, 0xe3539257, 0xc1b195d9, 0x7af32c4b,
		0x88ea1859, 0x0d66de23, 0x5ee4d838, 0xae17cf72,
		0xa3c47c44, 0x1a9cc14b, 0xe4d070af, 0x2052bcb7,
		0xf823b729, 0x3402a939,
	}

	factor = &bigNumber{
		0x05572736, 0x042ef0f4, 0x00ce5296, 0x07bf6aa2,
		0x0ed26033, 0x0f4fd6ed, 0x0a839a66, 0x0968c14b,
		0x04a2d780, 0x0b8d54b6, 0x01a7b8a5, 0x06aa0a1f,
		0x0d722fa2, 0x0683bf68, 0x0beb24f7, 0x022d962f,
	}

	// TODO: only use this one
	scalarAdjustment = &scalar{
		0x4a7bb0cf, 0xc873d6d5,
		0x23a70aad, 0xe933d8d7,
		0x129c96fd, 0xbb124b65,
		0x335dc163, 0x00000008,
		0x00000000, 0x00000000,
		0x00000000, 0x00000000,
		0x00000000, 0x00000000,
	}

	//BasePoint is the base point of the curve.
	BasePoint = &twExtendedPoint{
		&bigNumber{
			0x0ffffffe, 0x0fffffff, 0x0fffffff, 0x0fffffff,
			0x0fffffff, 0x0fffffff, 0x0fffffff, 0x0fffffff,
			0x00000003, 0x00000000, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		&bigNumber{
			0x0f752992, 0x081e6d37, 0x01c28721, 0x03078ead,
			0x0394666c, 0x0135cfd2, 0x00506061, 0x041149c5,
			0x0f5490b3, 0x031d30e4, 0x090dc141, 0x09020149,
			0x04c1e328, 0x052341b0, 0x03c10a1b, 0x01423785,
		},
		&bigNumber{
			0x0ffffffb, 0x0fffffff, 0x0fffffff, 0x0fffffff,
			0x0fffffff, 0x0fffffff, 0x0fffffff, 0x0fffffff,
			0x0ffffffe, 0x0fffffff, 0x0fffffff, 0x0fffffff,
			0x0fffffff, 0x0fffffff, 0x0fffffff, 0x0fffffff,
		},
		&bigNumber{
			0x00660415, 0x08f205b7, 0x0fd3824f, 0x0881c60c,
			0x0d08500d, 0x0377a638, 0x04672615, 0x08c66d5d,
			0x08e08e13, 0x0e52fa55, 0x01b6983d, 0x087770ae,
			0x0a0aa7ff, 0x04388f55, 0x05cf1a91, 0x0b4d9a78,
		},
	}

	modulus = &bigNumber{
		0xffffff, 0xffffffff, 0xffffff, 0xffffffff,
		0xffffff, 0xffffffff, 0xffffff, 0xffffffff,
		0xfffffe, 0xffffffff, 0xffffff, 0xffffffff,
		0xffffff, 0xffffffff, 0xffffff, 0xffffffff,
	}

	scalarOne       Scalar
	scalarOneFourth Scalar
)

func init() {
	oneBuf := [privKeyBytes]byte{0x01}
	scalarOne = NewScalar(oneBuf[:])
	scalarOneFourth = NewScalar(oneBuf[:])
	scalarOneFourth.Halve(scalarOneFourth)
	scalarOneFourth.Halve(scalarOneFourth)
}