551 lines
12 KiB
V
551 lines
12 KiB
V
module edwards25519
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const (
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// d is a constant in the curve equation.
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d_bytes = [u8(0xa3), 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, 0xab, 0xd8, 0x41, 0x41, 0x4d,
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0x0a, 0x70, 0x00, 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c, 0x73, 0xfe, 0x6f, 0x2b,
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0xee, 0x6c, 0x03, 0x52]
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id_bytes = [u8(1), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0]
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gen_bytes = [u8(0x58), 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
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0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
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0x66, 0x66, 0x66, 0x66]
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d_const = d_const_generate() or { panic(err) }
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d2_const = d2_const_generate() or { panic(err) }
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// id_point is the point at infinity.
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id_point = id_point_generate() or { panic(err) }
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// generator point
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gen_point = generator() or { panic(err) }
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)
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fn d_const_generate() ?Element {
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mut v := Element{}
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v.set_bytes(edwards25519.d_bytes)?
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return v
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}
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fn d2_const_generate() ?Element {
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mut v := Element{}
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v.add(edwards25519.d_const, edwards25519.d_const)
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return v
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}
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// id_point_generate is the point at infinity.
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fn id_point_generate() ?Point {
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mut p := Point{}
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p.set_bytes(edwards25519.id_bytes)?
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return p
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}
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// generator is the canonical curve basepoint. See TestGenerator for the
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// correspondence of this encoding with the values in RFC 8032.
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fn generator() ?Point {
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mut p := Point{}
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p.set_bytes(edwards25519.gen_bytes)?
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return p
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}
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// Point types.
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struct ProjectiveP1 {
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mut:
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x Element
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y Element
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z Element
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t Element
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}
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struct ProjectiveP2 {
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mut:
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x Element
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y Element
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z Element
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}
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// Point represents a point on the edwards25519 curve.
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//
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// This type works similarly to math/big.Int, and all arguments and receivers
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// are allowed to alias.
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//
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// The zero value is NOT valid, and it may be used only as a receiver.
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pub struct Point {
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mut:
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// The point is internally represented in extended coordinates (x, y, z, T)
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// where x = x/z, y = y/z, and xy = T/z per https://eprint.iacr.org/2008/522.
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x Element
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y Element
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z Element
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t Element
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// Make the type not comparable (i.e. used with == or as a map key), as
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// equivalent points can be represented by different values.
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// _ incomparable
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}
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fn check_initialized(points ...Point) {
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for _, p in points {
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if p.x == fe_zero && p.y == fe_zero {
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panic('edwards25519: use of uninitialized Point')
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}
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}
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}
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struct ProjectiveCached {
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mut:
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ypx Element // y + x
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ymx Element // y - x
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z Element
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t2d Element
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}
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struct AffineCached {
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mut:
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ypx Element // y + x
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ymx Element // y - x
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t2d Element
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}
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fn (mut v ProjectiveP2) zero() ProjectiveP2 {
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v.x.zero()
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v.y.one()
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v.z.one()
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return v
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}
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// set_bytes sets v = x, where x is a 32-byte encoding of v. If x does not
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// represent a valid point on the curve, set_bytes returns an error and
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// the receiver is unchanged. Otherwise, set_bytes returns v.
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//
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// Note that set_bytes accepts all non-canonical encodings of valid points.
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// That is, it follows decoding rules that match most implementations in
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// the ecosystem rather than RFC 8032.
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pub fn (mut v Point) set_bytes(x []u8) ?Point {
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// Specifically, the non-canonical encodings that are accepted are
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// 1) the ones where the edwards25519 element is not reduced (see the
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// (*edwards25519.Element).set_bytes docs) and
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// 2) the ones where the x-coordinate is zero and the sign bit is set.
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//
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// This is consistent with crypto/ed25519/internal/edwards25519. Read more
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// at https://hdevalence.ca/blog/2020-10-04-its-25519am, specifically the
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// "Canonical A, R" section.
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mut el0 := Element{}
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y := el0.set_bytes(x) or { return error('edwards25519: invalid point encoding length') }
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// -x² + y² = 1 + dx²y²
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// x² + dx²y² = x²(dy² + 1) = y² - 1
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// x² = (y² - 1) / (dy² + 1)
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// u = y² - 1
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mut el1 := Element{}
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y2 := el1.square(y)
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mut el2 := Element{}
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u := el2.subtract(y2, fe_one)
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// v = dy² + 1
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mut el3 := Element{}
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mut vv := el3.multiply(y2, edwards25519.d_const)
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vv = vv.add(vv, fe_one)
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// x = +√(u/v)
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mut el4 := Element{}
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mut xx, was_square := el4.sqrt_ratio(u, vv)
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if was_square == 0 {
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return error('edwards25519: invalid point encoding')
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}
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// selected the negative square root if the sign bit is set.
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mut el5 := Element{}
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xx_neg := el5.negate(xx)
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xx.selected(xx_neg, xx, int(x[31] >> 7))
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v.x.set(xx)
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v.y.set(y)
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v.z.one()
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v.t.multiply(xx, y) // xy = T / z
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return v
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}
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// set sets v = u, and returns v.
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pub fn (mut v Point) set(u Point) Point {
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v = u
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return v
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}
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// new_identity_point returns a new Point set to the identity.
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pub fn new_identity_point() Point {
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mut p := Point{}
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return p.set(edwards25519.id_point)
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}
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// new_generator_point returns a new Point set to the canonical generator.
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pub fn new_generator_point() Point {
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mut p := Point{}
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return p.set(edwards25519.gen_point)
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}
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fn (mut v ProjectiveCached) zero() ProjectiveCached {
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v.ypx.one()
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v.ymx.one()
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v.z.one()
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v.t2d.zero()
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return v
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}
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fn (mut v AffineCached) zero() AffineCached {
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v.ypx.one()
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v.ymx.one()
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v.t2d.zero()
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return v
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}
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// Encoding.
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// bytes returns the canonical 32-byte encoding of v, according to RFC 8032,
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// Section 5.1.2.
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pub fn (mut v Point) bytes() []u8 {
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// This function is outlined to make the allocations inline in the caller
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// rather than happen on the heap.
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mut buf := [32]u8{}
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return v.bytes_generic(mut buf)
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}
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fn (mut v Point) bytes_generic(mut buf [32]u8) []u8 {
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check_initialized(v)
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mut zinv := Element{}
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mut x := Element{}
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mut y := Element{}
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zinv.invert(v.z) // zinv = 1 / z
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x.multiply(v.x, zinv) // x = x / z
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y.multiply(v.y, zinv) // y = y / z
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mut out := copy_field_element(mut buf, mut y)
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unsafe {
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// out[31] |= u8(x.is_negative() << 7) //original one
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out[31] |= u8(x.is_negative() * 128) // x << 7 == x * 2^7
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}
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return out
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}
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fn copy_field_element(mut buf [32]u8, mut v Element) []u8 {
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// this fail in test
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/*
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copy(mut buf[..], v.bytes())
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return buf[..]
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*/
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// this pass the test
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mut out := []u8{len: 32}
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for i := 0; i <= buf.len - 1; i++ {
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out[i] = v.bytes()[i]
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}
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return out
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}
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// Conversions.
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fn (mut v ProjectiveP2) from_p1(p ProjectiveP1) ProjectiveP2 {
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v.x.multiply(p.x, p.t)
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v.y.multiply(p.y, p.z)
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v.z.multiply(p.z, p.t)
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return v
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}
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fn (mut v ProjectiveP2) from_p3(p Point) ProjectiveP2 {
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v.x.set(p.x)
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v.y.set(p.y)
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v.z.set(p.z)
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return v
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}
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fn (mut v Point) from_p1(p ProjectiveP1) Point {
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v.x.multiply(p.x, p.t)
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v.y.multiply(p.y, p.z)
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v.z.multiply(p.z, p.t)
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v.t.multiply(p.x, p.y)
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return v
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}
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fn (mut v Point) from_p2(p ProjectiveP2) Point {
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v.x.multiply(p.x, p.z)
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v.y.multiply(p.y, p.z)
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v.z.square(p.z)
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v.t.multiply(p.x, p.y)
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return v
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}
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fn (mut v ProjectiveCached) from_p3(p Point) ProjectiveCached {
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v.ypx.add(p.y, p.x)
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v.ymx.subtract(p.y, p.x)
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v.z.set(p.z)
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v.t2d.multiply(p.t, edwards25519.d2_const)
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return v
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}
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fn (mut v AffineCached) from_p3(p Point) AffineCached {
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v.ypx.add(p.y, p.x)
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v.ymx.subtract(p.y, p.x)
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v.t2d.multiply(p.t, edwards25519.d2_const)
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mut invz := Element{}
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invz.invert(p.z)
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v.ypx.multiply(v.ypx, invz)
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v.ymx.multiply(v.ymx, invz)
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v.t2d.multiply(v.t2d, invz)
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return v
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}
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// (Re)addition and subtraction.
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// add sets v = p + q, and returns v.
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pub fn (mut v Point) add(p Point, q Point) Point {
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check_initialized(p, q)
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mut pc := ProjectiveCached{}
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mut p1 := ProjectiveP1{}
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qcached := pc.from_p3(q)
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result := p1.add(p, qcached)
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return v.from_p1(result)
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}
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// subtract sets v = p - q, and returns v.
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pub fn (mut v Point) subtract(p Point, q Point) Point {
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check_initialized(p, q)
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mut pc := ProjectiveCached{}
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mut p1 := ProjectiveP1{}
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qcached := pc.from_p3(q)
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result := p1.sub(p, qcached)
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return v.from_p1(result)
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}
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fn (mut v ProjectiveP1) add(p Point, q ProjectiveCached) ProjectiveP1 {
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// var ypx, ymx, pp, mm, tt2d, zz2 edwards25519.Element
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mut ypx := Element{}
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mut ymx := Element{}
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mut pp := Element{}
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mut mm := Element{}
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mut tt2d := Element{}
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mut zz2 := Element{}
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ypx.add(p.y, p.x)
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ymx.subtract(p.y, p.x)
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pp.multiply(ypx, q.ypx)
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mm.multiply(ymx, q.ymx)
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tt2d.multiply(p.t, q.t2d)
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zz2.multiply(p.z, q.z)
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zz2.add(zz2, zz2)
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v.x.subtract(pp, mm)
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v.y.add(pp, mm)
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v.z.add(zz2, tt2d)
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v.t.subtract(zz2, tt2d)
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return v
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}
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fn (mut v ProjectiveP1) sub(p Point, q ProjectiveCached) ProjectiveP1 {
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mut ypx := Element{}
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mut ymx := Element{}
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mut pp := Element{}
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mut mm := Element{}
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mut tt2d := Element{}
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mut zz2 := Element{}
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ypx.add(p.y, p.x)
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ymx.subtract(p.y, p.x)
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pp.multiply(&ypx, q.ymx) // flipped sign
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mm.multiply(&ymx, q.ypx) // flipped sign
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tt2d.multiply(p.t, q.t2d)
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zz2.multiply(p.z, q.z)
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zz2.add(zz2, zz2)
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v.x.subtract(pp, mm)
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v.y.add(pp, mm)
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v.z.subtract(zz2, tt2d) // flipped sign
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v.t.add(zz2, tt2d) // flipped sign
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return v
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}
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fn (mut v ProjectiveP1) add_affine(p Point, q AffineCached) ProjectiveP1 {
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mut ypx := Element{}
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mut ymx := Element{}
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mut pp := Element{}
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mut mm := Element{}
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mut tt2d := Element{}
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mut z2 := Element{}
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ypx.add(p.y, p.x)
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ymx.subtract(p.y, p.x)
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pp.multiply(&ypx, q.ypx)
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mm.multiply(&ymx, q.ymx)
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tt2d.multiply(p.t, q.t2d)
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z2.add(p.z, p.z)
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v.x.subtract(pp, mm)
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v.y.add(pp, mm)
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v.z.add(z2, tt2d)
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v.t.subtract(z2, tt2d)
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return v
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}
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fn (mut v ProjectiveP1) sub_affine(p Point, q AffineCached) ProjectiveP1 {
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mut ypx := Element{}
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mut ymx := Element{}
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mut pp := Element{}
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mut mm := Element{}
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mut tt2d := Element{}
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mut z2 := Element{}
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ypx.add(p.y, p.x)
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ymx.subtract(p.y, p.x)
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pp.multiply(ypx, q.ymx) // flipped sign
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mm.multiply(ymx, q.ypx) // flipped sign
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tt2d.multiply(p.t, q.t2d)
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z2.add(p.z, p.z)
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v.x.subtract(pp, mm)
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v.y.add(pp, mm)
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v.z.subtract(z2, tt2d) // flipped sign
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v.t.add(z2, tt2d) // flipped sign
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return v
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}
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// Doubling.
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fn (mut v ProjectiveP1) double(p ProjectiveP2) ProjectiveP1 {
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// var xx, yy, zz2, xplusysq edwards25519.Element
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mut xx := Element{}
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mut yy := Element{}
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mut zz2 := Element{}
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mut xplusysq := Element{}
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xx.square(p.x)
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yy.square(p.y)
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zz2.square(p.z)
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zz2.add(zz2, zz2)
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xplusysq.add(p.x, p.y)
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xplusysq.square(xplusysq)
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v.y.add(yy, xx)
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v.z.subtract(yy, xx)
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v.x.subtract(xplusysq, v.y)
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v.t.subtract(zz2, v.z)
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return v
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}
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// Negation.
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// negate sets v = -p, and returns v.
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pub fn (mut v Point) negate(p Point) Point {
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check_initialized(p)
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v.x.negate(p.x)
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v.y.set(p.y)
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v.z.set(p.z)
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v.t.negate(p.t)
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return v
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}
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// equal returns 1 if v is equivalent to u, and 0 otherwise.
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pub fn (mut v Point) equal(u Point) int {
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check_initialized(v, u)
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mut t1 := Element{}
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mut t2 := Element{}
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mut t3 := Element{}
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mut t4 := Element{}
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t1.multiply(v.x, u.z)
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t2.multiply(u.x, v.z)
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t3.multiply(v.y, u.z)
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t4.multiply(u.y, v.z)
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return t1.equal(t2) & t3.equal(t4)
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}
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// Constant-time operations
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// selected sets v to a if cond == 1 and to b if cond == 0.
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fn (mut v ProjectiveCached) selected(a ProjectiveCached, b ProjectiveCached, cond int) ProjectiveCached {
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v.ypx.selected(a.ypx, b.ypx, cond)
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v.ymx.selected(a.ymx, b.ymx, cond)
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v.z.selected(a.z, b.z, cond)
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v.t2d.selected(a.t2d, b.t2d, cond)
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return v
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}
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// selected sets v to a if cond == 1 and to b if cond == 0.
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fn (mut v AffineCached) selected(a AffineCached, b AffineCached, cond int) AffineCached {
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v.ypx.selected(a.ypx, b.ypx, cond)
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v.ymx.selected(a.ymx, b.ymx, cond)
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v.t2d.selected(a.t2d, b.t2d, cond)
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return v
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}
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// cond_neg negates v if cond == 1 and leaves it unchanged if cond == 0.
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fn (mut v ProjectiveCached) cond_neg(cond int) ProjectiveCached {
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mut el := Element{}
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v.ypx.swap(mut v.ymx, cond)
|
|
v.t2d.selected(el.negate(v.t2d), v.t2d, cond)
|
|
return v
|
|
}
|
|
|
|
// cond_neg negates v if cond == 1 and leaves it unchanged if cond == 0.
|
|
fn (mut v AffineCached) cond_neg(cond int) AffineCached {
|
|
mut el := Element{}
|
|
v.ypx.swap(mut v.ymx, cond)
|
|
v.t2d.selected(el.negate(v.t2d), v.t2d, cond)
|
|
return v
|
|
}
|
|
|
|
fn check_on_curve(points ...Point) bool {
|
|
for p in points {
|
|
mut xx := Element{}
|
|
mut yy := Element{}
|
|
mut zz := Element{}
|
|
mut zzzz := Element{}
|
|
xx.square(p.x)
|
|
yy.square(p.y)
|
|
zz.square(p.z)
|
|
zzzz.square(zz)
|
|
// -x² + y² = 1 + dx²y²
|
|
// -(X/Z)² + (Y/Z)² = 1 + d(X/Z)²(Y/Z)²
|
|
// (-X² + Y²)/Z² = 1 + (dX²Y²)/Z⁴
|
|
// (-X² + Y²)*Z² = Z⁴ + dX²Y²
|
|
mut lhs := Element{}
|
|
mut rhs := Element{}
|
|
lhs.subtract(yy, xx)
|
|
lhs.multiply(lhs, zz)
|
|
rhs.multiply(edwards25519.d_const, xx)
|
|
rhs.multiply(rhs, yy)
|
|
rhs.add(rhs, zzzz)
|
|
|
|
if lhs.equal(rhs) != 1 {
|
|
return false
|
|
}
|
|
/*
|
|
if lhs.equal(rhs) != 1 {
|
|
lg.error('X, Y, and Z do not specify a point on the curve\nX = $p.x \nY = $p.y\nZ = $p.z')
|
|
}*/
|
|
|
|
// xy = T/Z
|
|
lhs.multiply(p.x, p.y)
|
|
rhs.multiply(p.z, p.t)
|
|
/*
|
|
if lhs.equal(rhs) != 1 {
|
|
lg.error('point $i is not valid\nX = $p.x\nY = $p.y\nZ = $p.z')
|
|
}*/
|
|
if lhs.equal(rhs) != 1 {
|
|
return false
|
|
}
|
|
}
|
|
return true
|
|
}
|