const std = @import("std");
const crypto = std.crypto;
const math = std.math;
const mem = std.mem;
const meta = std.meta;
const EncodingError = crypto.errors.EncodingError;
const IdentityElementError = crypto.errors.IdentityElementError;
const NonCanonicalError = crypto.errors.NonCanonicalError;
const NotSquareError = crypto.errors.NotSquareError;
pub const Secp256k1 = struct {
pub const Fe = @import("secp256k1/field.zig").Fe;
pub const scalar = @import("secp256k1/scalar.zig");
x: Fe,
y: Fe,
z: Fe = Fe.one,
is_base: bool = false,
pub const basePoint = Secp256k1{
.x = Fe.fromInt(55066263022277343669578718895168534326250603453777594175500187360389116729240) catch unreachable,
.y = Fe.fromInt(32670510020758816978083085130507043184471273380659243275938904335757337482424) catch unreachable,
.z = Fe.one,
.is_base = true,
};
pub const identityElement = Secp256k1{ .x = Fe.zero, .y = Fe.one, .z = Fe.zero };
pub const B = Fe.fromInt(7) catch unreachable;
pub const Endormorphism = struct {
const lambda: u256 = 37718080363155996902926221483475020450927657555482586988616620542887997980018;
const beta: u256 = 55594575648329892869085402983802832744385952214688224221778511981742606582254;
const lambda_s = s: {
var buf: [32]u8 = undefined;
mem.writeIntLittle(u256, &buf, Endormorphism.lambda);
break :s buf;
};
pub const SplitScalar = struct {
r1: [32]u8,
r2: [32]u8,
};
pub fn splitScalar(s: [32]u8, endian: std.builtin.Endian) SplitScalar {
const b1_neg_s = comptime s: {
var buf: [32]u8 = undefined;
mem.writeIntLittle(u256, &buf, 303414439467246543595250775667605759171);
break :s buf;
};
const b2_neg_s = comptime s: {
var buf: [32]u8 = undefined;
mem.writeIntLittle(u256, &buf, scalar.field_order - 64502973549206556628585045361533709077);
break :s buf;
};
const k = mem.readInt(u256, &s, endian);
const t1 = math.mulWide(u256, k, 21949224512762693861512883645436906316123769664773102907882521278123970637873);
const t2 = math.mulWide(u256, k, 103246583619904461035481197785446227098457807945486720222659797044629401272177);
const c1 = @truncate(u128, t1 >> 384) + @truncate(u1, t1 >> 383);
const c2 = @truncate(u128, t2 >> 384) + @truncate(u1, t2 >> 383);
var buf: [32]u8 = undefined;
mem.writeIntLittle(u256, &buf, c1);
const c1x = scalar.mul(buf, b1_neg_s, .Little) catch unreachable;
mem.writeIntLittle(u256, &buf, c2);
const c2x = scalar.mul(buf, b2_neg_s, .Little) catch unreachable;
const r2 = scalar.add(c1x, c2x, .Little) catch unreachable;
var r1 = scalar.mul(r2, lambda_s, .Little) catch unreachable;
r1 = scalar.sub(s, r1, .Little) catch unreachable;
return SplitScalar{ .r1 = r1, .r2 = r2 };
}
};
pub fn rejectIdentity(p: Secp256k1) IdentityElementError!void {
if (p.x.isZero()) {
return error.IdentityElement;
}
}
pub fn fromAffineCoordinates(p: AffineCoordinates) EncodingError!Secp256k1 {
const x = p.x;
const y = p.y;
const x3B = x.sq().mul(x).add(B);
const yy = y.sq();
const on_curve = @boolToInt(x3B.equivalent(yy));
const is_identity = @boolToInt(x.equivalent(AffineCoordinates.identityElement.x)) & @boolToInt(y.equivalent(AffineCoordinates.identityElement.y));
if ((on_curve | is_identity) == 0) {
return error.InvalidEncoding;
}
var ret = Secp256k1{ .x = x, .y = y, .z = Fe.one };
ret.z.cMov(Secp256k1.identityElement.z, is_identity);
return ret;
}
pub fn fromSerializedAffineCoordinates(xs: [32]u8, ys: [32]u8, endian: std.builtin.Endian) (NonCanonicalError || EncodingError)!Secp256k1 {
const x = try Fe.fromBytes(xs, endian);
const y = try Fe.fromBytes(ys, endian);
return fromAffineCoordinates(.{ .x = x, .y = y });
}
pub fn recoverY(x: Fe, is_odd: bool) NotSquareError!Fe {
const x3B = x.sq().mul(x).add(B);
var y = try x3B.sqrt();
const yn = y.neg();
y.cMov(yn, @boolToInt(is_odd) ^ @boolToInt(y.isOdd()));
return y;
}
pub fn fromSec1(s: []const u8) (EncodingError || NotSquareError || NonCanonicalError)!Secp256k1 {
if (s.len < 1) return error.InvalidEncoding;
const encoding_type = s[0];
const encoded = s[1..];
switch (encoding_type) {
0 => {
if (encoded.len != 0) return error.InvalidEncoding;
return Secp256k1.identityElement;
},
2, 3 => {
if (encoded.len != 32) return error.InvalidEncoding;
const x = try Fe.fromBytes(encoded[0..32].*, .Big);
const y_is_odd = (encoding_type == 3);
const y = try recoverY(x, y_is_odd);
return Secp256k1{ .x = x, .y = y };
},
4 => {
if (encoded.len != 64) return error.InvalidEncoding;
const x = try Fe.fromBytes(encoded[0..32].*, .Big);
const y = try Fe.fromBytes(encoded[32..64].*, .Big);
return Secp256k1.fromAffineCoordinates(.{ .x = x, .y = y });
},
else => return error.InvalidEncoding,
}
}
pub fn toCompressedSec1(p: Secp256k1) [33]u8 {
var out: [33]u8 = undefined;
const xy = p.affineCoordinates();
out[0] = if (xy.y.isOdd()) 3 else 2;
mem.copy(u8, out[1..], &xy.x.toBytes(.Big));
return out;
}
pub fn toUncompressedSec1(p: Secp256k1) [65]u8 {
var out: [65]u8 = undefined;
out[0] = 4;
const xy = p.affineCoordinates();
mem.copy(u8, out[1..33], &xy.x.toBytes(.Big));
mem.copy(u8, out[33..65], &xy.y.toBytes(.Big));
return out;
}
pub fn random() Secp256k1 {
const n = scalar.random(.Little);
return basePoint.mul(n, .Little) catch unreachable;
}
pub fn neg(p: Secp256k1) Secp256k1 {
return .{ .x = p.x, .y = p.y.neg(), .z = p.z };
}
pub fn dbl(p: Secp256k1) Secp256k1 {
var t0 = p.y.sq();
var Z3 = t0.dbl();
Z3 = Z3.dbl();
Z3 = Z3.dbl();
var t1 = p.y.mul(p.z);
var t2 = p.z.sq();
const t2_4 = t2.dbl().dbl();
t2 = t2_4.dbl().dbl().add(t2_4).add(t2);
var X3 = t2.mul(Z3);
var Y3 = t0.add(t2);
Z3 = t1.mul(Z3);
t1 = t2.dbl();
t2 = t1.add(t2);
t0 = t0.sub(t2);
Y3 = t0.mul(Y3);
Y3 = X3.add(Y3);
t1 = p.x.mul(p.y);
X3 = t0.mul(t1);
X3 = X3.dbl();
return .{
.x = X3,
.y = Y3,
.z = Z3,
};
}
pub fn addMixed(p: Secp256k1, q: AffineCoordinates) Secp256k1 {
var t0 = p.x.mul(q.x);
var t1 = p.y.mul(q.y);
var t3 = q.x.add(q.y);
var t4 = p.x.add(p.y1);
t3 = t3.mul(t4);
t4 = t0.add(t1);
t3 = t3.sub(t4);
t4 = q.y.mul(p.z);
t4 = t4.add(p.y);
var Y3 = q.x.mul(p.z);
Y3 = Y3.add(p.x);
var X3 = t0.dbl();
t0 = X3.add(t0);
const t2_4 = p.z.dbl().dbl();
var t2 = t2_4.dbl().dbl().add(t2_4).add(p.z);
var Z3 = t1.add(t2);
t1 = t1.sub(t2);
const Y3_4 = Y3.dbl().dbl();
Y3 = Y3_4.dbl().dbl().add(Y3_4).add(Y3);
X3 = t4.mul(Y3);
t2 = t3.mul(t1);
X3 = t2.sub(X3);
Y3 = Y3.mul(t0);
t1 = t1.mul(Z3);
Y3 = t1.add(Y3);
t0 = t0.mul(t3);
Z3 = Z3.mul(t4);
Z3 = Z3.add(t0);
var ret = Secp256k1{
.x = X3,
.y = Y3,
.z = Z3,
};
ret.cMov(p, @boolToInt(q.x.isZero()));
return ret;
}
pub fn add(p: Secp256k1, q: Secp256k1) Secp256k1 {
var t0 = p.x.mul(q.x);
var t1 = p.y.mul(q.y);
var t2 = p.z.mul(q.z);
var t3 = p.x.add(p.y);
var t4 = q.x.add(q.y);
t3 = t3.mul(t4);
t4 = t0.add(t1);
t3 = t3.sub(t4);
t4 = p.y.add(p.z);
var X3 = q.y.add(q.z);
t4 = t4.mul(X3);
X3 = t1.add(t2);
t4 = t4.sub(X3);
X3 = p.x.add(p.z);
var Y3 = q.x.add(q.z);
X3 = X3.mul(Y3);
Y3 = t0.add(t2);
Y3 = X3.sub(Y3);
X3 = t0.dbl();
t0 = X3.add(t0);
const t2_4 = t2.dbl().dbl();
t2 = t2_4.dbl().dbl().add(t2_4).add(t2);
var Z3 = t1.add(t2);
t1 = t1.sub(t2);
const Y3_4 = Y3.dbl().dbl();
Y3 = Y3_4.dbl().dbl().add(Y3_4).add(Y3);
X3 = t4.mul(Y3);
t2 = t3.mul(t1);
X3 = t2.sub(X3);
Y3 = Y3.mul(t0);
t1 = t1.mul(Z3);
Y3 = t1.add(Y3);
t0 = t0.mul(t3);
Z3 = Z3.mul(t4);
Z3 = Z3.add(t0);
return .{
.x = X3,
.y = Y3,
.z = Z3,
};
}
pub fn sub(p: Secp256k1, q: Secp256k1) Secp256k1 {
return p.add(q.neg());
}
pub fn subMixed(p: Secp256k1, q: AffineCoordinates) Secp256k1 {
return p.addMixed(q.neg());
}
pub fn affineCoordinates(p: Secp256k1) AffineCoordinates {
const zinv = p.z.invert();
var ret = AffineCoordinates{
.x = p.x.mul(zinv),
.y = p.y.mul(zinv),
};
ret.cMov(AffineCoordinates.identityElement, @boolToInt(p.x.isZero()));
return ret;
}
pub fn equivalent(a: Secp256k1, b: Secp256k1) bool {
if (a.sub(b).rejectIdentity()) {
return false;
} else |_| {
return true;
}
}
fn cMov(p: *Secp256k1, a: Secp256k1, c: u1) void {
p.x.cMov(a.x, c);
p.y.cMov(a.y, c);
p.z.cMov(a.z, c);
}
fn pcSelect(comptime n: usize, pc: *const [n]Secp256k1, b: u8) Secp256k1 {
var t = Secp256k1.identityElement;
comptime var i: u8 = 1;
inline while (i < pc.len) : (i += 1) {
t.cMov(pc[i], @truncate(u1, (@as(usize, b ^ i) -% 1) >> 8));
}
return t;
}
fn slide(s: [32]u8) [2 * 32 + 1]i8 {
var e: [2 * 32 + 1]i8 = undefined;
for (s) |x, i| {
e[i * 2 + 0] = @as(i8, @truncate(u4, x));
e[i * 2 + 1] = @as(i8, @truncate(u4, x >> 4));
}
var carry: i8 = 0;
for (e[0..64]) |*x| {
x.* += carry;
carry = (x.* + 8) >> 4;
x.* -= carry * 16;
std.debug.assert(x.* >= -8 and x.* <= 8);
}
e[64] = carry;
std.debug.assert(carry >= -8 and carry <= 8);
return e;
}
fn pcMul(pc: *const [9]Secp256k1, s: [32]u8, comptime vartime: bool) IdentityElementError!Secp256k1 {
std.debug.assert(vartime);
const e = slide(s);
var q = Secp256k1.identityElement;
var pos = e.len - 1;
while (true) : (pos -= 1) {
const slot = e[pos];
if (slot > 0) {
q = q.add(pc[@intCast(usize, slot)]);
} else if (slot < 0) {
q = q.sub(pc[@intCast(usize, -slot)]);
}
if (pos == 0) break;
q = q.dbl().dbl().dbl().dbl();
}
try q.rejectIdentity();
return q;
}
fn pcMul16(pc: *const [16]Secp256k1, s: [32]u8, comptime vartime: bool) IdentityElementError!Secp256k1 {
var q = Secp256k1.identityElement;
var pos: usize = 252;
while (true) : (pos -= 4) {
const slot = @truncate(u4, (s[pos >> 3] >> @truncate(u3, pos)));
if (vartime) {
if (slot != 0) {
q = q.add(pc[slot]);
}
} else {
q = q.add(pcSelect(16, pc, slot));
}
if (pos == 0) break;
q = q.dbl().dbl().dbl().dbl();
}
try q.rejectIdentity();
return q;
}
fn precompute(p: Secp256k1, comptime count: usize) [1 + count]Secp256k1 {
var pc: [1 + count]Secp256k1 = undefined;
pc[0] = Secp256k1.identityElement;
pc[1] = p;
var i: usize = 2;
while (i <= count) : (i += 1) {
pc[i] = if (i % 2 == 0) pc[i / 2].dbl() else pc[i - 1].add(p);
}
return pc;
}
const basePointPc = pc: {
@setEvalBranchQuota(50000);
break :pc precompute(Secp256k1.basePoint, 15);
};
pub fn mul(p: Secp256k1, s_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 {
const s = if (endian == .Little) s_ else Fe.orderSwap(s_);
if (p.is_base) {
return pcMul16(&basePointPc, s, false);
}
try p.rejectIdentity();
const pc = precompute(p, 15);
return pcMul16(&pc, s, false);
}
pub fn mulPublic(p: Secp256k1, s_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 {
const s = if (endian == .Little) s_ else Fe.orderSwap(s_);
const zero = comptime scalar.Scalar.zero.toBytes(.Little);
if (mem.eql(u8, &zero, &s)) {
return error.IdentityElement;
}
const pc = precompute(p, 8);
var lambda_p = try pcMul(&pc, Endormorphism.lambda_s, true);
var split_scalar = Endormorphism.splitScalar(s, .Little);
var px = p;
if (split_scalar.r1[split_scalar.r1.len / 2] != 0) {
split_scalar.r1 = scalar.neg(split_scalar.r1, .Little) catch zero;
px = px.neg();
}
if (split_scalar.r2[split_scalar.r2.len / 2] != 0) {
split_scalar.r2 = scalar.neg(split_scalar.r2, .Little) catch zero;
lambda_p = lambda_p.neg();
}
return mulDoubleBasePublicEndo(px, split_scalar.r1, lambda_p, split_scalar.r2);
}
fn mulDoubleBasePublicEndo(p1: Secp256k1, s1: [32]u8, p2: Secp256k1, s2: [32]u8) IdentityElementError!Secp256k1 {
var pc1_array: [9]Secp256k1 = undefined;
const pc1 = if (p1.is_base) basePointPc[0..9] else pc: {
pc1_array = precompute(p1, 8);
break :pc &pc1_array;
};
const pc2 = precompute(p2, 8);
std.debug.assert(s1[s1.len / 2] == 0);
std.debug.assert(s2[s2.len / 2] == 0);
const e1 = slide(s1);
const e2 = slide(s2);
var q = Secp256k1.identityElement;
var pos: usize = 2 * 32 / 2;
while (true) : (pos -= 1) {
const slot1 = e1[pos];
if (slot1 > 0) {
q = q.add(pc1[@intCast(usize, slot1)]);
} else if (slot1 < 0) {
q = q.sub(pc1[@intCast(usize, -slot1)]);
}
const slot2 = e2[pos];
if (slot2 > 0) {
q = q.add(pc2[@intCast(usize, slot2)]);
} else if (slot2 < 0) {
q = q.sub(pc2[@intCast(usize, -slot2)]);
}
if (pos == 0) break;
q = q.dbl().dbl().dbl().dbl();
}
try q.rejectIdentity();
return q;
}
pub fn mulDoubleBasePublic(p1: Secp256k1, s1_: [32]u8, p2: Secp256k1, s2_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 {
const s1 = if (endian == .Little) s1_ else Fe.orderSwap(s1_);
const s2 = if (endian == .Little) s2_ else Fe.orderSwap(s2_);
try p1.rejectIdentity();
var pc1_array: [9]Secp256k1 = undefined;
const pc1 = if (p1.is_base) basePointPc[0..9] else pc: {
pc1_array = precompute(p1, 8);
break :pc &pc1_array;
};
try p2.rejectIdentity();
var pc2_array: [9]Secp256k1 = undefined;
const pc2 = if (p2.is_base) basePointPc[0..9] else pc: {
pc2_array = precompute(p2, 8);
break :pc &pc2_array;
};
const e1 = slide(s1);
const e2 = slide(s2);
var q = Secp256k1.identityElement;
var pos: usize = 2 * 32;
while (true) : (pos -= 1) {
const slot1 = e1[pos];
if (slot1 > 0) {
q = q.add(pc1[@intCast(usize, slot1)]);
} else if (slot1 < 0) {
q = q.sub(pc1[@intCast(usize, -slot1)]);
}
const slot2 = e2[pos];
if (slot2 > 0) {
q = q.add(pc2[@intCast(usize, slot2)]);
} else if (slot2 < 0) {
q = q.sub(pc2[@intCast(usize, -slot2)]);
}
if (pos == 0) break;
q = q.dbl().dbl().dbl().dbl();
}
try q.rejectIdentity();
return q;
}
};
pub const AffineCoordinates = struct {
x: Secp256k1.Fe,
y: Secp256k1.Fe,
pub const identityElement = AffineCoordinates{ .x = Secp256k1.identityElement.x, .y = Secp256k1.identityElement.y };
fn cMov(p: *AffineCoordinates, a: AffineCoordinates, c: u1) void {
p.x.cMov(a.x, c);
p.y.cMov(a.y, c);
}
};
test "secp256k1" {
_ = @import("tests/secp256k1.zig");
}