    const std = @import("std");
    const crypto = std.crypto;
    const debug = std.debug;
    const fmt = std.fmt;
    const mem = std.mem;

    const EncodingError = crypto.errors.EncodingError;
    const IdentityElementError = crypto.errors.IdentityElementError;
    const NonCanonicalError = crypto.errors.NonCanonicalError;
    const NotSquareError = crypto.errors.NotSquareError;
    const WeakPublicKeyError = crypto.errors.WeakPublicKeyError;

    /// Group operations over Edwards25519.
    pub const Edwards25519 = struct {
        /// The underlying prime field.
        pub const Fe = @import("field.zig").Fe;
        /// Field arithmetic mod the order of the main subgroup.
        pub const scalar = @import("scalar.zig");
        /// Length in bytes of a compressed representation of a point.
        pub const encoded_length: usize = 32;

        x: Fe,
        y: Fe,
        z: Fe,
        t: Fe,

        is_base: bool = false,

        /// Decode an Edwards25519 point from its compressed (Y+sign) coordinates.
        pub fn fromBytes(s: [encoded_length]u8) EncodingError!Edwards25519 {
            const z = Fe.one;
            const y = Fe.fromBytes(s);
            var u = y.sq();
            var v = u.mul(Fe.edwards25519d);
            u = u.sub(z);
            v = v.add(z);
            var x = u.mul(v).pow2523().mul(u);
            const vxx = x.sq().mul(v);
            const has_m_root = vxx.sub(u).isZero();
            const has_p_root = vxx.add(u).isZero();
            if ((@intFromBool(has_m_root) | @intFromBool(has_p_root)) == 0) { // best-effort to avoid two conditional branches

                return error.InvalidEncoding;
            }
            x.cMov(x.mul(Fe.sqrtm1), 1 - @intFromBool(has_m_root));
            x.cMov(x.neg(), @intFromBool(x.isNegative()) ^ (s[31] >> 7));
            const t = x.mul(y);
            return Edwards25519{ .x = x, .y = y, .z = z, .t = t };
        }

        /// Encode an Edwards25519 point.
        pub fn toBytes(p: Edwards25519) [encoded_length]u8 {
            const zi = p.z.invert();
            var s = p.y.mul(zi).toBytes();
            s[31] ^= @as(u8, @intFromBool(p.x.mul(zi).isNegative())) << 7;
            return s;
        }

        /// Check that the encoding of a point is canonical.
        pub fn rejectNonCanonical(s: [32]u8) NonCanonicalError!void {
            return Fe.rejectNonCanonical(s, true);
        }

        /// The edwards25519 base point.
        pub const basePoint = Edwards25519{
            .x = Fe{ .limbs = .{ 1738742601995546, 1146398526822698, 2070867633025821, 562264141797630, 587772402128613 } },
            .y = Fe{ .limbs = .{ 1801439850948184, 1351079888211148, 450359962737049, 900719925474099, 1801439850948198 } },
            .z = Fe.one,
            .t = Fe{ .limbs = .{ 1841354044333475, 16398895984059, 755974180946558, 900171276175154, 1821297809914039 } },
            .is_base = true,
        };

        pub const identityElement = Edwards25519{ .x = Fe.zero, .y = Fe.one, .z = Fe.one, .t = Fe.zero };

        /// Reject the neutral element.
        pub fn rejectIdentity(p: Edwards25519) IdentityElementError!void {
            if (p.x.isZero()) {
                return error.IdentityElement;
            }
        }

        /// Multiply a point by the cofactor
        pub fn clearCofactor(p: Edwards25519) Edwards25519 {
            return p.dbl().dbl().dbl();
        }

        /// Check that the point does not generate a low-order group.
        /// Return a `WeakPublicKey` error if it does.
        pub fn rejectLowOrder(p: Edwards25519) WeakPublicKeyError!void {
            const zi = p.z.invert();
            const x = p.x.mul(zi);
            const y = p.y.mul(zi);
            const x_neg = x.neg();
            const iy = Fe.sqrtm1.mul(y);
            if (x.isZero() or y.isZero() or iy.equivalent(x) or iy.equivalent(x_neg)) {
                return error.WeakPublicKey;
            }
        }

        /// Flip the sign of the X coordinate.
        pub inline fn neg(p: Edwards25519) Edwards25519 {
            return .{ .x = p.x.neg(), .y = p.y, .z = p.z, .t = p.t.neg() };
        }

        /// Double an Edwards25519 point.
        pub fn dbl(p: Edwards25519) Edwards25519 {
            const t0 = p.x.add(p.y).sq();
            var x = p.x.sq();
            var z = p.y.sq();
            const y = z.add(x);
            z = z.sub(x);
            x = t0.sub(y);
            const t = p.z.sq2().sub(z);
            return .{
                .x = x.mul(t),
                .y = y.mul(z),
                .z = z.mul(t),
                .t = x.mul(y),
            };
        }

        /// Add two Edwards25519 points.
        pub fn add(p: Edwards25519, q: Edwards25519) Edwards25519 {
            const a = p.y.sub(p.x).mul(q.y.sub(q.x));
            const b = p.x.add(p.y).mul(q.x.add(q.y));
            const c = p.t.mul(q.t).mul(Fe.edwards25519d2);
            var d = p.z.mul(q.z);
            d = d.add(d);
            const x = b.sub(a);
            const y = b.add(a);
            const z = d.add(c);
            const t = d.sub(c);
            return .{
                .x = x.mul(t),
                .y = y.mul(z),
                .z = z.mul(t),
                .t = x.mul(y),
            };
        }

        /// Subtract two Edwards25519 points.
        pub fn sub(p: Edwards25519, q: Edwards25519) Edwards25519 {
            return p.add(q.neg());
        }

        inline fn cMov(p: *Edwards25519, a: Edwards25519, c: u64) void {
            p.x.cMov(a.x, c);
            p.y.cMov(a.y, c);
            p.z.cMov(a.z, c);
            p.t.cMov(a.t, c);
        }

        inline fn pcSelect(comptime n: usize, pc: *const [n]Edwards25519, b: u8) Edwards25519 {
            var t = Edwards25519.identityElement;
            comptime var i: u8 = 1;
            inline while (i < pc.len) : (i += 1) {
                t.cMov(pc[i], ((@as(usize, b ^ i) -% 1) >> 8) & 1);
            }
            return t;
        }

        fn slide(s: [32]u8) [2 * 32]i8 {
            const reduced = if ((s[s.len - 1] & 0x80) == 0) s else scalar.reduce(s);
            var e: [2 * 32]i8 = undefined;
            for (reduced, 0..) |x, i| {
                e[i * 2 + 0] = @as(i8, @as(u4, @truncate(x)));
                e[i * 2 + 1] = @as(i8, @as(u4, @truncate(x >> 4)));
            }
            // Now, e[0..63] is between 0 and 15, e[63] is between 0 and 7

            var carry: i8 = 0;
            for (e[0..63]) |*x| {
                x.* += carry;
                carry = (x.* + 8) >> 4;
                x.* -= carry * 16;
            }
            e[63] += carry;
            // Now, e[*] is between -8 and 8, including e[63]

            return e;
        }

        // Scalar multiplication with a 4-bit window and the first 8 multiples.

        // This requires the scalar to be converted to non-adjacent form.

        // Based on real-world benchmarks, we only use this for multi-scalar multiplication.

        // NAF could be useful to half the size of precomputation tables, but we intentionally

        // avoid these to keep the standard library lightweight.

        fn pcMul(pc: *const [9]Edwards25519, s: [32]u8, comptime vartime: bool) IdentityElementError!Edwards25519 {
            std.debug.assert(vartime);
            const e = slide(s);
            var q = Edwards25519.identityElement;
            var pos: usize = 2 * 32 - 1;
            while (true) : (pos -= 1) {
                const slot = e[pos];
                if (slot > 0) {
                    q = q.add(pc[@as(usize, @intCast(slot))]);
                } else if (slot < 0) {
                    q = q.sub(pc[@as(usize, @intCast(-slot))]);
                }
                if (pos == 0) break;
                q = q.dbl().dbl().dbl().dbl();
            }
            try q.rejectIdentity();
            return q;
        }

        // Scalar multiplication with a 4-bit window and the first 15 multiples.

        fn pcMul16(pc: *const [16]Edwards25519, s: [32]u8, comptime vartime: bool) IdentityElementError!Edwards25519 {
            var q = Edwards25519.identityElement;
            var pos: usize = 252;
            while (true) : (pos -= 4) {
                const slot: u4 = @truncate((s[pos >> 3] >> @as(u3, @truncate(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: Edwards25519, comptime count: usize) [1 + count]Edwards25519 {
            var pc: [1 + count]Edwards25519 = undefined;
            pc[0] = Edwards25519.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(10000);
            break :pc precompute(Edwards25519.basePoint, 15);
        };

        /// Multiply an Edwards25519 point by a scalar without clamping it.
        /// Return error.WeakPublicKey if the base generates a small-order group,
        /// and error.IdentityElement if the result is the identity element.
        pub fn mul(p: Edwards25519, s: [32]u8) (IdentityElementError || WeakPublicKeyError)!Edwards25519 {
            const pc = if (p.is_base) basePointPc else pc: {
                const xpc = precompute(p, 15);
                xpc[4].rejectIdentity() catch return error.WeakPublicKey;
                break :pc xpc;
            };
            return pcMul16(&pc, s, false);
        }

        /// Multiply an Edwards25519 point by a *PUBLIC* scalar *IN VARIABLE TIME*
        /// This can be used for signature verification.
        pub fn mulPublic(p: Edwards25519, s: [32]u8) (IdentityElementError || WeakPublicKeyError)!Edwards25519 {
            if (p.is_base) {
                return pcMul16(&basePointPc, s, true);
            } else {
                const pc = precompute(p, 8);
                pc[4].rejectIdentity() catch return error.WeakPublicKey;
                return pcMul(&pc, s, true);
            }
        }

        /// Double-base multiplication of public parameters - Compute (p1*s1)+(p2*s2) *IN VARIABLE TIME*
        /// This can be used for signature verification.
        pub fn mulDoubleBasePublic(p1: Edwards25519, s1: [32]u8, p2: Edwards25519, s2: [32]u8) (IdentityElementError || WeakPublicKeyError)!Edwards25519 {
            var pc1_array: [9]Edwards25519 = undefined;
            const pc1 = if (p1.is_base) basePointPc[0..9] else pc: {
                pc1_array = precompute(p1, 8);
                pc1_array[4].rejectIdentity() catch return error.WeakPublicKey;
                break :pc &pc1_array;
            };
            var pc2_array: [9]Edwards25519 = undefined;
            const pc2 = if (p2.is_base) basePointPc[0..9] else pc: {
                pc2_array = precompute(p2, 8);
                pc2_array[4].rejectIdentity() catch return error.WeakPublicKey;
                break :pc &pc2_array;
            };
            const e1 = slide(s1);
            const e2 = slide(s2);
            var q = Edwards25519.identityElement;
            var pos: usize = 2 * 32 - 1;
            while (true) : (pos -= 1) {
                const slot1 = e1[pos];
                if (slot1 > 0) {
                    q = q.add(pc1[@as(usize, @intCast(slot1))]);
                } else if (slot1 < 0) {
                    q = q.sub(pc1[@as(usize, @intCast(-slot1))]);
                }
                const slot2 = e2[pos];
                if (slot2 > 0) {
                    q = q.add(pc2[@as(usize, @intCast(slot2))]);
                } else if (slot2 < 0) {
                    q = q.sub(pc2[@as(usize, @intCast(-slot2))]);
                }
                if (pos == 0) break;
                q = q.dbl().dbl().dbl().dbl();
            }
            try q.rejectIdentity();
            return q;
        }

        /// Multiscalar multiplication *IN VARIABLE TIME* for public data
        /// Computes ps0*ss0 + ps1*ss1 + ps2*ss2... faster than doing many of these operations individually
        pub fn mulMulti(comptime count: usize, ps: [count]Edwards25519, ss: [count][32]u8) (IdentityElementError || WeakPublicKeyError)!Edwards25519 {
            var pcs: [count][9]Edwards25519 = undefined;

            var bpc: [9]Edwards25519 = undefined;
            @memcpy(&bpc, basePointPc[0..bpc.len]);

            for (ps, 0..) |p, i| {
                if (p.is_base) {
                    pcs[i] = bpc;
                } else {
                    pcs[i] = precompute(p, 8);
                    pcs[i][4].rejectIdentity() catch return error.WeakPublicKey;
                }
            }
            var es: [count][2 * 32]i8 = undefined;
            for (ss, 0..) |s, i| {
                es[i] = slide(s);
            }
            var q = Edwards25519.identityElement;
            var pos: usize = 2 * 32 - 1;
            while (true) : (pos -= 1) {
                for (es, 0..) |e, i| {
                    const slot = e[pos];
                    if (slot > 0) {
                        q = q.add(pcs[i][@as(usize, @intCast(slot))]);
                    } else if (slot < 0) {
                        q = q.sub(pcs[i][@as(usize, @intCast(-slot))]);
                    }
                }
                if (pos == 0) break;
                q = q.dbl().dbl().dbl().dbl();
            }
            try q.rejectIdentity();
            return q;
        }

        /// Multiply an Edwards25519 point by a scalar after "clamping" it.
        /// Clamping forces the scalar to be a multiple of the cofactor in
        /// order to prevent small subgroups attacks.
        /// This is strongly recommended for DH operations.
        /// Return error.WeakPublicKey if the resulting point is
        /// the identity element.
        pub fn clampedMul(p: Edwards25519, s: [32]u8) (IdentityElementError || WeakPublicKeyError)!Edwards25519 {
            var t: [32]u8 = s;
            scalar.clamp(&t);
            return mul(p, t);
        }

        // montgomery -- recover y = sqrt(x^3 + A*x^2 + x)

        fn xmontToYmont(x: Fe) NotSquareError!Fe {
            var x2 = x.sq();
            const x3 = x.mul(x2);
            x2 = x2.mul32(Fe.edwards25519a_32);
            return x.add(x2).add(x3).sqrt();
        }

        // montgomery affine coordinates to edwards extended coordinates

        fn montToEd(x: Fe, y: Fe) Edwards25519 {
            const x_plus_one = x.add(Fe.one);
            const x_minus_one = x.sub(Fe.one);
            const x_plus_one_y_inv = x_plus_one.mul(y).invert(); // 1/((x+1)*y)

            // xed = sqrt(-A-2)*x/y

            const xed = x.mul(Fe.edwards25519sqrtam2).mul(x_plus_one_y_inv).mul(x_plus_one);

            // yed = (x-1)/(x+1) or 1 if the denominator is 0

            var yed = x_plus_one_y_inv.mul(y).mul(x_minus_one);
            yed.cMov(Fe.one, @intFromBool(x_plus_one_y_inv.isZero()));

            return Edwards25519{
                .x = xed,
                .y = yed,
                .z = Fe.one,
                .t = xed.mul(yed),
            };
        }

        /// Elligator2 map - Returns Montgomery affine coordinates
        pub fn elligator2(r: Fe) struct { x: Fe, y: Fe, not_square: bool } {
            const rr2 = r.sq2().add(Fe.one).invert();
            var x = rr2.mul32(Fe.edwards25519a_32).neg(); // x=x1

            var x2 = x.sq();
            const x3 = x2.mul(x);
            x2 = x2.mul32(Fe.edwards25519a_32); // x2 = A*x1^2

            const gx1 = x3.add(x).add(x2); // gx1 = x1^3 + A*x1^2 + x1

            const not_square = !gx1.isSquare();

            // gx1 not a square => x = -x1-A

            x.cMov(x.neg(), @intFromBool(not_square));
            x2 = Fe.zero;
            x2.cMov(Fe.edwards25519a, @intFromBool(not_square));
            x = x.sub(x2);

            // We have y = sqrt(gx1) or sqrt(gx2) with gx2 = gx1*(A+x1)/(-x1)

            // but it is about as fast to just recompute y from the curve equation.

            const y = xmontToYmont(x) catch unreachable;
            return .{ .x = x, .y = y, .not_square = not_square };
        }

        /// Map a 64-bit hash into an Edwards25519 point
        pub fn fromHash(h: [64]u8) Edwards25519 {
            const fe_f = Fe.fromBytes64(h);
            var elr = elligator2(fe_f);

            const y_sign = !elr.not_square;
            const y_neg = elr.y.neg();
            elr.y.cMov(y_neg, @intFromBool(elr.y.isNegative()) ^ @intFromBool(y_sign));
            return montToEd(elr.x, elr.y).clearCofactor();
        }

        fn stringToPoints(comptime n: usize, ctx: []const u8, s: []const u8) [n]Edwards25519 {
            debug.assert(n <= 2);
            const H = crypto.hash.sha2.Sha512;
            const h_l: usize = 48;
            var xctx = ctx;
            var hctx: [H.digest_length]u8 = undefined;
            if (ctx.len > 0xff) {
                var st = H.init(.{});
                st.update("H2C-OVERSIZE-DST-");
                st.update(ctx);
                st.final(&hctx);
                xctx = hctx[0..];
            }
            const empty_block = [_]u8{0} ** H.block_length;
            var t = [3]u8{ 0, n * h_l, 0 };
            var xctx_len_u8 = [1]u8{@as(u8, @intCast(xctx.len))};
            var st = H.init(.{});
            st.update(empty_block[0..]);
            st.update(s);
            st.update(t[0..]);
            st.update(xctx);
            st.update(xctx_len_u8[0..]);
            var u_0: [H.digest_length]u8 = undefined;
            st.final(&u_0);
            var u: [n * H.digest_length]u8 = undefined;
            var i: usize = 0;
            while (i < n * H.digest_length) : (i += H.digest_length) {
                u[i..][0..H.digest_length].* = u_0;
                var j: usize = 0;
                while (i > 0 and j < H.digest_length) : (j += 1) {
                    u[i + j] ^= u[i + j - H.digest_length];
                }
                t[2] += 1;
                st = H.init(.{});
                st.update(u[i..][0..H.digest_length]);
                st.update(t[2..3]);
                st.update(xctx);
                st.update(xctx_len_u8[0..]);
                st.final(u[i..][0..H.digest_length]);
            }
            var px: [n]Edwards25519 = undefined;
            i = 0;
            while (i < n) : (i += 1) {
                @memset(u_0[0 .. H.digest_length - h_l], 0);
                u_0[H.digest_length - h_l ..][0..h_l].* = u[i * h_l ..][0..h_l].*;
                px[i] = fromHash(u_0);
            }
            return px;
        }

        /// Hash a context `ctx` and a string `s` into an Edwards25519 point
        ///
        /// This function implements the edwards25519_XMD:SHA-512_ELL2_RO_ and edwards25519_XMD:SHA-512_ELL2_NU_
        /// methods from the "Hashing to Elliptic Curves" standard document.
        ///
        /// Although not strictly required by the standard, it is recommended to avoid NUL characters in
        /// the context in order to be compatible with other implementations.
        pub fn fromString(comptime random_oracle: bool, ctx: []const u8, s: []const u8) Edwards25519 {
            if (random_oracle) {
                const px = stringToPoints(2, ctx, s);
                return px[0].add(px[1]);
            } else {
                return stringToPoints(1, ctx, s)[0];
            }
        }

        /// Map a 32 bit uniform bit string into an edwards25519 point
        pub fn fromUniform(r: [32]u8) Edwards25519 {
            var s = r;
            const x_sign = s[31] >> 7;
            s[31] &= 0x7f;
            const elr = elligator2(Fe.fromBytes(s));
            var p = montToEd(elr.x, elr.y);
            const p_neg = p.neg();
            p.cMov(p_neg, @intFromBool(p.x.isNegative()) ^ x_sign);
            return p.clearCofactor();
        }
    };

    const htest = @import("../test.zig");

    test "edwards25519 packing/unpacking" {
        const s = [_]u8{170} ++ [_]u8{0} ** 31;
        var b = Edwards25519.basePoint;
        const pk = try b.mul(s);
        var buf: [128]u8 = undefined;
        try std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{s}", .{std.fmt.fmtSliceHexUpper(&pk.toBytes())}), "074BC7E0FCBD587FDBC0969444245FADC562809C8F6E97E949AF62484B5B81A6");

        const small_order_ss: [7][32]u8 = .{
            .{
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 0 (order 4)

            },
            .{
                0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 1 (order 1)

            },
            .{
                0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4, 0x89, 0xf2, 0xef, 0x98, 0xf0, 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6, 0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05, // 270738550114484064931822528722565878893680426757531351946374360975030340202(order 8)

            },
            .{
                0xc7, 0x17, 0x6a, 0x70, 0x3d, 0x4d, 0xd8, 0x4f, 0xba, 0x3c, 0x0b, 0x76, 0x0d, 0x10, 0x67, 0x0f, 0x2a, 0x20, 0x53, 0xfa, 0x2c, 0x39, 0xcc, 0xc6, 0x4e, 0xc7, 0xfd, 0x77, 0x92, 0xac, 0x03, 0x7a, // 55188659117513257062467267217118295137698188065244968500265048394206261417927 (order 8)

            },
            .{
                0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p-1 (order 2)

            },
            .{
                0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p (=0, order 4)

            },
            .{
                0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p+1 (=1, order 1)

            },
        };
        for (small_order_ss) |small_order_s| {
            const small_p = try Edwards25519.fromBytes(small_order_s);
            try std.testing.expectError(error.WeakPublicKey, small_p.mul(s));
        }
    }

    test "edwards25519 point addition/subtraction" {
        var s1: [32]u8 = undefined;
        var s2: [32]u8 = undefined;
        crypto.random.bytes(&s1);
        crypto.random.bytes(&s2);
        const p = try Edwards25519.basePoint.clampedMul(s1);
        const q = try Edwards25519.basePoint.clampedMul(s2);
        const r = p.add(q).add(q).sub(q).sub(q);
        try r.rejectIdentity();
        try std.testing.expectError(error.IdentityElement, r.sub(p).rejectIdentity());
        try std.testing.expectError(error.IdentityElement, p.sub(p).rejectIdentity());
        try std.testing.expectError(error.IdentityElement, p.sub(q).add(q).sub(p).rejectIdentity());
    }

    test "edwards25519 uniform-to-point" {
        var r = [32]u8{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 };
        var p = Edwards25519.fromUniform(r);
        try htest.assertEqual("0691eee3cf70a0056df6bfa03120635636581b5c4ea571dfc680f78c7e0b4137", p.toBytes()[0..]);

        r[31] = 0xff;
        p = Edwards25519.fromUniform(r);
        try htest.assertEqual("f70718e68ef42d90ca1d936bb2d7e159be6c01d8095d39bd70487c82fe5c973a", p.toBytes()[0..]);
    }

    // Test vectors from draft-irtf-cfrg-hash-to-curve-12

    test "edwards25519 hash-to-curve operation" {
        var p = Edwards25519.fromString(true, "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_RO_", "abc");
        try htest.assertEqual("31558a26887f23fb8218f143e69d5f0af2e7831130bd5b432ef23883b895839a", p.toBytes()[0..]);

        p = Edwards25519.fromString(false, "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_NU_", "abc");
        try htest.assertEqual("42fa27c8f5a1ae0aa38bb59d5938e5145622ba5dedd11d11736fa2f9502d7367", p.toBytes()[0..]);
    }

    test "edwards25519 implicit reduction of invalid scalars" {
        const s = [_]u8{0} ** 31 ++ [_]u8{255};
        const p1 = try Edwards25519.basePoint.mulPublic(s);
        const p2 = try Edwards25519.basePoint.mul(s);
        const p3 = try p1.mulPublic(s);
        const p4 = try p1.mul(s);

        try std.testing.expectEqualSlices(u8, p1.toBytes()[0..], p2.toBytes()[0..]);
        try std.testing.expectEqualSlices(u8, p3.toBytes()[0..], p4.toBytes()[0..]);

        try htest.assertEqual("339f189ecc5fbebe9895345c72dc07bda6e615f8a40e768441b6f529cd6c671a", p1.toBytes()[0..]);
        try htest.assertEqual("a501e4c595a3686d8bee7058c7e6af7fd237f945c47546910e37e0e79b1bafb0", p3.toBytes()[0..]);
    }