    const std = @import("std");
    const fmt = std.fmt;

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

    /// Group operations over Edwards25519.
    pub const Ristretto255 = struct {
        /// The underlying elliptic curve.
        pub const Curve = @import("edwards25519.zig").Edwards25519;
        /// The underlying prime field.
        pub const Fe = Curve.Fe;
        /// Field arithmetic mod the order of the main subgroup.
        pub const scalar = Curve.scalar;
        /// Length in byte of an encoded element.
        pub const encoded_length: usize = 32;

        p: Curve,

        fn sqrtRatioM1(u: Fe, v: Fe) struct { ratio_is_square: u32, root: Fe } {
            const v3 = v.sq().mul(v); // v^3

            var x = v3.sq().mul(u).mul(v).pow2523().mul(v3).mul(u); // uv^3(uv^7)^((q-5)/8)

            const vxx = x.sq().mul(v); // vx^2

            const m_root_check = vxx.sub(u); // vx^2-u

            const p_root_check = vxx.add(u); // vx^2+u

            const f_root_check = u.mul(Fe.sqrtm1).add(vxx); // vx^2+u*sqrt(-1)

            const has_m_root = m_root_check.isZero();
            const has_p_root = p_root_check.isZero();
            const has_f_root = f_root_check.isZero();
            const x_sqrtm1 = x.mul(Fe.sqrtm1); // x*sqrt(-1)

            x.cMov(x_sqrtm1, @boolToInt(has_p_root) | @boolToInt(has_f_root));
            return .{ .ratio_is_square = @boolToInt(has_m_root) | @boolToInt(has_p_root), .root = x.abs() };
        }

        fn rejectNonCanonical(s: [encoded_length]u8) NonCanonicalError!void {
            if ((s[0] & 1) != 0) {
                return error.NonCanonical;
            }
            try Fe.rejectNonCanonical(s, false);
        }

        /// Reject the neutral element.
        pub inline fn rejectIdentity(p: Ristretto255) IdentityElementError!void {
            return p.p.rejectIdentity();
        }

        /// The base point (Ristretto is a curve in desguise).
        pub const basePoint = Ristretto255{ .p = Curve.basePoint };

        /// Decode a Ristretto255 representative.
        pub fn fromBytes(s: [encoded_length]u8) (NonCanonicalError || EncodingError)!Ristretto255 {
            try rejectNonCanonical(s);
            const s_ = Fe.fromBytes(s);
            const ss = s_.sq(); // s^2

            const u1_ = Fe.one.sub(ss); // (1-s^2)

            const u1u1 = u1_.sq(); // (1-s^2)^2

            const u2_ = Fe.one.add(ss); // (1+s^2)

            const u2u2 = u2_.sq(); // (1+s^2)^2

            const v = Fe.edwards25519d.mul(u1u1).neg().sub(u2u2); // -(d*u1^2)-u2^2

            const v_u2u2 = v.mul(u2u2); // v*u2^2

            const inv_sqrt = sqrtRatioM1(Fe.one, v_u2u2);
            var x = inv_sqrt.root.mul(u2_);
            const y = inv_sqrt.root.mul(x).mul(v).mul(u1_);
            x = x.mul(s_);
            x = x.add(x).abs();
            const t = x.mul(y);
            if ((1 - inv_sqrt.ratio_is_square) | @boolToInt(t.isNegative()) | @boolToInt(y.isZero()) != 0) {
                return error.InvalidEncoding;
            }
            const p: Curve = .{
                .x = x,
                .y = y,
                .z = Fe.one,
                .t = t,
            };
            return Ristretto255{ .p = p };
        }

        /// Encode to a Ristretto255 representative.
        pub fn toBytes(e: Ristretto255) [encoded_length]u8 {
            const p = &e.p;
            var u1_ = p.z.add(p.y); // Z+Y

            const zmy = p.z.sub(p.y); // Z-Y

            u1_ = u1_.mul(zmy); // (Z+Y)*(Z-Y)

            const u2_ = p.x.mul(p.y); // X*Y

            const u1_u2u2 = u2_.sq().mul(u1_); // u1*u2^2

            const inv_sqrt = sqrtRatioM1(Fe.one, u1_u2u2);
            const den1 = inv_sqrt.root.mul(u1_);
            const den2 = inv_sqrt.root.mul(u2_);
            const z_inv = den1.mul(den2).mul(p.t); // den1*den2*T

            const ix = p.x.mul(Fe.sqrtm1); // X*sqrt(-1)

            const iy = p.y.mul(Fe.sqrtm1); // Y*sqrt(-1)

            const eden = den1.mul(Fe.edwards25519sqrtamd); // den1/sqrt(a-d)

            const t_z_inv = p.t.mul(z_inv); // T*z_inv

            const rotate = @boolToInt(t_z_inv.isNegative());
            var x = p.x;
            var y = p.y;
            var den_inv = den2;
            x.cMov(iy, rotate);
            y.cMov(ix, rotate);
            den_inv.cMov(eden, rotate);

            const x_z_inv = x.mul(z_inv);
            const yneg = y.neg();
            y.cMov(yneg, @boolToInt(x_z_inv.isNegative()));

            return p.z.sub(y).mul(den_inv).abs().toBytes();
        }

        fn elligator(t: Fe) Curve {
            const r = t.sq().mul(Fe.sqrtm1); // sqrt(-1)*t^2

            const u = r.add(Fe.one).mul(Fe.edwards25519eonemsqd); // (r+1)*(1-d^2)

            var c = comptime Fe.one.neg(); // -1

            const v = c.sub(r.mul(Fe.edwards25519d)).mul(r.add(Fe.edwards25519d)); // (c-r*d)*(r+d)

            const ratio_sqrt = sqrtRatioM1(u, v);
            const wasnt_square = 1 - ratio_sqrt.ratio_is_square;
            var s = ratio_sqrt.root;
            const s_prime = s.mul(t).abs().neg(); // -|s*t|

            s.cMov(s_prime, wasnt_square);
            c.cMov(r, wasnt_square);

            const n = r.sub(Fe.one).mul(c).mul(Fe.edwards25519sqdmone).sub(v); // c*(r-1)*(d-1)^2-v

            const w0 = s.add(s).mul(v); // 2s*v

            const w1 = n.mul(Fe.edwards25519sqrtadm1); // n*sqrt(ad-1)

            const ss = s.sq(); // s^2

            const w2 = Fe.one.sub(ss); // 1-s^2

            const w3 = Fe.one.add(ss); // 1+s^2

            return .{ .x = w0.mul(w3), .y = w2.mul(w1), .z = w1.mul(w3), .t = w0.mul(w2) };
        }

        /// Map a 64-bit string into a Ristretto255 group element
        pub fn fromUniform(h: [64]u8) Ristretto255 {
            const p0 = elligator(Fe.fromBytes(h[0..32].*));
            const p1 = elligator(Fe.fromBytes(h[32..64].*));
            return Ristretto255{ .p = p0.add(p1) };
        }

        /// Double a Ristretto255 element.
        pub inline fn dbl(p: Ristretto255) Ristretto255 {
            return .{ .p = p.p.dbl() };
        }

        /// Add two Ristretto255 elements.
        pub inline fn add(p: Ristretto255, q: Ristretto255) Ristretto255 {
            return .{ .p = p.p.add(q.p) };
        }

        /// Multiply a Ristretto255 element with a scalar.
        /// Return error.WeakPublicKey if the resulting element is
        /// the identity element.
        pub inline fn mul(p: Ristretto255, s: [encoded_length]u8) (IdentityElementError || WeakPublicKeyError)!Ristretto255 {
            return Ristretto255{ .p = try p.p.mul(s) };
        }

        /// Return true if two Ristretto255 elements are equivalent
        pub fn equivalent(p: Ristretto255, q: Ristretto255) bool {
            const p_ = &p.p;
            const q_ = &q.p;
            const a = p_.x.mul(q_.y).equivalent(p_.y.mul(q_.x));
            const b = p_.y.mul(q_.y).equivalent(p_.x.mul(q_.x));
            return (@boolToInt(a) | @boolToInt(b)) != 0;
        }
    };

    test "ristretto255" {
        const p = Ristretto255.basePoint;
        var buf: [256]u8 = undefined;
        try std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{s}", .{std.fmt.fmtSliceHexUpper(&p.toBytes())}), "E2F2AE0A6ABC4E71A884A961C500515F58E30B6AA582DD8DB6A65945E08D2D76");

        var r: [Ristretto255.encoded_length]u8 = undefined;
        _ = try fmt.hexToBytes(r[0..], "6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919");
        var q = try Ristretto255.fromBytes(r);
        q = q.dbl().add(p);
        try std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{s}", .{std.fmt.fmtSliceHexUpper(&q.toBytes())}), "E882B131016B52C1D3337080187CF768423EFCCBB517BB495AB812C4160FF44E");

        const s = [_]u8{15} ++ [_]u8{0} ** 31;
        const w = try p.mul(s);
        try std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{s}", .{std.fmt.fmtSliceHexUpper(&w.toBytes())}), "E0C418F7C8D9C4CDD7395B93EA124F3AD99021BB681DFC3302A9D99A2E53E64E");

        try std.testing.expect(p.dbl().dbl().dbl().dbl().equivalent(w.add(p)));

        const h = [_]u8{69} ** 32 ++ [_]u8{42} ** 32;
        const ph = Ristretto255.fromUniform(h);
        try std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{s}", .{std.fmt.fmtSliceHexUpper(&ph.toBytes())}), "DCCA54E037A4311EFBEEF413ACD21D35276518970B7A61DC88F8587B493D5E19");
    }