From 7227ec8c207df33f26c143bfd8e1b833211dcbf6 Mon Sep 17 00:00:00 2001 From: Eugene Siegel Date: Thu, 18 Jul 2024 19:47:51 -0400 Subject: [PATCH] ellswift: introduce ElligatorSwift encoding and decoding funcs The BIP324 ElligatorSwift test vectors are also included. --- btcec/ellswift.go | 391 ++++++++++++++++++++ btcec/ellswift_test.go | 819 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 1210 insertions(+) create mode 100644 btcec/ellswift.go create mode 100644 btcec/ellswift_test.go diff --git a/btcec/ellswift.go b/btcec/ellswift.go new file mode 100644 index 0000000000..02346357ea --- /dev/null +++ b/btcec/ellswift.go @@ -0,0 +1,391 @@ +package btcec + +import ( + "crypto/rand" + "fmt" + + "github.com/btcsuite/btcd/chaincfg/chainhash" +) + +var ( + // c is sqrt(-3) (mod p) + c FieldVal + + cBytes = [32]byte{ + 0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, + 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, + 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, + 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x52, + } + + // ErrPointNotOnCurve is returned when we're unable to find a point on the + // curve. + ErrPointNotOnCurve = fmt.Errorf("point does not exist on secp256k1 curve") +) + +func init() { + c.SetByteSlice(cBytes[:]) +} + +// XSwiftEC() takes two field elements (u, t) and gives us an x-coordinate that +// is on the secp256k1 curve. This is used to take an ElligatorSwift-encoded +// public key (u, t) and return the point on the curve it maps to. +// TODO: Rewrite these so to avoid new(FieldVal).Add(...) usage? +// NOTE: u, t MUST be normalized. The result x is normalized. +func XSwiftEC(u, t *FieldVal) *FieldVal { + // 1. Let u' = u if u != 0, else = 1 + if u.IsZero() { + u.SetInt(1) + } + + // 2. Let t' = t if t != 0, else 1 + if t.IsZero() { + t.SetInt(1) + } + + // 3. Let t'' = t' if g(u') != -(t'^2); t'' = 2t' otherwise + // g(x) = x^3 + ax + b, a = 0, b = 7 + + // Calculate g(u'). + gu := new(FieldVal).SquareVal(u).Mul(u).AddInt(7).Normalize() + + // Calculate the right-hand side of the equation (-t'^2) + rhs := new(FieldVal).SquareVal(t).Negate(1).Normalize() + + if gu.Equals(rhs) { + // t'' = 2t' + t = t.Add(t) + } + + // 4. X = (u'^3 + b - t''^2) / (2t'') + tSquared := new(FieldVal).SquareVal(t).Negate(1) + xNum := new(FieldVal).SquareVal(u).Mul(u).AddInt(7).Add(tSquared) + xDenom := new(FieldVal).Add2(t, t).Inverse() + x := xNum.Mul(xDenom) + + // 5. Y = (X+t'') / (u' * c) + yNum := new(FieldVal).Add2(x, t) + yDenom := new(FieldVal).Mul2(u, &c).Inverse() + y := yNum.Mul(yDenom) + + // 6. Return the first x in (u'+4Y^2, -X/2Y - u'/2, X/2Y - u'/2) for which + // x^3 + b is square. + + // 6a. Calculate u' +4Y^2 and determine if x^3+7 is square. + ySqr := new(FieldVal).Add(y).Mul(y) + quadYSqr := new(FieldVal).Add(ySqr).MulInt(4) + firstX := new(FieldVal).Add(u).Add(quadYSqr) + + firstXCurve := new(FieldVal).Add(firstX).Square().Mul(firstX).AddInt(7) + + // Now determine if firstXCurve is square (on the curve). + if new(FieldVal).SquareRootVal(firstXCurve) { + return firstX.Normalize() + } + + // 6b. Calculate -X/2Y - u'/2 and determine if x^3 + 7 is square + doubleYInv := new(FieldVal).Add(y).Add(y).Inverse() + xDivDoubleYInv := new(FieldVal).Add(x).Mul(doubleYInv) + negXDivDoubleYInv := new(FieldVal).Add(xDivDoubleYInv).Negate(1) + invTwo := new(FieldVal).AddInt(2).Inverse() + negUDivTwo := new(FieldVal).Add(u).Mul(invTwo).Negate(1) + secondX := new(FieldVal).Add(negXDivDoubleYInv).Add(negUDivTwo) + + secondXCurve := new(FieldVal).Add(secondX).Square().Mul(secondX).AddInt(7) + + // Now determine if secondXCurve is square. + if new(FieldVal).SquareRootVal(secondXCurve) { + return secondX.Normalize() + } + + // 6c. Calculate X/2Y -u'/2 and determine if x^3 + 7 is square + thirdX := new(FieldVal).Add(xDivDoubleYInv).Add(negUDivTwo) + + thirdXCurve := new(FieldVal).Add(thirdX).Square().Mul(thirdX).AddInt(7) + + // Now determine if thirdXCurve is square. + if new(FieldVal).SquareRootVal(thirdXCurve) { + return thirdX.Normalize() + } + + // Should have found a square above. + panic("unreachable - no calculated x-values were square") +} + +// XSwiftECInv takes two field elements (u, x) (where x is on the curve) and +// returns a field element t. This is used to take a random field element u and +// a point on the curve and return a field element t where (u, t) forms the +// ElligatorSwift encoding. +// TODO: Rewrite these so to avoid new(FieldVal).Add(...) usage? +// NOTE: u, x MUST be normalized. The result `t` is normalized. +func XSwiftECInv(u, x *FieldVal, caseNum int) *FieldVal { + v := new(FieldVal) + s := new(FieldVal) + twoInv := new(FieldVal).AddInt(2).Inverse() + + if caseNum&2 == 0 { + // If lift_x(-x-u) succeeds, return None + if _, found := liftX(new(FieldVal).Add(x).Add(u).Negate(2)); found { + return nil + } + + // Let v = x + v.Add(x) + + // Let s = -(u^3+7)/(u^2 + uv + v^2) + uSqr := new(FieldVal).Add(u).Square() + vSqr := new(FieldVal).Add(v).Square() + sDenom := new(FieldVal).Add(u).Mul(v).Add(uSqr).Add(vSqr) + sNum := new(FieldVal).Add(uSqr).Mul(u).AddInt(7) + + s = sDenom.Inverse().Mul(sNum).Negate(1) + } else { + // Let s = x - u + negU := new(FieldVal).Add(u).Negate(1) + s.Add(x).Add(negU).Normalize() + + // If s = 0, return None + if s.IsZero() { + return nil + } + + // Let r be the square root of -s(4(u^3 + 7) + 3u^2s) + uSqr := new(FieldVal).Add(u).Square() + lhs := new(FieldVal).Add(uSqr).Mul(u).AddInt(7).MulInt(4) + rhs := new(FieldVal).Add(uSqr).MulInt(3).Mul(s) + + // Add the two terms together and multiply by -s. + lhs.Add(rhs).Normalize().Mul(s).Negate(1) + + r := new(FieldVal) + if !r.SquareRootVal(lhs) { + // If no square root was found, return None. + return nil + } + + if caseNum&1 == 1 && r.Normalize().IsZero() { + // If case & 1 = 1 and r = 0, return None. + return nil + } + + // Let v = (r/s - u)/2 + sInv := new(FieldVal).Add(s).Inverse() + uNeg := new(FieldVal).Add(u).Negate(1) + + v.Add(r).Mul(sInv).Add(uNeg).Mul(twoInv) + } + + w := new(FieldVal) + + if !w.SquareRootVal(s) { + // If no square root was found, return None. + return nil + } + + switch caseNum & 5 { + case 0: + // If case & 5 = 0, return -w(u(1-c)/2 + v) + oneMinusC := new(FieldVal).Add(&c).Negate(1).AddInt(1) + t := new(FieldVal).Add(u).Mul(oneMinusC).Mul(twoInv).Add(v).Mul(w). + Negate(1).Normalize() + + return t + + case 1: + // If case & 5 = 1, return w(u(1+c)/2 + v) + onePlusC := new(FieldVal).Add(&c).AddInt(1) + t := new(FieldVal).Add(u).Mul(onePlusC).Mul(twoInv).Add(v).Mul(w). + Normalize() + + return t + + case 4: + // If case & 5 = 4, return w(u(1-c)/2 + v) + oneMinusC := new(FieldVal).Add(&c).Negate(1).AddInt(1) + t := new(FieldVal).Add(u).Mul(oneMinusC).Mul(twoInv).Add(v).Mul(w). + Normalize() + + return t + + case 5: + // If case & 5 = 5, return -w(u(1+c)/2 + v) + onePlusC := new(FieldVal).Add(&c).AddInt(1) + t := new(FieldVal).Add(u).Mul(onePlusC).Mul(twoInv).Add(v).Mul(w). + Negate(1).Normalize() + + return t + } + + panic("should not reach here") +} + +// XElligatorSwift takes the x-coordinate of a point on secp256k1 and generates +// ElligatorSwift encoding of that point composed of two field elements (u, t). +// NOTE: x MUST be normalized. The return values u, t are normalized. +func XElligatorSwift(x *FieldVal) (*FieldVal, *FieldVal, error) { + // We'll choose a random `u` value and a random case so that we can + // generate a `t` value. + for { + // Choose random u value. + var randUBytes [32]byte + _, err := rand.Read(randUBytes[:]) + if err != nil { + return nil, nil, err + } + + u := new(FieldVal) + overflow := u.SetBytes(&randUBytes) + if overflow == 1 { + u.Normalize() + } + + // Choose a random case in the interval [0, 7] + var randCaseByte [1]byte + _, err = rand.Read(randCaseByte[:]) + if err != nil { + return nil, nil, err + } + + caseNum := randCaseByte[0] & 7 + + // Find t, if none is found, continue with the loop. + t := XSwiftECInv(u, x, int(caseNum)) + if t != nil { + return u, t, nil + } + } +} + +// EllswiftCreate generates a random private key and returns that along with +// the ElligatorSwift encoding of its corresponding public key. +func EllswiftCreate() (*PrivateKey, [64]byte, error) { + var randPrivKeyBytes [64]byte + + // Generate a random private key + _, err := rand.Read(randPrivKeyBytes[:]) + if err != nil { + return nil, [64]byte{}, err + } + + privKey, _ := PrivKeyFromBytes(randPrivKeyBytes[:]) + + // Fetch the x-coordinate of the public key. + x := getXCoord(privKey) + + // Get the ElligatorSwift encoding of the public key. + u, t, err := XElligatorSwift(x) + if err != nil { + return nil, [64]byte{}, err + } + + uBytes := u.Bytes() + tBytes := t.Bytes() + + // ellswift_pub = bytes(u) || bytes(t), its encoding as 64 bytes + var ellswiftPub [64]byte + copy(ellswiftPub[0:32], (*uBytes)[:]) + copy(ellswiftPub[32:64], (*tBytes)[:]) + + // Return (priv, ellswift_pub) + return privKey, ellswiftPub, nil +} + +// EllswiftECDHXOnly takes the ElligatorSwift-encoded public key of a +// counter-party and performs ECDH with our private key. +func EllswiftECDHXOnly(ellswiftTheirs [64]byte, privKey *PrivateKey) ([32]byte, + error) { + + // Let u = int(ellswift_theirs[:32]) mod p. + // Let t = int(ellswift_theirs[32:]) mod p. + uBytesTheirs := ellswiftTheirs[0:32] + tBytesTheirs := ellswiftTheirs[32:64] + + var uTheirs FieldVal + overflow := uTheirs.SetByteSlice(uBytesTheirs[:]) + if overflow { + uTheirs.Normalize() + } + + var tTheirs FieldVal + overflow = tTheirs.SetByteSlice(tBytesTheirs[:]) + if overflow { + tTheirs.Normalize() + } + + // Calculate bytes(x(privâ‹…lift_x(XSwiftEC(u, t)))) + xTheirs := XSwiftEC(&uTheirs, &tTheirs) + pubKey, found := liftX(xTheirs) + if !found { + return [32]byte{}, ErrPointNotOnCurve + } + + var pubJacobian JacobianPoint + pubKey.AsJacobian(&pubJacobian) + + var sharedPoint JacobianPoint + ScalarMultNonConst(&privKey.Key, &pubJacobian, &sharedPoint) + sharedPoint.ToAffine() + + return *sharedPoint.X.Bytes(), nil +} + +// getXCoord fetches the corresponding public key's x-coordinate given a +// private key. +func getXCoord(privKey *PrivateKey) *FieldVal { + var result JacobianPoint + ScalarBaseMultNonConst(&privKey.Key, &result) + result.ToAffine() + return &result.X +} + +// liftX returns the point P with x-coordinate `x` and even y-coordinate. If a +// point exists on the curve, it returns true and false otherwise. +// TODO: Use quadratic residue formula instead (see: BIP340)? +func liftX(x *FieldVal) (*PublicKey, bool) { + ySqr := new(FieldVal).Add(x).Square().Mul(x).AddInt(7) + + y := new(FieldVal) + if !y.SquareRootVal(ySqr) { + // If we've reached here, the point does not exist on the curve. + return nil, false + } + + if !y.Normalize().IsOdd() { + return NewPublicKey(x, y), true + } + + // Negate y if it's odd. + if !y.Negate(1).Normalize().IsOdd() { + return NewPublicKey(x, y), true + } + + return nil, false +} + +// V2Ecdh performs x-only ecdh and returns a shared secret composed of a tagged +// hash which itself is composed of two ElligatorSwift-encoded public keys and +// the x-only ecdh point. +func V2Ecdh(priv *PrivateKey, ellswiftTheirs, ellswiftOurs [64]byte, + initiating bool) (*chainhash.Hash, error) { + + ecdhPoint, err := EllswiftECDHXOnly(ellswiftTheirs, priv) + if err != nil { + return nil, err + } + + if initiating { + // Initiating, place our public key encoding first. + var msg []byte + msg = append(msg, ellswiftOurs[:]...) + msg = append(msg, ellswiftTheirs[:]...) + msg = append(msg, ecdhPoint[:]...) + return chainhash.TaggedHash([]byte("bip324_ellswift_xonly_ecdh"), msg), + nil + } + + var msg []byte + msg = append(msg, ellswiftTheirs[:]...) + msg = append(msg, ellswiftOurs[:]...) + msg = append(msg, ecdhPoint[:]...) + return chainhash.TaggedHash([]byte("bip324_ellswift_xonly_ecdh"), msg), nil +} diff --git a/btcec/ellswift_test.go b/btcec/ellswift_test.go new file mode 100644 index 0000000000..d4e85db667 --- /dev/null +++ b/btcec/ellswift_test.go @@ -0,0 +1,819 @@ +package btcec + +import ( + "testing" +) + +// TestXSwiftECVectors checks the BIP324 test vectors for the XSwiftEC function. +func TestXSwiftECVectors(t *testing.T) { + tests := []struct { + ellswift string + expectedX string + }{ + { + ellswift: "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + expectedX: "edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0c", + }, + { + ellswift: "000000000000000000000000000000000000000000000000000000000000000001d3475bf7655b0fb2d852921035b2ef607f49069b97454e6795251062741771", + expectedX: "b5da00b73cd6560520e7c364086e7cd23a34bf60d0e707be9fc34d4cd5fdfa2c", + }, + { + ellswift: "000000000000000000000000000000000000000000000000000000000000000082277c4a71f9d22e66ece523f8fa08741a7c0912c66a69ce68514bfd3515b49f", + expectedX: "f482f2e241753ad0fb89150d8491dc1e34ff0b8acfbb442cfe999e2e5e6fd1d2", + }, + { + ellswift: "00000000000000000000000000000000000000000000000000000000000000008421cc930e77c9f514b6915c3dbe2a94c6d8f690b5b739864ba6789fb8a55dd0", + expectedX: "9f59c40275f5085a006f05dae77eb98c6fd0db1ab4a72ac47eae90a4fc9e57e0", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000bde70df51939b94c9c24979fa7dd04ebd9b3572da7802290438af2a681895441", + expectedX: "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa9fffffd6b", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000d19c182d2759cd99824228d94799f8c6557c38a1c0d6779b9d4b729c6f1ccc42", + expectedX: "70720db7e238d04121f5b1afd8cc5ad9d18944c6bdc94881f502b7a3af3aecff", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0c", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2664bbd5", + expectedX: "50873db31badcc71890e4f67753a65757f97aaa7dd5f1e82b753ace32219064b", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff7028de7d", + expectedX: "1eea9cc59cfcf2fa151ac6c274eea4110feb4f7b68c5965732e9992e976ef68e", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbcfb7e7", + expectedX: "12303941aedc208880735b1f1795c8e55be520ea93e103357b5d2adb7ed59b8e", + }, + { + ellswift: "0000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffff3113ad9", + expectedX: "7eed6b70e7b0767c7d7feac04e57aa2a12fef5e0f48f878fcbb88b3b6b5e0783", + }, + { + ellswift: "0a2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f8530000000000000000000000000000000000000000000000000000000000000000", + expectedX: "532167c11200b08c0e84a354e74dcc40f8b25f4fe686e30869526366278a0688", + }, + { + ellswift: "0a2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f853fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "532167c11200b08c0e84a354e74dcc40f8b25f4fe686e30869526366278a0688", + }, + { + ellswift: "0ffde9ca81d751e9cdaffc1a50779245320b28996dbaf32f822f20117c22fbd6c74d99efceaa550f1ad1c0f43f46e7ff1ee3bd0162b7bf55f2965da9c3450646", + expectedX: "74e880b3ffd18fe3cddf7902522551ddf97fa4a35a3cfda8197f947081a57b8f", + }, + { + ellswift: "0ffde9ca81d751e9cdaffc1a50779245320b28996dbaf32f822f20117c22fbd6ffffffffffffffffffffffffffffffffffffffffffffffffffffffff156ca896", + expectedX: "377b643fce2271f64e5c8101566107c1be4980745091783804f654781ac9217c", + }, + { + ellswift: "123658444f32be8f02ea2034afa7ef4bbe8adc918ceb49b12773b625f490b368ffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dc5fe11", + expectedX: "ed16d65cf3a9538fcb2c139f1ecbc143ee14827120cbc2659e667256800b8142", + }, + { + ellswift: "146f92464d15d36e35382bd3ca5b0f976c95cb08acdcf2d5b3570617990839d7ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3145e93b", + expectedX: "0d5cd840427f941f65193079ab8e2e83024ef2ee7ca558d88879ffd879fb6657", + }, + { + ellswift: "15fdf5cf09c90759add2272d574d2bb5fe1429f9f3c14c65e3194bf61b82aa73ffffffffffffffffffffffffffffffffffffffffffffffffffffffff04cfd906", + expectedX: "16d0e43946aec93f62d57eb8cde68951af136cf4b307938dd1447411e07bffe1", + }, + { + ellswift: "1f67edf779a8a649d6def60035f2fa22d022dd359079a1a144073d84f19b92d50000000000000000000000000000000000000000000000000000000000000000", + expectedX: "025661f9aba9d15c3118456bbe980e3e1b8ba2e047c737a4eb48a040bb566f6c", + }, + { + ellswift: "1f67edf779a8a649d6def60035f2fa22d022dd359079a1a144073d84f19b92d5fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "025661f9aba9d15c3118456bbe980e3e1b8ba2e047c737a4eb48a040bb566f6c", + }, + { + ellswift: "1fe1e5ef3fceb5c135ab7741333ce5a6e80d68167653f6b2b24bcbcfaaaff507fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "98bec3b2a351fa96cfd191c1778351931b9e9ba9ad1149f6d9eadca80981b801", + }, + { + ellswift: "4056a34a210eec7892e8820675c860099f857b26aad85470ee6d3cf1304a9dcf375e70374271f20b13c9986ed7d3c17799698cfc435dbed3a9f34b38c823c2b4", + expectedX: "868aac2003b29dbcad1a3e803855e078a89d16543ac64392d122417298cec76e", + }, + { + ellswift: "4197ec3723c654cfdd32ab075506648b2ff5070362d01a4fff14b336b78f963fffffffffffffffffffffffffffffffffffffffffffffffffffffffffb3ab1e95", + expectedX: "ba5a6314502a8952b8f456e085928105f665377a8ce27726a5b0eb7ec1ac0286", + }, + { + ellswift: "47eb3e208fedcdf8234c9421e9cd9a7ae873bfbdbc393723d1ba1e1e6a8e6b24ffffffffffffffffffffffffffffffffffffffffffffffffffffffff7cd12cb1", + expectedX: "d192d52007e541c9807006ed0468df77fd214af0a795fe119359666fdcf08f7c", + }, + { + ellswift: "5eb9696a2336fe2c3c666b02c755db4c0cfd62825c7b589a7b7bb442e141c1d693413f0052d49e64abec6d5831d66c43612830a17df1fe4383db896468100221", + expectedX: "ef6e1da6d6c7627e80f7a7234cb08a022c1ee1cf29e4d0f9642ae924cef9eb38", + }, + { + ellswift: "7bf96b7b6da15d3476a2b195934b690a3a3de3e8ab8474856863b0de3af90b0e0000000000000000000000000000000000000000000000000000000000000000", + expectedX: "50851dfc9f418c314a437295b24feeea27af3d0cd2308348fda6e21c463e46ff", + }, + { + ellswift: "7bf96b7b6da15d3476a2b195934b690a3a3de3e8ab8474856863b0de3af90b0efffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "50851dfc9f418c314a437295b24feeea27af3d0cd2308348fda6e21c463e46ff", + }, + { + ellswift: "851b1ca94549371c4f1f7187321d39bf51c6b7fb61f7cbf027c9da62021b7a65fc54c96837fb22b362eda63ec52ec83d81bedd160c11b22d965d9f4a6d64d251", + expectedX: "3e731051e12d33237eb324f2aa5b16bb868eb49a1aa1fadc19b6e8761b5a5f7b", + }, + { + ellswift: "943c2f775108b737fe65a9531e19f2fc2a197f5603e3a2881d1d83e4008f91250000000000000000000000000000000000000000000000000000000000000000", + expectedX: "311c61f0ab2f32b7b1f0223fa72f0a78752b8146e46107f8876dd9c4f92b2942", + }, + { + ellswift: "943c2f775108b737fe65a9531e19f2fc2a197f5603e3a2881d1d83e4008f9125fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "311c61f0ab2f32b7b1f0223fa72f0a78752b8146e46107f8876dd9c4f92b2942", + }, + { + ellswift: "a0f18492183e61e8063e573606591421b06bc3513631578a73a39c1c3306239f2f32904f0d2a33ecca8a5451705bb537d3bf44e071226025cdbfd249fe0f7ad6", + expectedX: "97a09cf1a2eae7c494df3c6f8a9445bfb8c09d60832f9b0b9d5eabe25fbd14b9", + }, + { + ellswift: "a1ed0a0bd79d8a23cfe4ec5fef5ba5cccfd844e4ff5cb4b0f2e71627341f1c5b17c499249e0ac08d5d11ea1c2c8ca7001616559a7994eadec9ca10fb4b8516dc", + expectedX: "65a89640744192cdac64b2d21ddf989cdac7500725b645bef8e2200ae39691f2", + }, + { + ellswift: "ba94594a432721aa3580b84c161d0d134bc354b690404d7cd4ec57c16d3fbe98ffffffffffffffffffffffffffffffffffffffffffffffffffffffffea507dd7", + expectedX: "5e0d76564aae92cb347e01a62afd389a9aa401c76c8dd227543dc9cd0efe685a", + }, + { + ellswift: "bcaf7219f2f6fbf55fe5e062dce0e48c18f68103f10b8198e974c184750e1be3932016cbf69c4471bd1f656c6a107f1973de4af7086db897277060e25677f19a", + expectedX: "2d97f96cac882dfe73dc44db6ce0f1d31d6241358dd5d74eb3d3b50003d24c2b", + }, + { + ellswift: "bcaf7219f2f6fbf55fe5e062dce0e48c18f68103f10b8198e974c184750e1be3ffffffffffffffffffffffffffffffffffffffffffffffffffffffff6507d09a", + expectedX: "e7008afe6e8cbd5055df120bd748757c686dadb41cce75e4addcc5e02ec02b44", + }, + { + ellswift: "c5981bae27fd84401c72a155e5707fbb811b2b620645d1028ea270cbe0ee225d4b62aa4dca6506c1acdbecc0552569b4b21436a5692e25d90d3bc2eb7ce24078", + expectedX: "948b40e7181713bc018ec1702d3d054d15746c59a7020730dd13ecf985a010d7", + }, + { + ellswift: "c894ce48bfec433014b931a6ad4226d7dbd8eaa7b6e3faa8d0ef94052bcf8cff336eeb3919e2b4efb746c7f71bbca7e9383230fbbc48ffafe77e8bcc69542471", + expectedX: "f1c91acdc2525330f9b53158434a4d43a1c547cff29f15506f5da4eb4fe8fa5a", + }, + { + ellswift: "cbb0deab125754f1fdb2038b0434ed9cb3fb53ab735391129994a535d925f6730000000000000000000000000000000000000000000000000000000000000000", + expectedX: "872d81ed8831d9998b67cb7105243edbf86c10edfebb786c110b02d07b2e67cd", + }, + { + ellswift: "d917b786dac35670c330c9c5ae5971dfb495c8ae523ed97ee2420117b171f41effffffffffffffffffffffffffffffffffffffffffffffffffffffff2001f6f6", + expectedX: "e45b71e110b831f2bdad8651994526e58393fde4328b1ec04d59897142584691", + }, + { + ellswift: "e28bd8f5929b467eb70e04332374ffb7e7180218ad16eaa46b7161aa679eb4260000000000000000000000000000000000000000000000000000000000000000", + expectedX: "66b8c980a75c72e598d383a35a62879f844242ad1e73ff12edaa59f4e58632b5", + }, + { + ellswift: "e28bd8f5929b467eb70e04332374ffb7e7180218ad16eaa46b7161aa679eb426fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "66b8c980a75c72e598d383a35a62879f844242ad1e73ff12edaa59f4e58632b5", + }, + { + ellswift: "e7ee5814c1706bf8a89396a9b032bc014c2cac9c121127dbf6c99278f8bb53d1dfd04dbcda8e352466b6fcd5f2dea3e17d5e133115886eda20db8a12b54de71b", + expectedX: "e842c6e3529b234270a5e97744edc34a04d7ba94e44b6d2523c9cf0195730a50", + }, + { + ellswift: "f292e46825f9225ad23dc057c1d91c4f57fcb1386f29ef10481cb1d22518593fffffffffffffffffffffffffffffffffffffffffffffffffffffffff7011c989", + expectedX: "3cea2c53b8b0170166ac7da67194694adacc84d56389225e330134dab85a4d55", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f0000000000000000000000000000000000000000000000000000000000000000", + expectedX: "edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0c", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f01d3475bf7655b0fb2d852921035b2ef607f49069b97454e6795251062741771", + expectedX: "b5da00b73cd6560520e7c364086e7cd23a34bf60d0e707be9fc34d4cd5fdfa2c", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f4218f20ae6c646b363db68605822fb14264ca8d2587fdd6fbc750d587e76a7ee", + expectedX: "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa9fffffd6b", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f82277c4a71f9d22e66ece523f8fa08741a7c0912c66a69ce68514bfd3515b49f", + expectedX: "f482f2e241753ad0fb89150d8491dc1e34ff0b8acfbb442cfe999e2e5e6fd1d2", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f8421cc930e77c9f514b6915c3dbe2a94c6d8f690b5b739864ba6789fb8a55dd0", + expectedX: "9f59c40275f5085a006f05dae77eb98c6fd0db1ab4a72ac47eae90a4fc9e57e0", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fd19c182d2759cd99824228d94799f8c6557c38a1c0d6779b9d4b729c6f1ccc42", + expectedX: "70720db7e238d04121f5b1afd8cc5ad9d18944c6bdc94881f502b7a3af3aecff", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2ffffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0c", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffff2664bbd5", + expectedX: "50873db31badcc71890e4f67753a65757f97aaa7dd5f1e82b753ace32219064b", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffff7028de7d", + expectedX: "1eea9cc59cfcf2fa151ac6c274eea4110feb4f7b68c5965732e9992e976ef68e", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbcfb7e7", + expectedX: "12303941aedc208880735b1f1795c8e55be520ea93e103357b5d2adb7ed59b8e", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3113ad9", + expectedX: "7eed6b70e7b0767c7d7feac04e57aa2a12fef5e0f48f878fcbb88b3b6b5e0783", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff13cea4a70000000000000000000000000000000000000000000000000000000000000000", + expectedX: "649984435b62b4a25d40c6133e8d9ab8c53d4b059ee8a154a3be0fcf4e892edb", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff13cea4a7fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "649984435b62b4a25d40c6133e8d9ab8c53d4b059ee8a154a3be0fcf4e892edb", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff15028c590063f64d5a7f1c14915cd61eac886ab295bebd91992504cf77edb028bdd6267f", + expectedX: "3fde5713f8282eead7d39d4201f44a7c85a5ac8a0681f35e54085c6b69543374", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2715de860000000000000000000000000000000000000000000000000000000000000000", + expectedX: "3524f77fa3a6eb4389c3cb5d27f1f91462086429cd6c0cb0df43ea8f1e7b3fb4", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2715de86fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "3524f77fa3a6eb4389c3cb5d27f1f91462086429cd6c0cb0df43ea8f1e7b3fb4", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2c2c5709e7156c417717f2feab147141ec3da19fb759575cc6e37b2ea5ac9309f26f0f66", + expectedX: "d2469ab3e04acbb21c65a1809f39caafe7a77c13d10f9dd38f391c01dc499c52", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3a08cc1efffffffffffffffffffffffffffffffffffffffffffffffffffffffff760e9f0", + expectedX: "38e2a5ce6a93e795e16d2c398bc99f0369202ce21e8f09d56777b40fc512bccc", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3e91257d932016cbf69c4471bd1f656c6a107f1973de4af7086db897277060e25677f19a", + expectedX: "864b3dc902c376709c10a93ad4bbe29fce0012f3dc8672c6286bba28d7d6d6fc", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff795d6c1c322cadf599dbb86481522b3cc55f15a67932db2afa0111d9ed6981bcd124bf44", + expectedX: "766dfe4a700d9bee288b903ad58870e3d4fe2f0ef780bcac5c823f320d9a9bef", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff8e426f0392389078c12b1a89e9542f0593bc96b6bfde8224f8654ef5d5cda935a3582194", + expectedX: "faec7bc1987b63233fbc5f956edbf37d54404e7461c58ab8631bc68e451a0478", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff91192139ffffffffffffffffffffffffffffffffffffffffffffffffffffffff45f0f1eb", + expectedX: "ec29a50bae138dbf7d8e24825006bb5fc1a2cc1243ba335bc6116fb9e498ec1f", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff98eb9ab76e84499c483b3bf06214abfe065dddf43b8601de596d63b9e45a166a580541fe", + expectedX: "1e0ff2dee9b09b136292a9e910f0d6ac3e552a644bba39e64e9dd3e3bbd3d4d4", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff9b77b7f2c74d99efceaa550f1ad1c0f43f46e7ff1ee3bd0162b7bf55f2965da9c3450646", + expectedX: "8b7dd5c3edba9ee97b70eff438f22dca9849c8254a2f3345a0a572ffeaae0928", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff9b77b7f2ffffffffffffffffffffffffffffffffffffffffffffffffffffffff156ca896", + expectedX: "0881950c8f51d6b9a6387465d5f12609ef1bb25412a08a74cb2dfb200c74bfbf", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffa2f5cd838816c16c4fe8a1661d606fdb13cf9af04b979a2e159a09409ebc8645d58fde02", + expectedX: "2f083207b9fd9b550063c31cd62b8746bd543bdc5bbf10e3a35563e927f440c8", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffb13f75c00000000000000000000000000000000000000000000000000000000000000000", + expectedX: "4f51e0be078e0cddab2742156adba7e7a148e73157072fd618cd60942b146bd0", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffb13f75c0fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "4f51e0be078e0cddab2742156adba7e7a148e73157072fd618cd60942b146bd0", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffe7bc1f8d0000000000000000000000000000000000000000000000000000000000000000", + expectedX: "16c2ccb54352ff4bd794f6efd613c72197ab7082da5b563bdf9cb3edaafe74c2", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffe7bc1f8dfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", + expectedX: "16c2ccb54352ff4bd794f6efd613c72197ab7082da5b563bdf9cb3edaafe74c2", + }, + { + ellswift: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffef64d162750546ce42b0431361e52d4f5242d8f24f33e6b1f99b591647cbc808f462af51", + expectedX: "d41244d11ca4f65240687759f95ca9efbab767ededb38fd18c36e18cd3b6f6a9", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffff0e5be52372dd6e894b2a326fc3605a6e8f3c69c710bf27d630dfe2004988b78eb6eab36", + expectedX: "64bf84dd5e03670fdb24c0f5d3c2c365736f51db6c92d95010716ad2d36134c8", + }, + { + ellswift: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffefbb982fffffffffffffffffffffffffffffffffffffffffffffffffffffffff6d6db1f", + expectedX: "1c92ccdfcf4ac550c28db57cff0c8515cb26936c786584a70114008d6c33a34b", + }, + } + + for _, test := range tests { + // The test.ellswift variable is 128-bytes long and is composed of two + // 64-byte hexadecimal strings. The first 64-byte hex string is the u + // value and the other is the t-value. + uVal := setHex(test.ellswift[0:64]).Normalize() + tVal := setHex(test.ellswift[64:128]).Normalize() + + xVal := setHex(test.expectedX) + + if !XSwiftEC(uVal, tVal).Equals(xVal) { + t.Fatalf("encoding not equal to x") + } + } +} + +// TestXSwiftECInvVectors tests that the inverse of the ElligatorSwift encoding +// XSwiftECInv works as expected. In other words, given a u-value and an +// x-value, that the correct t-value is returned. Each test case has a cases +// array that determines which t-value should be returned for each +// corresponding case. +func TestXSwiftECInvVectors(t *testing.T) { + tests := []struct { + u string + x string + cases []string + }{ + { + u: "05ff6bdad900fc3261bc7fe34e2fb0f569f06e091ae437d3a52e9da0cbfb9590", + x: "80cdf63774ec7022c89a5a8558e373a279170285e0ab27412dbce510bdfe23fc", + cases: []string{ + "", + "", + "45654798ece071ba79286d04f7f3eb1c3f1d17dd883610f2ad2efd82a287466b", + "0aeaa886f6b76c7158452418cbf5033adc5747e9e9b5d3b2303db96936528557", + "", + "", + "ba9ab867131f8e4586d792fb080c14e3c0e2e82277c9ef0d52d1027c5d78b5c4", + "f51557790948938ea7badbe7340afcc523a8b816164a2c4dcfc24695c9ad76d8", + }, + }, + { + u: "1737a85f4c8d146cec96e3ffdca76d9903dcf3bd53061868d478c78c63c2aa9e", + x: "39e48dd150d2f429be088dfd5b61882e7e8407483702ae9a5ab35927b15f85ea", + cases: []string{ + "1be8cc0b04be0c681d0c6a68f733f82c6c896e0c8a262fcd392918e303a7abf4", + "605b5814bf9b8cb066667c9e5480d22dc5b6c92f14b4af3ee0a9eb83b03685e3", + "", + "", + "e41733f4fb41f397e2f3959708cc07d3937691f375d9d032c6d6e71bfc58503b", + "9fa4a7eb4064734f99998361ab7f2dd23a4936d0eb4b50c11f56147b4fc9764c", + "", + "", + }, + }, + { + u: "1aaa1ccebf9c724191033df366b36f691c4d902c228033ff4516d122b2564f68", + x: "c75541259d3ba98f207eaa30c69634d187d0b6da594e719e420f4898638fc5b0", + cases: []string{ + "", + "", + "", + "", + "", + "", + "", + "", + }, + }, + { + u: "2323a1d079b0fd72fc8bb62ec34230a815cb0596c2bfac998bd6b84260f5dc26", + x: "239342dfb675500a34a196310b8d87d54f49dcac9da50c1743ceab41a7b249ff", + cases: []string{ + "f63580b8aa49c4846de56e39e1b3e73f171e881eba8c66f614e67e5c975dfc07", + "b6307b332e699f1cf77841d90af25365404deb7fed5edb3090db49e642a156b6", + "", + "", + "09ca7f4755b63b7b921a91c61e4c18c0e8e177e145739909eb1981a268a20028", + "49cf84ccd19660e30887be26f50dac9abfb2148012a124cf6f24b618bd5ea579", + "", + "", + }, + }, + { + u: "2dc90e640cb646ae9164c0b5a9ef0169febe34dc4437d6e46acb0e27e219d1e8", + x: "d236f19bf349b9516e9b3f4a5610fe960141cb23bbc8291b9534f1d71de62a47", + cases: []string{ + "e69df7d9c026c36600ebdf588072675847c0c431c8eb730682533e964b6252c9", + "4f18bbdf7c2d6c5f818c18802fa35cd069eaa79fff74e4fc837c80d93fece2f8", + "", + "", + "196208263fd93c99ff1420a77f8d98a7b83f3bce37148cf97dacc168b49da966", + "b0e7442083d293a07e73e77fd05ca32f96155860008b1b037c837f25c0131937", + "", + "", + }, + }, + { + u: "3edd7b3980e2f2f34d1409a207069f881fda5f96f08027ac4465b63dc278d672", + x: "053a98de4a27b1961155822b3a3121f03b2a14458bd80eb4a560c4c7a85c149c", + cases: []string{ + "", + "", + "b3dae4b7dcf858e4c6968057cef2b156465431526538199cf52dc1b2d62fda30", + "4aa77dd55d6b6d3cfa10cc9d0fe42f79232e4575661049ae36779c1d0c666d88", + "", + "", + "4c251b482307a71b39697fa8310d4ea9b9abcead9ac7e6630ad23e4c29d021ff", + "b558822aa29492c305ef3362f01bd086dcd1ba8a99efb651c98863e1f3998ea7", + }, + }, + { + u: "4295737efcb1da6fb1d96b9ca7dcd1e320024b37a736c4948b62598173069f70", + x: "fa7ffe4f25f88362831c087afe2e8a9b0713e2cac1ddca6a383205a266f14307", + cases: []string{ + "", + "", + "", + "", + "", + "", + "", + "", + }, + }, + { + u: "587c1a0cee91939e7f784d23b963004a3bf44f5d4e32a0081995ba20b0fca59e", + x: "2ea988530715e8d10363907ff25124524d471ba2454d5ce3be3f04194dfd3a3c", + cases: []string{ + "cfd5a094aa0b9b8891b76c6ab9438f66aa1c095a65f9f70135e8171292245e74", + "a89057d7c6563f0d6efa19ae84412b8a7b47e791a191ecdfdf2af84fd97bc339", + "475d0ae9ef46920df07b34117be5a0817de1023e3cc32689e9be145b406b0aef", + "a0759178ad80232454f827ef05ea3e72ad8d75418e6d4cc1cd4f5306c5e7c453", + "302a5f6b55f464776e48939546bc709955e3f6a59a0608feca17e8ec6ddb9dbb", + "576fa82839a9c0f29105e6517bbed47584b8186e5e6e132020d507af268438f6", + "b8a2f51610b96df20f84cbee841a5f7e821efdc1c33cd9761641eba3bf94f140", + "5f8a6e87527fdcdbab07d810fa15c18d52728abe7192b33e32b0acf83a1837dc", + }, + }, + { + u: 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