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ellswift: introduce ElligatorSwift encoding and decoding funcs

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The BIP324 ElligatorSwift test vectors are also included.
This commit is contained in:
Eugene Siegel 2024-07-18 19:47:51 -04:00
parent 67b8efd3ba
commit d0706cdac4
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GPG key ID: 118759E83439A9B1
2 changed files with 1211 additions and 0 deletions
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392
btcec/ellswift.go Normal file
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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,
}
ellswiftTag = []byte("bip324_ellswift_xonly_ecdh")
// 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(priv⋅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(ellswiftTag, msg), nil
}
var msg []byte
msg = append(msg, ellswiftTheirs[:]...)
msg = append(msg, ellswiftOurs[:]...)
msg = append(msg, ecdhPoint[:]...)
return chainhash.TaggedHash(ellswiftTag, msg), nil
}

819
btcec/ellswift_test.go Normal file
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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: "5fa88b3365a635cbbcee003cce9ef51dd1a310de277e441abccdb7be1e4ba249",
x: "79461ff62bfcbcac4249ba84dd040f2cec3c63f725204dc7f464c16bf0ff3170",
cases: []string{
"",
"",
"6bb700e1f4d7e236e8d193ff4a76c1b3bcd4e2b25acac3d51c8dac653fe909a0",
"f4c73410633da7f63a4f1d55aec6dd32c4c6d89ee74075edb5515ed90da9e683",
"",
"",
"9448ff1e0b281dc9172e6c00b5893e4c432b1d4da5353c2ae3725399c016f28f",
"0b38cbef9cc25809c5b0e2aa513922cd3b39276118bf8a124aaea125f25615ac",
},
},
{
u: "6fb31c7531f03130b42b155b952779efbb46087dd9807d241a48eac63c3d96d6",
x: "56f81be753e8d4ae4940ea6f46f6ec9fda66a6f96cc95f506cb2b57490e94260",
cases: []string{
"",
"",
"59059774795bdb7a837fbe1140a5fa59984f48af8df95d57dd6d1c05437dcec1",
"22a644db79376ad4e7b3a009e58b3f13137c54fdf911122cc93667c47077d784",
"",
"",
"a6fa688b86a424857c8041eebf5a05a667b0b7507206a2a82292e3f9bc822d6e",
"dd59bb2486c8952b184c5ff61a74c0ecec83ab0206eeedd336c9983a8f8824ab",
},
},
{
u: "704cd226e71cb6826a590e80dac90f2d2f5830f0fdf135a3eae3965bff25ff12",
x: "138e0afa68936ee670bd2b8db53aedbb7bea2a8597388b24d0518edd22ad66ec",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "725e914792cb8c8949e7e1168b7cdd8a8094c91c6ec2202ccd53a6a18771edeb",
x: "8da16eb86d347376b6181ee9748322757f6b36e3913ddfd332ac595d788e0e44",
cases: []string{
"dd357786b9f6873330391aa5625809654e43116e82a5a5d82ffd1d6624101fc4",
"a0b7efca01814594c59c9aae8e49700186ca5d95e88bcc80399044d9c2d8613d",
"",
"",
"22ca8879460978cccfc6e55a9da7f69ab1bcee917d5a5a27d002e298dbefdc6b",
"5f481035fe7eba6b3a63655171b68ffe7935a26a1774337fc66fbb253d279af2",
"",
"",
},
},
{
u: "78fe6b717f2ea4a32708d79c151bf503a5312a18c0963437e865cc6ed3f6ae97",
x: "8701948e80d15b5cd8f72863eae40afc5aced5e73f69cbc8179a33902c094d98",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "7c37bb9c5061dc07413f11acd5a34006e64c5c457fdb9a438f217255a961f50d",
x: "5c1a76b44568eb59d6789a7442d9ed7cdc6226b7752b4ff8eaf8e1a95736e507",
cases: []string{
"",
"",
"b94d30cd7dbff60b64620c17ca0fafaa40b3d1f52d077a60a2e0cafd145086c2",
"",
"",
"",
"46b2cf32824009f49b9df3e835f05055bf4c2e0ad2f8859f5d1f3501ebaf756d",
"",
},
},
{
u: "82388888967f82a6b444438a7d44838e13c0d478b9ca060da95a41fb94303de6",
x: "29e9654170628fec8b4972898b113cf98807f4609274f4f3140d0674157c90a0",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "91298f5770af7a27f0a47188d24c3b7bf98ab2990d84b0b898507e3c561d6472",
x: "144f4ccbd9a74698a88cbf6fd00ad886d339d29ea19448f2c572cac0a07d5562",
cases: []string{
"e6a0ffa3807f09dadbe71e0f4be4725f2832e76cad8dc1d943ce839375eff248",
"837b8e68d4917544764ad0903cb11f8615d2823cefbb06d89049dbabc69befda",
"",
"",
"195f005c7f80f6252418e1f0b41b8da0d7cd189352723e26bc317c6b8a1009e7",
"7c8471972b6e8abb89b52f6fc34ee079ea2d7dc31044f9276fb6245339640c55",
"",
"",
},
},
{
u: "b682f3d03bbb5dee4f54b5ebfba931b4f52f6a191e5c2f483c73c66e9ace97e1",
x: "904717bf0bc0cb7873fcdc38aa97f19e3a62630972acff92b24cc6dda197cb96",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "c17ec69e665f0fb0dbab48d9c2f94d12ec8a9d7eacb58084833091801eb0b80b",
x: "147756e66d96e31c426d3cc85ed0c4cfbef6341dd8b285585aa574ea0204b55e",
cases: []string{
"6f4aea431a0043bdd03134d6d9159119ce034b88c32e50e8e36c4ee45eac7ae9",
"fd5be16d4ffa2690126c67c3ef7cb9d29b74d397c78b06b3605fda34dc9696a6",
"5e9c60792a2f000e45c6250f296f875e174efc0e9703e628706103a9dd2d82c7",
"",
"90b515bce5ffbc422fcecb2926ea6ee631fcb4773cd1af171c93b11aa1538146",
"02a41e92b005d96fed93983c1083462d648b2c683874f94c9fa025ca23696589",
"a1639f86d5d0fff1ba39daf0d69078a1e8b103f168fc19d78f9efc5522d27968",
"",
},
},
{
u: "c25172fc3f29b6fc4a1155b8575233155486b27464b74b8b260b499a3f53cb14",
x: "1ea9cbdb35cf6e0329aa31b0bb0a702a65123ed008655a93b7dcd5280e52e1ab",
cases: []string{
"",
"",
"7422edc7843136af0053bb8854448a8299994f9ddcefd3a9a92d45462c59298a",
"78c7774a266f8b97ea23d05d064f033c77319f923f6b78bce4e20bf05fa5398d",
"",
"",
"8bdd12387bcec950ffac4477abbb757d6666b06223102c5656d2bab8d3a6d2a5",
"873888b5d990746815dc2fa2f9b0fcc388ce606dc09487431b1df40ea05ac2a2",
},
},
{
u: "cab6626f832a4b1280ba7add2fc5322ff011caededf7ff4db6735d5026dc0367",
x: "2b2bef0852c6f7c95d72ac99a23802b875029cd573b248d1f1b3fc8033788eb6",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "d8621b4ffc85b9ed56e99d8dd1dd24aedcecb14763b861a17112dc771a104fd2",
x: "812cabe972a22aa67c7da0c94d8a936296eb9949d70c37cb2b2487574cb3ce58",
cases: []string{
"fbc5febc6fdbc9ae3eb88a93b982196e8b6275a6d5a73c17387e000c711bd0e3",
"8724c96bd4e5527f2dd195a51c468d2d211ba2fac7cbe0b4b3434253409fb42d",
"",
"",
"043a014390243651c147756c467de691749d8a592a58c3e8c781fff28ee42b4c",
"78db36942b1aad80d22e6a5ae3b972d2dee45d0538341f4b4cbcbdabbf604802",
"",
"",
},
},
{
u: "da463164c6f4bf7129ee5f0ec00f65a675a8adf1bd931b39b64806afdcda9a22",
x: "25b9ce9b390b408ed611a0f13ff09a598a57520e426ce4c649b7f94f2325620d",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "dafc971e4a3a7b6dcfb42a08d9692d82ad9e7838523fcbda1d4827e14481ae2d",
x: "250368e1b5c58492304bd5f72696d27d526187c7adc03425e2b7d81dbb7e4e02",
cases: []string{
"",
"",
"370c28f1be665efacde6aa436bf86fe21e6e314c1e53dd040e6c73a46b4c8c49",
"cd8acee98ffe56531a84d7eb3e48fa4034206ce825ace907d0edf0eaeb5e9ca2",
"",
"",
"c8f3d70e4199a105321955bc9407901de191ceb3e1ac22fbf1938c5a94b36fe6",
"327531167001a9ace57b2814c1b705bfcbdf9317da5316f82f120f1414a15f8d",
},
},
{
u: "e0294c8bc1a36b4166ee92bfa70a5c34976fa9829405efea8f9cd54dcb29b99e",
x: "ae9690d13b8d20a0fbbf37bed8474f67a04e142f56efd78770a76b359165d8a1",
cases: []string{
"",
"",
"dcd45d935613916af167b029058ba3a700d37150b9df34728cb05412c16d4182",
"",
"",
"",
"232ba26ca9ec6e950e984fd6fa745c58ff2c8eaf4620cb8d734fabec3e92baad",
"",
},
},
{
u: "e148441cd7b92b8b0e4fa3bd68712cfd0d709ad198cace611493c10e97f5394e",
x: "164a639794d74c53afc4d3294e79cdb3cd25f99f6df45c000f758aba54d699c0",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "e4b00ec97aadcca97644d3b0c8a931b14ce7bcf7bc8779546d6e35aa5937381c",
x: "94e9588d41647b3fcc772dc8d83c67ce3be003538517c834103d2cd49d62ef4d",
cases: []string{
"c88d25f41407376bb2c03a7fffeb3ec7811cc43491a0c3aac0378cdc78357bee",
"51c02636ce00c2345ecd89adb6089fe4d5e18ac924e3145e6669501cd37a00d4",
"205b3512db40521cb200952e67b46f67e09e7839e0de44004138329ebd9138c5",
"58aab390ab6fb55c1d1b80897a207ce94a78fa5b4aa61a33398bcae9adb20d3e",
"3772da0bebf8c8944d3fc5800014c1387ee33bcb6e5f3c553fc8732287ca8041",
"ae3fd9c931ff3dcba132765249f7601b2a1e7536db1ceba19996afe22c85fb5b",
"dfa4caed24bfade34dff6ad1984b90981f6187c61f21bbffbec7cd60426ec36a",
"a7554c6f54904aa3e2e47f7685df8316b58705a4b559e5ccc6743515524deef1",
},
},
{
u: "e5bbb9ef360d0a501618f0067d36dceb75f5be9a620232aa9fd5139d0863fde5",
x: "e5bbb9ef360d0a501618f0067d36dceb75f5be9a620232aa9fd5139d0863fde5",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
{
u: "e6bcb5c3d63467d490bfa54fbbc6092a7248c25e11b248dc2964a6e15edb1457",
x: "19434a3c29cb982b6f405ab04439f6d58db73da1ee4db723d69b591da124e7d8",
cases: []string{
"67119877832ab8f459a821656d8261f544a553b89ae4f25c52a97134b70f3426",
"ffee02f5e649c07f0560eff1867ec7b32d0e595e9b1c0ea6e2a4fc70c97cd71f",
"b5e0c189eb5b4bacd025b7444d74178be8d5246cfa4a9a207964a057ee969992",
"5746e4591bf7f4c3044609ea372e908603975d279fdef8349f0b08d32f07619d",
"98ee67887cd5470ba657de9a927d9e0abb5aac47651b0da3ad568eca48f0c809",
"0011fd0a19b63f80fa9f100e7981384cd2f1a6a164e3f1591d5b038e36832510",
"4a1f3e7614a4b4532fda48bbb28be874172adb9305b565df869b5fa71169629d",
"a8b91ba6e4080b3cfbb9f615c8d16f79fc68a2d8602107cb60f4f72bd0f89a92",
},
},
{
u: "f28fba64af766845eb2f4302456e2b9f8d80affe57e7aae42738d7cddb1c2ce6",
x: "f28fba64af766845eb2f4302456e2b9f8d80affe57e7aae42738d7cddb1c2ce6",
cases: []string{
"4f867ad8bb3d840409d26b67307e62100153273f72fa4b7484becfa14ebe7408",
"5bbc4f59e452cc5f22a99144b10ce8989a89a995ec3cea1c91ae10e8f721bb5d",
"",
"",
"b079852744c27bfbf62d9498cf819deffeacd8c08d05b48b7b41305db1418827",
"a443b0a61bad33a0dd566ebb4ef317676576566a13c315e36e51ef1608de40d2",
"",
"",
},
},
{
u: "f455605bc85bf48e3a908c31023faf98381504c6c6d3aeb9ede55f8dd528924d",
x: "d31fbcd5cdb798f6c00db6692f8fe8967fa9c79dd10958f4a194f01374905e99",
cases: []string{
"",
"",
"0c00c5715b56fe632d814ad8a77f8e66628ea47a6116834f8c1218f3a03cbd50",
"df88e44fac84fa52df4d59f48819f18f6a8cd4151d162afaf773166f57c7ff46",
"",
"",
"f3ff3a8ea4a9019cd27eb527588071999d715b859ee97cb073ede70b5fc33edf",
"20771bb0537b05ad20b2a60b77e60e7095732beae2e9d505088ce98fa837fce9",
},
},
{
u: "f58cd4d9830bad322699035e8246007d4be27e19b6f53621317b4f309b3daa9d",
x: "78ec2b3dc0948de560148bbc7c6dc9633ad5df70a5a5750cbed721804f082a3b",
cases: []string{
"6c4c580b76c7594043569f9dae16dc2801c16a1fbe12860881b75f8ef929bce5",
"94231355e7385c5f25ca436aa64191471aea4393d6e86ab7a35fe2afacaefd0d",
"dff2a1951ada6db574df834048149da3397a75b829abf58c7e69db1b41ac0989",
"a52b66d3c907035548028bf804711bf422aba95f1a666fc86f4648e05f29caae",
"93b3a7f48938a6bfbca9606251e923d7fe3e95e041ed79f77e48a07006d63f4a",
"6bdcecaa18c7a3a0da35bc9559be6eb8e515bc6c291795485ca01d4f5350ff22",
"200d5e6ae525924a8b207cbfb7eb625cc6858a47d6540a73819624e3be53f2a6",
"5ad4992c36f8fcaab7fd7407fb8ee40bdd5456a0e599903790b9b71ea0d63181",
},
},
{
u: "fd7d912a40f182a3588800d69ebfb5048766da206fd7ebc8d2436c81cbef6421",
x: "8d37c862054debe731694536ff46b273ec122b35a9bf1445ac3c4ff9f262c952",
cases: []string{
"",
"",
"",
"",
"",
"",
"",
"",
},
},
}
for _, test := range tests {
uVal := setHex(test.u).Normalize()
xVal := setHex(test.x).Normalize()
// Loop through each individual case in the list of cases and ensure
// that the correct t-value is calculated.
for caseNum, expTString := range test.cases {
tVal := XSwiftECInv(uVal, xVal, caseNum)
if tVal == nil {
if expTString != "" {
t.Fatalf("t value different than expected")
}
continue
}
expectedT := setHex(expTString)
if !tVal.Equals(expectedT) {
t.Fatalf("t value different than expected")
}
}
}
}