btcec: Slightly optimize NAF and add several tests.
This slightly optimizes the NAF function by avoiding returning the unused bit when there is not a carry. It also adds a bunch of additional unit tests which I made while debugging.
This commit is contained in:
Jimmy Song
Dave Collins
parent
1238b7e55a
commit
1bdb713285
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@ -747,9 +747,9 @@ func NAF(k []byte) ([]byte, []byte) {
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}
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if carry {
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retPos[0] = 1
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return retPos, retNeg
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}
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return retPos, retNeg
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return retPos[1:], retNeg[1:]
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}
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// ScalarMult returns k*(Bx, By) where k is a big endian integer.
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@ -65,7 +65,6 @@ func TestAddJacobian(t *testing.T) {
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"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
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"1",
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},
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// Addition with z1=z2=1 different x values.
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{
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"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
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@ -397,6 +396,15 @@ func TestDoubleJacobian(t *testing.T) {
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"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
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"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
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},
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// From btcd issue #709.
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{
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"201e3f75715136d2f93c4f4598f91826f94ca01f4233a5bd35de9708859ca50d",
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"bdf18566445e7562c6ada68aef02d498d7301503de5b18c6aef6e2b1722412e1",
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"0000000000000000000000000000000000000000000000000000000000000001",
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"4a5e0559863ebb4e9ed85f5c4fa76003d05d9a7626616e614a1f738621e3c220",
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"00000000000000000000000000000000000000000000000000000001b1388778",
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"7be30acc88bceac58d5b4d15de05a931ae602a07bcb6318d5dedc563e4482993",
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},
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}
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t.Logf("Running %d tests", len(tests))
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@ -591,6 +599,46 @@ func TestBaseMultVerify(t *testing.T) {
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}
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func TestScalarMult(t *testing.T) {
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tests := []struct {
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x string
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y string
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k string
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rx string
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ry string
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}{
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// base mult, essentially.
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{
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"79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
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"483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8",
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"18e14a7b6a307f426a94f8114701e7c8e774e7f9a47e2c2035db29a206321725",
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"50863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352",
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"2cd470243453a299fa9e77237716103abc11a1df38855ed6f2ee187e9c582ba6",
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},
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// From btcd issue #709.
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{
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"000000000000000000000000000000000000000000000000000000000000002c",
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"420e7a99bba18a9d3952597510fd2b6728cfeafc21a4e73951091d4d8ddbe94e",
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"a2e8ba2e8ba2e8ba2e8ba2e8ba2e8ba219b51835b55cc30ebfe2f6599bc56f58",
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"a2112dcdfbcd10ae1133a358de7b82db68e0a3eb4b492cc8268d1e7118c98788",
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"27fc7463b7bb3c5f98ecf2c84a6272bb1681ed553d92c69f2dfe25a9f9fd3836",
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},
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}
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s256 := S256()
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for i, test := range tests {
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x, _ := new(big.Int).SetString(test.x, 16)
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y, _ := new(big.Int).SetString(test.y, 16)
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k, _ := new(big.Int).SetString(test.k, 16)
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xWant, _ := new(big.Int).SetString(test.rx, 16)
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yWant, _ := new(big.Int).SetString(test.ry, 16)
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xGot, yGot := s256.ScalarMult(x, y, k.Bytes())
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if xGot.Cmp(xWant) != 0 || yGot.Cmp(yWant) != 0 {
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t.Fatalf("%d: bad output: got (%X, %X), want (%X, %X)", i, xGot, yGot, xWant, yWant)
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}
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}
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}
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func TestScalarMultRand(t *testing.T) {
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// Strategy for this test:
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// Get a random exponent from the generator point at first
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// This creates a new point which is used in the next iteration
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@ -617,6 +665,118 @@ func TestScalarMult(t *testing.T) {
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}
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}
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func TestSplitK(t *testing.T) {
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tests := []struct {
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k string
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k1, k2 string
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s1, s2 int
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}{
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{
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"6df2b5d30854069ccdec40ae022f5c948936324a4e9ebed8eb82cfd5a6b6d766",
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"00000000000000000000000000000000b776e53fb55f6b006a270d42d64ec2b1",
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"00000000000000000000000000000000d6cc32c857f1174b604eefc544f0c7f7",
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-1, -1,
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},
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{
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"6ca00a8f10632170accc1b3baf2a118fa5725f41473f8959f34b8f860c47d88d",
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"0000000000000000000000000000000007b21976c1795723c1bfbfa511e95b84",
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"00000000000000000000000000000000d8d2d5f9d20fc64fd2cf9bda09a5bf90",
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1, -1,
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},
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{
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"b2eda8ab31b259032d39cbc2a234af17fcee89c863a8917b2740b67568166289",
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"00000000000000000000000000000000507d930fecda7414fc4a523b95ef3c8c",
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"00000000000000000000000000000000f65ffb179df189675338c6185cb839be",
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-1, -1,
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},
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{
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"f6f00e44f179936f2befc7442721b0633f6bafdf7161c167ffc6f7751980e3a0",
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"0000000000000000000000000000000008d0264f10bcdcd97da3faa38f85308d",
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"0000000000000000000000000000000065fed1506eb6605a899a54e155665f79",
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-1, -1,
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},
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{
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"8679085ab081dc92cdd23091ce3ee998f6b320e419c3475fae6b5b7d3081996e",
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"0000000000000000000000000000000089fbf24fbaa5c3c137b4f1cedc51d975",
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"00000000000000000000000000000000d38aa615bd6754d6f4d51ccdaf529fea",
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-1, -1,
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},
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{
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"6b1247bb7931dfcae5b5603c8b5ae22ce94d670138c51872225beae6bba8cdb3",
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"000000000000000000000000000000008acc2a521b21b17cfb002c83be62f55d",
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"0000000000000000000000000000000035f0eff4d7430950ecb2d94193dedc79",
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-1, -1,
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},
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{
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"a2e8ba2e8ba2e8ba2e8ba2e8ba2e8ba219b51835b55cc30ebfe2f6599bc56f58",
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"0000000000000000000000000000000045c53aa1bb56fcd68c011e2dad6758e4",
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"00000000000000000000000000000000a2e79d200f27f2360fba57619936159b",
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-1, -1,
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},
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}
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s256 := S256()
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for i, test := range tests {
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k, ok := new(big.Int).SetString(test.k, 16)
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if !ok {
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t.Errorf("%d: bad value for k: %s", i, test.k)
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}
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k1, k2, k1Sign, k2Sign := s256.splitK(k.Bytes())
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k1str := fmt.Sprintf("%064x", k1)
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if test.k1 != k1str {
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t.Errorf("%d: bad k1: got %v, want %v", i, k1str, test.k1)
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}
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k2str := fmt.Sprintf("%064x", k2)
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if test.k2 != k2str {
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t.Errorf("%d: bad k2: got %v, want %v", i, k2str, test.k2)
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}
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if test.s1 != k1Sign {
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t.Errorf("%d: bad k1 sign: got %d, want %d", i, k1Sign, test.s1)
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}
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if test.s2 != k2Sign {
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t.Errorf("%d: bad k2 sign: got %d, want %d", i, k2Sign, test.s2)
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}
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k1Int := new(big.Int).SetBytes(k1)
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k1SignInt := new(big.Int).SetInt64(int64(k1Sign))
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k1Int.Mul(k1Int, k1SignInt)
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k2Int := new(big.Int).SetBytes(k2)
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k2SignInt := new(big.Int).SetInt64(int64(k2Sign))
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k2Int.Mul(k2Int, k2SignInt)
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gotK := new(big.Int).Mul(k2Int, s256.lambda)
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gotK.Add(k1Int, gotK)
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gotK.Mod(gotK, s256.N)
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if k.Cmp(gotK) != 0 {
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t.Errorf("%d: bad k: got %X, want %X", i, gotK.Bytes(), k.Bytes())
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}
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}
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}
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func TestSplitKRand(t *testing.T) {
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s256 := S256()
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for i := 0; i < 1024; i++ {
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bytesK := make([]byte, 32)
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_, err := rand.Read(bytesK)
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if err != nil {
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t.Fatalf("failed to read random data at %d", i)
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break
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}
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k := new(big.Int).SetBytes(bytesK)
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k1, k2, k1Sign, k2Sign := s256.splitK(bytesK)
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k1Int := new(big.Int).SetBytes(k1)
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k1SignInt := new(big.Int).SetInt64(int64(k1Sign))
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k1Int.Mul(k1Int, k1SignInt)
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k2Int := new(big.Int).SetBytes(k2)
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k2SignInt := new(big.Int).SetInt64(int64(k2Sign))
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k2Int.Mul(k2Int, k2SignInt)
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gotK := new(big.Int).Mul(k2Int, s256.lambda)
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gotK.Add(k1Int, gotK)
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gotK.Mod(gotK, s256.N)
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if k.Cmp(gotK) != 0 {
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t.Errorf("%d: bad k: got %X, want %X", i, gotK.Bytes(), k.Bytes())
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}
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}
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}
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// Test this curve's usage with the ecdsa package.
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func testKeyGeneration(t *testing.T, c *KoblitzCurve, tag string) {
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@ -660,6 +820,42 @@ func TestSignAndVerify(t *testing.T) {
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}
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func TestNAF(t *testing.T) {
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tests := []string{
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"6df2b5d30854069ccdec40ae022f5c948936324a4e9ebed8eb82cfd5a6b6d766",
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"b776e53fb55f6b006a270d42d64ec2b1",
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"d6cc32c857f1174b604eefc544f0c7f7",
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"45c53aa1bb56fcd68c011e2dad6758e4",
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"a2e79d200f27f2360fba57619936159b",
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}
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negOne := big.NewInt(-1)
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one := big.NewInt(1)
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two := big.NewInt(2)
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for i, test := range tests {
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want, _ := new(big.Int).SetString(test, 16)
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nafPos, nafNeg := NAF(want.Bytes())
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got := big.NewInt(0)
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// Check that the NAF representation comes up with the right number
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for i := 0; i < len(nafPos); i++ {
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bytePos := nafPos[i]
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byteNeg := nafNeg[i]
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for j := 7; j >= 0; j-- {
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got.Mul(got, two)
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if bytePos&0x80 == 0x80 {
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got.Add(got, one)
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} else if byteNeg&0x80 == 0x80 {
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got.Add(got, negOne)
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}
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bytePos <<= 1
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byteNeg <<= 1
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}
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}
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if got.Cmp(want) != 0 {
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t.Errorf("%d: Failed NAF got %X want %X", i, got, want)
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}
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}
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}
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func TestNAFRand(t *testing.T) {
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negOne := big.NewInt(-1)
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one := big.NewInt(1)
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two := big.NewInt(2)
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