// TestEquals ensures that checking two field values for equality via Equals
// works as expected.
func TestEquals(t *testing.T) {
tests := []struct {
in1 string // hex encoded value
in2 string // hex encoded value
expected bool // expected equality
}{
{"0", "0", true},
{"0", "1", false},
{"1", "0", false},
// 2^32 - 1 == 2^32 - 1?
{"ffffffff", "ffffffff", true},
// 2^64 - 1 == 2^64 - 2?
{"ffffffffffffffff", "fffffffffffffffe", false},
// 0 == prime (mod prime)?
{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
// 1 == prime+1 (mod prime)?
{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30", true},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
result := f.Equals(f2)
if result != test.expected {
t.Errorf("fieldVal.Equals #%d wrong result\n"+
"got: %v\nwant: %v", i, result, test.expected)
continue
}
}
}
// TestMul ensures that multiplying two field valuess via Mul works as expected.
func TestMul(t *testing.T) {
tests := []struct {
in1 string // first hex encoded value
in2 string // second hex encoded value to multiply with
expected string // expected hex encoded value
}{
{"0", "0", "0"},
{"1", "0", "0"},
{"0", "1", "0"},
{"1", "1", "1"},
// secp256k1 prime-1 * 2
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
"2",
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
},
// secp256k1 prime * 3
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "3", "0"},
// secp256k1 prime-1 * 8
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
"8",
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
},
// Random samples.
{
"cfb81753d5ef499a98ecc04c62cb7768c2e4f1740032946db1c12e405248137e",
"58f355ad27b4d75fb7db0442452e732c436c1f7c5a7c4e214fa9cc031426a7d3",
"1018cd2d7c2535235b71e18db9cd98027386328d2fa6a14b36ec663c4c87282b",
},
{
"26e9d61d1cdf3920e9928e85fa3df3e7556ef9ab1d14ec56d8b4fc8ed37235bf",
"2dfc4bbe537afee979c644f8c97b31e58be5296d6dbc460091eae630c98511cf",
"da85f48da2dc371e223a1ae63bd30b7e7ee45ae9b189ac43ff357e9ef8cf107a",
},
{
"5db64ed5afb71646c8b231585d5b2bf7e628590154e0854c4c29920b999ff351",
"279cfae5eea5d09ade8e6a7409182f9de40981bc31c84c3d3dfe1d933f152e9a",
"2c78fbae91792dd0b157abe3054920049b1879a7cc9d98cfda927d83be411b37",
},
{
"b66dfc1f96820b07d2bdbd559c19319a3a73c97ceb7b3d662f4fe75ecb6819e6",
"bf774aba43e3e49eb63a6e18037d1118152568f1a3ac4ec8b89aeb6ff8008ae1",
"c4f016558ca8e950c21c3f7fc15f640293a979c7b01754ee7f8b3340d4902ebb",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Mul(f2).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Mul #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestInverse ensures that finding the multiplicative inverse via Inverse works
// as expected.
func TestInverse(t *testing.T) {
tests := []struct {
in string // hex encoded value
expected string // expected hex encoded value
}{
// secp256k1 prime (aka 0)
{"0", "0"},
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
// secp256k1 prime-1
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
},
// secp256k1 prime-2
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
"7fffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffe17",
},
// Random sampling
{
"16fb970147a9acc73654d4be233cc48b875ce20a2122d24f073d29bd28805aca",
"987aeb257b063df0c6d1334051c47092b6d8766c4bf10c463786d93f5bc54354",
},
{
"69d1323ce9f1f7b3bd3c7320b0d6311408e30281e273e39a0d8c7ee1c8257919",
"49340981fa9b8d3dad72de470b34f547ed9179c3953797d0943af67806f4bb6",
},
{
"e0debf988ae098ecda07d0b57713e97c6d213db19753e8c95aa12a2fc1cc5272",
"64f58077b68af5b656b413ea366863f7b2819f8d27375d9c4d9804135ca220c2",
},
{
"dcd394f91f74c2ba16aad74a22bb0ed47fe857774b8f2d6c09e28bfb14642878",
"fb848ec64d0be572a63c38fe83df5e7f3d032f60bf8c969ef67d36bf4ada22a9",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Inverse().Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Inverse #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestAdd ensures that adding two field values together via Add works as
// expected.
func TestAdd(t *testing.T) {
tests := []struct {
in1 string // first hex encoded value
in2 string // second hex encoded value to add
expected string // expected hex encoded value
}{
{"0", "1", "1"},
{"1", "0", "1"},
{"1", "1", "2"},
// secp256k1 prime-1 + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
// secp256k1 prime + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
// Random samples.
{
"2b2012f975404e5065b4292fb8bed0a5d315eacf24c74d8b27e73bcc5430edcc",
"2c3cefa4e4753e8aeec6ac4c12d99da4d78accefda3b7885d4c6bab46c86db92",
"575d029e59b58cdb547ad57bcb986e4aaaa0b7beff02c610fcadf680c0b7c95e",
},
{
"8131e8722fe59bb189692b96c9f38de92885730f1dd39ab025daffb94c97f79c",
"ff5454b765f0aab5f0977dcc629becc84cabeb9def48e79c6aadb2622c490fa9",
"80863d2995d646677a00a9632c8f7ab175315ead0d1c824c9088b21c78e10b16",
},
{
"c7c95e93d0892b2b2cdd77e80eb646ea61be7a30ac7e097e9f843af73fad5c22",
"3afe6f91a74dfc1c7f15c34907ee981656c37236d946767dd53ccad9190e437c",
"02c7ce2577d72747abf33b3116a4df00b881ec6785c47ffc74c105d158bba36f",
},
{
"fd1c26f6a23381e5d785ba889494ec059369b888ad8431cd67d8c934b580dbe1",
"a475aa5a31dcca90ef5b53c097d9133d6b7117474b41e7877bb199590fc0489c",
"a191d150d4104c76c6e10e492c6dff42fedacfcff8c61954e38a628ec541284e",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Add(f2).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Add #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestAdd2 ensures that adding two field values together via Add2 works as
// expected.
func TestAdd2(t *testing.T) {
tests := []struct {
in1 string // first hex encoded value
in2 string // second hex encoded value to add
expected string // expected hex encoded value
}{
{"0", "1", "1"},
{"1", "0", "1"},
{"1", "1", "2"},
// secp256k1 prime-1 + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
// secp256k1 prime + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
// Random samples.
{
"ad82b8d1cc136e23e9fd77fe2c7db1fe5a2ecbfcbde59ab3529758334f862d28",
"4d6a4e95d6d61f4f46b528bebe152d408fd741157a28f415639347a84f6f574b",
"faed0767a2e98d7330b2a0bcea92df3eea060d12380e8ec8b62a9fdb9ef58473",
},
{
"f3f43a2540054a86e1df98547ec1c0e157b193e5350fb4a3c3ea214b228ac5e7",
"25706572592690ea3ddc951a1b48b504a4c83dc253756e1b96d56fdfb3199522",
"19649f97992bdb711fbc2d6e9a0a75e5fc79d1a7888522bf5abf912bd5a45eda",
},
{
"6915bb94eef13ff1bb9b2633d997e13b9b1157c713363cc0e891416d6734f5b8",
"11f90d6ac6fe1c4e8900b1c85fb575c251ec31b9bc34b35ada0aea1c21eded22",
"7b0ec8ffb5ef5c40449bd7fc394d56fdecfd8980cf6af01bc29c2b898922e2da",
},
{
"48b0c9eae622eed9335b747968544eb3e75cb2dc8128388f948aa30f88cabde4",
"0989882b52f85f9d524a3a3061a0e01f46d597839d2ba637320f4b9510c8d2d5",
"523a5216391b4e7685a5aea9c9f52ed32e324a601e53dec6c699eea4999390b9",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Add2(f, f2).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Add2 #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestAddInt ensures that adding an integer to field values via AddInt works as
// expected.
func TestAddInt(t *testing.T) {
tests := []struct {
in1 string // hex encoded value
in2 uint // unsigned integer to add to the value above
expected string // expected hex encoded value
}{
{"0", 1, "1"},
{"1", 0, "1"},
{"1", 1, "2"},
// secp256k1 prime-1 + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", 1, "0"},
// secp256k1 prime + 1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 1, "1"},
// Random samples.
{
"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d6c1",
0x10f,
"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d7d0",
},
{
"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41deea9cecf",
0x2cf11d41,
"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41e1b9aec10",
},
{
"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f7105122c9c",
0x4829aa2d,
"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f714d3bd6c9",
},
{
"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee09a015e2a6",
0xa21265a5,
"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee0a4228484b",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.AddInt(test.in2).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.AddInt #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestIsOdd ensures that checking if a field value IsOdd works as expected.
func TestIsOdd(t *testing.T) {
tests := []struct {
in string // hex encoded value
expected bool // expected oddness
}{
{"0", false},
{"1", true},
{"2", false},
// 2^32 - 1
{"ffffffff", true},
// 2^64 - 2
{"fffffffffffffffe", false},
// secp256k1 prime
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in)
result := f.IsOdd()
if result != test.expected {
t.Errorf("fieldVal.IsOdd #%d wrong result\n"+
"got: %v\nwant: %v", i, result, test.expected)
continue
}
}
}
// TestSetInt ensures that setting a field value to various native integers
// works as expected.
func TestSetInt(t *testing.T) {
tests := []struct {
in uint
raw [10]uint32
}{
{5, [10]uint32{5, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
// 2^26
{67108864, [10]uint32{67108864, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
// 2^26 + 1
{67108865, [10]uint32{67108865, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
// 2^32 - 1
{4294967295, [10]uint32{4294967295, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetInt(test.in)
result := f.TstRawInts()
if !reflect.DeepEqual(result, test.raw) {
t.Errorf("fieldVal.Set #%d wrong result\ngot: %v\n"+
"want: %v", i, result, test.raw)
continue
}
}
}
// TestNegate ensures that negating field values via Negate works as expected.
func TestNegate(t *testing.T) {
tests := []struct {
in string // hex encoded value
expected string // expected hex encoded value
}{
// secp256k1 prime (aka 0)
{"0", "0"},
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
// secp256k1 prime-1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e"},
// secp256k1 prime-2
{"2", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d"},
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "2"},
// Random sampling
{
"b3d9aac9c5e43910b4385b53c7e78c21d4cd5f8e683c633aed04c233efc2e120",
"4c2655363a1bc6ef4bc7a4ac381873de2b32a07197c39cc512fb3dcb103d1b0f",
},
{
"f8a85984fee5a12a7c8dd08830d83423c937d77c379e4a958e447a25f407733f",
"757a67b011a5ed583722f77cf27cbdc36c82883c861b56a71bb85d90bf888f0",
},
{
"45ee6142a7fda884211e93352ed6cb2807800e419533be723a9548823ece8312",
"ba119ebd5802577bdee16ccad12934d7f87ff1be6acc418dc56ab77cc131791d",
},
{
"53c2a668f07e411a2e473e1c3b6dcb495dec1227af27673761d44afe5b43d22b",
"ac3d59970f81bee5d1b8c1e3c49234b6a213edd850d898c89e2bb500a4bc2a04",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Negate(1).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Negate #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// TestSquare ensures that squaring field values via Square works as expected.
func TestSquare(t *testing.T) {
tests := []struct {
in string // hex encoded value
expected string // expected hex encoded value
}{
// secp256k1 prime (aka 0)
{"0", "0"},
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
// secp256k1 prime-1
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
// secp256k1 prime-2
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "4"},
// Random sampling
{
"b0ba920360ea8436a216128047aab9766d8faf468895eb5090fc8241ec758896",
"133896b0b69fda8ce9f648b9a3af38f345290c9eea3cbd35bafcadf7c34653d3",
},
{
"c55d0d730b1d0285a1599995938b042a756e6e8857d390165ffab480af61cbd5",
"cd81758b3f5877cbe7e5b0a10cebfa73bcbf0957ca6453e63ee8954ab7780bee",
},
{
"e89c1f9a70d93651a1ba4bca5b78658f00de65a66014a25544d3365b0ab82324",
"39ffc7a43e5dbef78fd5d0354fb82c6d34f5a08735e34df29da14665b43aa1f",
},
{
"7dc26186079d22bcbe1614aa20ae627e62d72f9be7ad1e99cac0feb438956f05",
"bf86bcfc4edb3d81f916853adfda80c07c57745b008b60f560b1912f95bce8ae",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.Square().Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.Square #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}
// BenchmarkAddJacobianNotZOne benchmarks the secp256k1 curve addJacobian
// function with Z values other than one so the optimizations associated with
// Z=1 aren't used.
func BenchmarkAddJacobianNotZOne(b *testing.B) {
b.StopTimer()
x1 := btcec.NewFieldVal().SetHex("d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718")
y1 := btcec.NewFieldVal().SetHex("5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190")
z1 := btcec.NewFieldVal().SetHex("2")
x2 := btcec.NewFieldVal().SetHex("91abba6a34b7481d922a4bd6a04899d5a686f6cf6da4e66a0cb427fb25c04bd4")
y2 := btcec.NewFieldVal().SetHex("03fede65e30b4e7576a2abefc963ddbf9fdccbf791b77c29beadefe49951f7d1")
z2 := btcec.NewFieldVal().SetHex("3")
x3, y3, z3 := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
curve := btcec.S256()
b.StartTimer()
for i := 0; i < b.N; i++ {
curve.TstAddJacobian(x1, y1, z1, x2, y2, z2, x3, y3, z3)
}
}
// BenchmarkAddJacobian benchmarks the secp256k1 curve addJacobian function with
// Z values of 1 so that the associated optimizations are used.
func BenchmarkAddJacobian(b *testing.B) {
b.StopTimer()
x1 := btcec.NewFieldVal().SetHex("34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6")
y1 := btcec.NewFieldVal().SetHex("0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232")
z1 := btcec.NewFieldVal().SetHex("1")
x2 := btcec.NewFieldVal().SetHex("34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6")
y2 := btcec.NewFieldVal().SetHex("0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232")
z2 := btcec.NewFieldVal().SetHex("1")
x3, y3, z3 := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
curve := btcec.S256()
b.StartTimer()
for i := 0; i < b.N; i++ {
curve.TstAddJacobian(x1, y1, z1, x2, y2, z2, x3, y3, z3)
}
}
// TestZero ensures that zeroing a field value zero works as expected.
func TestZero(t *testing.T) {
f := btcec.NewFieldVal().SetInt(2)
f.Zero()
for idx, rawInt := range f.TstRawInts() {
if rawInt != 0 {
t.Errorf("internal field integer at index #%d is not "+
"zero - got %d", idx, rawInt)
}
}
}
// TestIsZero ensures that checking if a field IsZero works as expected.
func TestIsZero(t *testing.T) {
f := btcec.NewFieldVal()
if !f.IsZero() {
t.Errorf("new field value is not zero - got %v (rawints %x)", f,
f.TstRawInts())
}
f.SetInt(1)
if f.IsZero() {
t.Errorf("field claims it's zero when it's not - got %v "+
"(raw rawints %x)", f, f.TstRawInts())
}
f.Zero()
if !f.IsZero() {
t.Errorf("field claims it's not zero when it is - got %v "+
"(raw rawints %x)", f, f.TstRawInts())
}
}
// TestStringer ensures the stringer returns the appropriate hex string.
func TestStringer(t *testing.T) {
tests := []struct {
in string
expected string
}{
{"0", "0000000000000000000000000000000000000000000000000000000000000000"},
{"1", "0000000000000000000000000000000000000000000000000000000000000001"},
{"a", "000000000000000000000000000000000000000000000000000000000000000a"},
{"b", "000000000000000000000000000000000000000000000000000000000000000b"},
{"c", "000000000000000000000000000000000000000000000000000000000000000c"},
{"d", "000000000000000000000000000000000000000000000000000000000000000d"},
{"e", "000000000000000000000000000000000000000000000000000000000000000e"},
{"f", "000000000000000000000000000000000000000000000000000000000000000f"},
{"f0", "00000000000000000000000000000000000000000000000000000000000000f0"},
// 2^26-1
{
"3ffffff",
"0000000000000000000000000000000000000000000000000000000003ffffff",
},
// 2^32-1
{
"ffffffff",
"00000000000000000000000000000000000000000000000000000000ffffffff",
},
// 2^64-1
{
"ffffffffffffffff",
"000000000000000000000000000000000000000000000000ffffffffffffffff",
},
// 2^96-1
{
"ffffffffffffffffffffffff",
"0000000000000000000000000000000000000000ffffffffffffffffffffffff",
},
// 2^128-1
{
"ffffffffffffffffffffffffffffffff",
"00000000000000000000000000000000ffffffffffffffffffffffffffffffff",
},
// 2^160-1
{
"ffffffffffffffffffffffffffffffffffffffff",
"000000000000000000000000ffffffffffffffffffffffffffffffffffffffff",
},
// 2^192-1
{
"ffffffffffffffffffffffffffffffffffffffffffffffff",
"0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffff",
},
// 2^224-1
{
"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
},
// 2^256-4294968273 (the btcec prime, so should result in 0)
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
"0000000000000000000000000000000000000000000000000000000000000000",
},
// 2^256-4294968274 (the secp256k1 prime+1, so should result in 1)
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
"0000000000000000000000000000000000000000000000000000000000000001",
},
// Invalid hex
{"g", "0000000000000000000000000000000000000000000000000000000000000000"},
{"1h", "0000000000000000000000000000000000000000000000000000000000000000"},
{"i1", "0000000000000000000000000000000000000000000000000000000000000000"},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in)
result := f.String()
if result != test.expected {
t.Errorf("fieldVal.String #%d wrong result\ngot: %v\n"+
"want: %v", i, result, test.expected)
continue
}
}
}
// TestAddJacobian tests addition of points projected in Jacobian coordinates.
func TestAddJacobian(t *testing.T) {
tests := []struct {
x1, y1, z1 string // Coordinates (in hex) of first point to add
x2, y2, z2 string // Coordinates (in hex) of second point to add
x3, y3, z3 string // Coordinates (in hex) of expected point
}{
// Addition with a point at infinity (left hand side).
// ∞ + P = P
{
"0",
"0",
"0",
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
},
// Addition with a point at infinity (right hand side).
// P + ∞ = P
{
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
"0",
"0",
"0",
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
},
// Addition with z1=z2=1 different x values.
{
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
"0cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a6",
"e205f79361bbe0346b037b4010985dbf4f9e1e955e7d0d14aca876bfa79aad87",
"44a5646b446e3877a648d6d381370d9ef55a83b666ebce9df1b1d7d65b817b2f",
},
// Addition with z1=z2=1 same x opposite y.
// P(x, y, z) + P(x, -y, z) = infinity
{
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
"1",
"0",
"0",
"0",
},
// Addition with z1=z2=1 same point.
// P(x, y, z) + P(x, y, z) = 2P
{
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
},
// Addition with z1=z2 (!=1) different x values.
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"5d2fe112c21891d440f65a98473cb626111f8a234d2cd82f22172e369f002147",
"98e3386a0a622a35c4561ffb32308d8e1c6758e10ebb1b4ebd3d04b4eb0ecbe8",
"2",
"cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a60",
"817de4d86ef80d1ac0ded00426176fd3e787a5579f43452b2a1db021e6ac3778",
"129591ad11b8e1de99235b4e04dc367bd56a0ed99baf3a77c6c75f5a6e05f08d",
},
// Addition with z1=z2 (!=1) same x opposite y.
// P(x, y, z) + P(x, -y, z) = infinity
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"a470ab21467813b6e0496d2c2b70c11446bab4fcbc9a52b7f225f30e869aea9f",
"2",
"0",
"0",
"0",
},
// Addition with z1=z2 (!=1) same point.
// P(x, y, z) + P(x, y, z) = 2P
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
},
// Addition with z1!=z2 and z2=1 different x values.
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
"1",
"3ef1f68795a6ccd1181e23eab80a1b9a2cebdcde755413bf097936eb5b91b4f3",
"0bef26c377c068d606f6802130bb7e9f3c3d2abcfa1a295950ed81133561cb04",
"252b235a2371c3bd3246b69c09b86cf7aad41db3375e74ef8d8ebeb4dc0be11a",
},
// Addition with z1!=z2 and z2=1 same x opposite y.
// P(x, y, z) + P(x, -y, z) = infinity
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
"1",
"0",
"0",
"0",
},
// Addition with z1!=z2 and z2=1 same point.
// P(x, y, z) + P(x, y, z) = 2P
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
},
// Addition with z1!=z2 and z2!=1 different x values.
// P(x, y, z) + P(x, y, z) = 2P
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"91abba6a34b7481d922a4bd6a04899d5a686f6cf6da4e66a0cb427fb25c04bd4",
"03fede65e30b4e7576a2abefc963ddbf9fdccbf791b77c29beadefe49951f7d1",
"3",
"3f07081927fd3f6dadd4476614c89a09eba7f57c1c6c3b01fa2d64eac1eef31e",
"949166e04ebc7fd95a9d77e5dfd88d1492ecffd189792e3944eb2b765e09e031",
"eb8cba81bcffa4f44d75427506737e1f045f21e6d6f65543ee0e1d163540c931",
}, // Addition with z1!=z2 and z2!=1 same x opposite y.
// P(x, y, z) + P(x, -y, z) = infinity
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
"cafc41904dd5428934f7d075129c8ba46eb622d4fc88d72cd1401452664add18",
"3",
"0",
"0",
"0",
},
// Addition with z1!=z2 and z2!=1 same point.
// P(x, y, z) + P(x, y, z) = 2P
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
"3503be6fb22abd76cb082f8aed63745b9149dd2b037728d32ebfebac99b51f17",
"3",
"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
// Convert hex to field values.
x1 := btcec.NewFieldVal().SetHex(test.x1)
y1 := btcec.NewFieldVal().SetHex(test.y1)
z1 := btcec.NewFieldVal().SetHex(test.z1)
x2 := btcec.NewFieldVal().SetHex(test.x2)
y2 := btcec.NewFieldVal().SetHex(test.y2)
z2 := btcec.NewFieldVal().SetHex(test.z2)
x3 := btcec.NewFieldVal().SetHex(test.x3)
y3 := btcec.NewFieldVal().SetHex(test.y3)
z3 := btcec.NewFieldVal().SetHex(test.z3)
// Ensure the test data is using points that are actually on
// the curve (or the point at infinity).
if !z1.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x1, y1, z1) {
t.Errorf("#%d first point is not on the curve -- "+
"invalid test data", i)
continue
}
if !z2.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x2, y2, z2) {
t.Errorf("#%d second point is not on the curve -- "+
"invalid test data", i)
continue
}
if !z3.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x3, y3, z3) {
t.Errorf("#%d expected point is not on the curve -- "+
"invalid test data", i)
continue
}
// Add the two points.
rx, ry, rz := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
btcec.S256().TstAddJacobian(x1, y1, z1, x2, y2, z2, rx, ry, rz)
// Ensure result matches expected.
if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
continue
}
}
}
// TestDoubleJacobian tests doubling of points projected in Jacobian
// coordinates.
func TestDoubleJacobian(t *testing.T) {
tests := []struct {
x1, y1, z1 string // Coordinates (in hex) of point to double
x3, y3, z3 string // Coordinates (in hex) of expected point
}{
// Doubling a point at infinity is still infinity.
{
"0",
"0",
"0",
"0",
"0",
"0",
},
// Doubling with z1=1.
{
"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
"1",
"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
},
// Doubling with z1!=1.
{
"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
"2",
"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
// Convert hex to field values.
x1 := btcec.NewFieldVal().SetHex(test.x1)
y1 := btcec.NewFieldVal().SetHex(test.y1)
z1 := btcec.NewFieldVal().SetHex(test.z1)
x3 := btcec.NewFieldVal().SetHex(test.x3)
y3 := btcec.NewFieldVal().SetHex(test.y3)
z3 := btcec.NewFieldVal().SetHex(test.z3)
// Ensure the test data is using points that are actually on
// the curve (or the point at infinity).
if !z1.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x1, y1, z1) {
t.Errorf("#%d first point is not on the curve -- "+
"invalid test data", i)
continue
}
if !z3.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x3, y3, z3) {
t.Errorf("#%d expected point is not on the curve -- "+
"invalid test data", i)
continue
}
// Double the point.
rx, ry, rz := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
btcec.S256().TstDoubleJacobian(x1, y1, z1, rx, ry, rz)
// Ensure result matches expected.
if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
continue
}
}
}
// TestNormalize ensures that normalizing the internal field words works as
// expected.
func TestNormalize(t *testing.T) {
tests := []struct {
raw [10]uint32 // Intentionally denormalized value
normalized [10]uint32 // Normalized form of the raw value
}{
{
[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^26
{
[10]uint32{0x04000000, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000000, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^26 + 1
{
[10]uint32{0x04000001, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000001, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^32 - 1
{
[10]uint32{0xffffffff, 0x00, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x03ffffff, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^32
{
[10]uint32{0x04000000, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000000, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^32 + 1
{
[10]uint32{0x04000001, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000001, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
},
// 2^64 - 1
{
[10]uint32{0xffffffff, 0xffffffc0, 0xfc0, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x03ffffff, 0x03ffffff, 0xfff, 0, 0, 0, 0, 0, 0, 0},
},
// 2^64
{
[10]uint32{0x04000000, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000000, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
},
// 2^64 + 1
{
[10]uint32{0x04000001, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000001, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
},
// 2^96 - 1
{
[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0x3ffc0, 0, 0, 0, 0, 0, 0},
[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
},
// 2^96
{
[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x40000, 0, 0, 0, 0, 0, 0},
},
// 2^128 - 1
{
[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffc0, 0, 0, 0, 0, 0},
[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0xffffff, 0, 0, 0, 0, 0},
},
// 2^128
{
[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0ffffff, 0, 0, 0, 0, 0},
[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x1000000, 0, 0, 0, 0, 0},
},
// 2^256 - 4294968273 (secp256k1 prime)
{
[10]uint32{0xfffffc2f, 0xffffff80, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
},
// 2^256 - 1
{
[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
[10]uint32{0x000003d0, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().TstSetRawInts(test.raw).Normalize()
result := f.TstRawInts()
if !reflect.DeepEqual(result, test.normalized) {
t.Errorf("fieldVal.Set #%d wrong normalized result\n"+
"got: %x\nwant: %x", i, result, test.normalized)
continue
}
}
}
// TestMulInt ensures that adding an integer to field values via MulInt works as
// expected.
func TestMulInt(t *testing.T) {
tests := []struct {
in1 string // hex encoded value
in2 uint // unsigned integer to multiply with value above
expected string // expected hex encoded value
}{
{"0", 0, "0"},
{"1", 0, "0"},
{"0", 1, "0"},
{"1", 1, "1"},
// secp256k1 prime-1 * 2
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
2,
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
},
// secp256k1 prime * 3
{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 3, "0"},
// secp256k1 prime-1 * 8
{
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
8,
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
},
// Random samples for first value. The second value is limited
// to 8 since that is the maximum int used in the elliptic curve
// calculations.
{
"b75674dc9180d306c692163ac5e089f7cef166af99645c0c23568ab6d967288a",
6,
"4c06bd2b6904f228a76c8560a3433bced9a8681d985a2848d407404d186b0280",
},
{
"54873298ac2b5ba8591c125ae54931f5ea72040aee07b208d6135476fb5b9c0e",
3,
"fd9597ca048212f90b543710afdb95e1bf560c20ca17161a8239fd64f212d42a",
},
{
"7c30fbd363a74c17e1198f56b090b59bbb6c8755a74927a6cba7a54843506401",
5,
"6cf4eb20f2447c77657fccb172d38c0aa91ea4ac446dc641fa463a6b5091fba7",
},
{
"fb4529be3e027a3d1587d8a500b72f2d312e3577340ef5175f96d113be4c2ceb",
8,
"da294df1f013d1e8ac3ec52805b979698971abb9a077a8bafcb688a4f261820f",
},
}
t.Logf("Running %d tests", len(tests))
for i, test := range tests {
f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
result := f.MulInt(test.in2).Normalize()
if !result.Equals(expected) {
t.Errorf("fieldVal.MulInt #%d wrong result\n"+
"got: %v\nwant: %v", i, result, expected)
continue
}
}
}