mirror of
https://github.com/J08nY/std-curves.git
synced 2026-01-10 05:48:08 -05:00
Add support for extension field curves.
This commit is contained in:
J08nY
4
.gitignore
vendored
4
.gitignore
vendored
@@ -2,4 +2,6 @@
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node_modules/
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package-lock.json
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public/
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src/
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src/
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.idea/
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*.sage.py
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17
analyze.sage
17
analyze.sage
@@ -110,12 +110,25 @@ def get_curve_group(data):
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return E, G
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elif data["field"]["type"] == "Binary":
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F.<x> = GF(2)[]
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poly = sum(x^i for i in [data["field"]["poly"]["m"], data["field"]["poly"].get("e1"), data["field"]["poly"].get("e2"), data["field"]["poly"].get("e3"), 0] if i is not None)
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K = GF(2^data["field"]["poly"]["m"], name="x", modulus=poly)
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poly = sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["field"]["poly"])
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K = GF(2^data["field"]["degree"], name="x", modulus=poly)
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E = EllipticCurve(K, (1, K.fetch_int(int(data["params"]["a"], 16)), 0, 0, K.fetch_int(int(data["params"]["b"], 16))))
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E.set_order(int(data["order"], 16) * int(data["cofactor"], 16))
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G = E(K.fetch_int(int(data["generator"]["x"], 16)), K.fetch_int(int(data["generator"]["y"], 16)))
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return E, G
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elif data["field"]["type"] == "Extension":
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base = int(data["field"]["base"], 16)
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F.<x> = GF(base)[]
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poly = sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["field"]["poly"])
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K = GF(base^data["field"]["degree"], name="x", modulus=poly)
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a = K(sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["params"]["a"]))
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b = K(sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["params"]["b"]))
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E = EllipticCurve(K, (a, b))
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E.set_order(int(data["order"], 16) * int(data["cofactor"], 16))
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gx = K(sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["generator"]["x"]))
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gy = K(sum(F(int(elem["coeff"], 16)) * x^elem["power"] for elem in data["generator"]["y"]))
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G = E(gx, gy)
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return E, G
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else:
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raise ValueError()
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154
nist/curves.json
154
nist/curves.json
@@ -242,16 +242,18 @@
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{
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"name": "K-163",
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"category": "nist",
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"desc": "",
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"desc": "Koblitz curve.",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 163,
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"e1": 7,
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"e2": 6,
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"e3": 3
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},
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"bits": 163
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"poly": [
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{"power": 163, "coeff": "0x01"},
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{"power": 7, "coeff": "0x01"},
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{"power": 6, "coeff": "0x01"},
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{"power": 3, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 163,
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"degree": 163
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},
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"form": "Weierstrass",
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"params": {
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@@ -283,13 +285,15 @@
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"desc": "",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 163,
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"e1": 7,
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"e2": 6,
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"e3": 3
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},
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"bits": 163
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"poly": [
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{"power": 163, "coeff": "0x01"},
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{"power": 7, "coeff": "0x01"},
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{"power": 6, "coeff": "0x01"},
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{"power": 3, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 163,
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"degree": 163
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},
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"form": "Weierstrass",
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"params": {
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@@ -319,14 +323,16 @@
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{
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"name": "K-233",
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"category": "nist",
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"desc": "",
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"desc": "Koblitz curve.",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 233,
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"e1": 74
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},
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"bits": 233
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"poly": [
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{"power": 233, "coeff": "0x01"},
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{"power": 74, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 233,
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"degree": 233
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},
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"form": "Weierstrass",
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"params": {
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@@ -359,11 +365,13 @@
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"desc": "",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 233,
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"e1": 74
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},
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"bits": 233
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"poly": [
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{"power": 233, "coeff": "0x01"},
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{"power": 74, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 233,
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"degree": 233
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},
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"form": "Weierstrass",
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"params": {
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@@ -394,16 +402,18 @@
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{
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"name": "K-283",
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"category": "nist",
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"desc": "",
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"desc": "Koblitz curve.",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 283,
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"e1": 12,
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"e2": 7,
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"e3": 5
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},
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"bits": 283
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"poly": [
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{"power": 283, "coeff": "0x01"},
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{"power": 12, "coeff": "0x01"},
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{"power": 7, "coeff": "0x01"},
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{"power": 5, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 283,
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"degree": 283
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},
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"form": "Weierstrass",
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"params": {
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@@ -436,13 +446,15 @@
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"desc": "",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 283,
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"e1": 12,
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"e2": 7,
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"e3": 5
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},
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"bits": 283
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"poly": [
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{"power": 283, "coeff": "0x01"},
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{"power": 12, "coeff": "0x01"},
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{"power": 7, "coeff": "0x01"},
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{"power": 5, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 283,
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"degree": 283
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},
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"form": "Weierstrass",
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"params": {
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@@ -472,14 +484,16 @@
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{
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"name": "K-409",
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"category": "nist",
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"desc": "",
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"desc": "Koblitz curve.",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 409,
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"e1": 87
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},
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"bits": 409
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"poly": [
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{"power": 409, "coeff": "0x01"},
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{"power": 87, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 409,
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"degree": 409
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},
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"form": "Weierstrass",
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"params": {
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@@ -510,11 +524,13 @@
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"desc": "",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 409,
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"e1": 87
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},
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"bits": 409
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"poly": [
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{"power": 409, "coeff": "0x01"},
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{"power": 87, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 409,
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"degree": 409
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},
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"form": "Weierstrass",
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"params": {
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@@ -542,16 +558,18 @@
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{
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"name": "K-571",
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"category": "nist",
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"desc": "",
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"desc": "Koblitz curve.",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 571,
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"e1": 10,
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"e2": 5,
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"e3": 2
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},
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"bits": 571
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"poly": [
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{"power": 571, "coeff": "0x01"},
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{"power": 10, "coeff": "0x01"},
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{"power": 5, "coeff": "0x01"},
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{"power": 2, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 571,
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"degree": 571
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},
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"form": "Weierstrass",
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"params": {
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@@ -582,13 +600,15 @@
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"desc": "",
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"field": {
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"type": "Binary",
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"poly": {
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"m": 571,
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"e1": 10,
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"e2": 5,
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"e3": 2
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},
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"bits": 571
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"poly": [
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{"power": 571, "coeff": "0x01"},
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{"power": 10, "coeff": "0x01"},
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{"power": 5, "coeff": "0x01"},
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{"power": 2, "coeff": "0x01"},
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{"power": 0, "coeff": "0x01"}
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],
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"bits": 571,
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"degree": 571
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},
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"form": "Weierstrass",
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"params": {
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@@ -363,6 +363,38 @@
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]
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}
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},
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{
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"name": "Fp254n2BNa",
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"category": "other",
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"desc": "Curve used in: https://eprint.iacr.org/2010/354.pdf",
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"field": {
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"type": "Extension",
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"base": "0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001",
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"bits": 508,
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"degree": 2,
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"poly": [
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{"power": 2, "coeff": "0x01"},
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{"power": 0, "coeff": "0x05"}
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]
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},
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"form": "Weierstrass",
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"params": {
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"a": [{"power": 0, "coeff": "0x00"}],
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"b": [{"power": 1, "coeff": "0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000000"}]
|
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},
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"generator": {
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"x": [
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{"power": 1, "coeff": "0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72"},
|
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{"power": 0, "coeff": "0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5"}
|
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],
|
||||
"y": [
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{"power": 1, "coeff": "0x0ee97d6de9902a27d00e952232a78700863bc9aa9be960C32f5bf9fd0a32d345"},
|
||||
{"power": 0, "coeff": "0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627"}
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]
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},
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"order": "0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001",
|
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"cofactor": "0x2370fb049d410fbe4e761a9886e50241dc42cf101e0000017e80600000000001"
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},
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{
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"name": "Fp254BNb",
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"category": "other",
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79
schema.json
79
schema.json
@@ -5,35 +5,51 @@
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"type": "string",
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"pattern": "^(0x[0-9a-fA-F]+|[0-9]+)$"
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},
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"Polynomial": {
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"type": "array",
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"items": {
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"type": "object",
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"properties": {
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"power": {"type": "integer"},
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"coeff": {"$ref": "#/definitions/Number"}
|
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}
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}
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},
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"Element": {
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"anyOf": [
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{"$ref": "#/definitions/Number"},
|
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{"$ref": "#/definitions/Polynomial"}
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||||
]
|
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},
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"Weierstrass": {
|
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"type": "object",
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"properties": {
|
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"a": {"$ref": "#/definitions/Number"},
|
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"b": {"$ref": "#/definitions/Number"}
|
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"a": {"$ref": "#/definitions/Element"},
|
||||
"b": {"$ref": "#/definitions/Element"}
|
||||
},
|
||||
"required": ["a", "b"]
|
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},
|
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"Edwards": {
|
||||
"type": "object",
|
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"properties": {
|
||||
"c": {"$ref": "#/definitions/Number"},
|
||||
"d": {"$ref": "#/definitions/Number"}
|
||||
"c": {"$ref": "#/definitions/Element"},
|
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"d": {"$ref": "#/definitions/Element"}
|
||||
},
|
||||
"required": ["c", "d"]
|
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},
|
||||
"TwistedEdwards": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"a": {"$ref": "#/definitions/Number"},
|
||||
"d": {"$ref": "#/definitions/Number"}
|
||||
"a": {"$ref": "#/definitions/Element"},
|
||||
"d": {"$ref": "#/definitions/Element"}
|
||||
},
|
||||
"required": ["a", "d"]
|
||||
},
|
||||
"Montgomery": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"a": {"$ref": "#/definitions/Number"},
|
||||
"b": {"$ref": "#/definitions/Number"}
|
||||
"a": {"$ref": "#/definitions/Element"},
|
||||
"b": {"$ref": "#/definitions/Element"}
|
||||
},
|
||||
"required": ["a", "b"]
|
||||
},
|
||||
@@ -46,43 +62,33 @@
|
||||
},
|
||||
"required": ["p", "bits"]
|
||||
},
|
||||
"Trinomial": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"m": {"type": "integer"},
|
||||
"e1": {"type": "integer"}
|
||||
},
|
||||
"required": ["m", "e1"]
|
||||
},
|
||||
"Pentanomial": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"m": {"type": "integer"},
|
||||
"e1": {"type": "integer"},
|
||||
"e2": {"type": "integer"},
|
||||
"e3": {"type": "integer"}
|
||||
},
|
||||
"required": ["m", "e1", "e2", "e3"]
|
||||
},
|
||||
"BinaryField": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"type": {"const": "Binary"},
|
||||
"poly": {
|
||||
"anyOf": [
|
||||
{"$ref": "#/definitions/Trinomial"},
|
||||
{"$ref": "#/definitions/Pentanomial"}
|
||||
]
|
||||
},
|
||||
"base": {"const": "0x02"},
|
||||
"degree": {"type": "integer"},
|
||||
"poly": {"$ref": "#/definitions/Polynomial"},
|
||||
"bits": {"type": "integer"}
|
||||
},
|
||||
"required": ["poly", "bits"]
|
||||
"required": ["degree", "poly", "bits"]
|
||||
},
|
||||
"ExtenstionField": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"type": {"const": "Extension"},
|
||||
"base": {"$ref": "#/definitions/Number"},
|
||||
"degree": {"type": "integer"},
|
||||
"poly": {"$ref": "#/definitions/Polynomial"},
|
||||
"bits": {"type": "integer"}
|
||||
},
|
||||
"required": ["base", "degree", "poly", "bits"]
|
||||
},
|
||||
"Point": {
|
||||
"type": "object",
|
||||
"properties": {
|
||||
"x": {"$ref": "#/definitions/Number"},
|
||||
"y": {"$ref": "#/definitions/Number"}
|
||||
"x": {"$ref": "#/definitions/Element"},
|
||||
"y": {"$ref": "#/definitions/Element"}
|
||||
},
|
||||
"required": ["x", "y"]
|
||||
},
|
||||
@@ -96,7 +102,8 @@
|
||||
"field": {
|
||||
"oneOf": [
|
||||
{"$ref": "#/definitions/PrimeField"},
|
||||
{"$ref": "#/definitions/BinaryField"}
|
||||
{"$ref": "#/definitions/BinaryField"},
|
||||
{"$ref": "#/definitions/ExtenstionField"}
|
||||
]
|
||||
},
|
||||
"form": {
|
||||
|
||||
240
secg/curves.json
240
secg/curves.json
@@ -899,10 +899,12 @@
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"bits": 113,
|
||||
"poly": {
|
||||
"m": 113,
|
||||
"e1": 9
|
||||
}
|
||||
"poly": [
|
||||
{"power": 113, "coeff": "0x01"},
|
||||
{"power": 9, "coeff": "0x01"},
|
||||
{"power": 0, "coeff": "0x01"}
|
||||
],
|
||||
"degree": 113
|
||||
},
|
||||
"params": {
|
||||
"a": "0x003088250ca6e7c7fe649ce85820f7",
|
||||
@@ -927,10 +929,12 @@
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"bits": 113,
|
||||
"poly": {
|
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x963/curves.json
167
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]
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||||
},
|
||||
"params": {
|
||||
"a": "0x000000000000000000000000000000000000000000000000000000000000000000000001",
|
||||
@@ -304,11 +319,13 @@
|
||||
"oid": "",
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"poly": [
|
||||
{"power": 409, "coeff": "0x01"},
|
||||
{"power": 87, "coeff": "0x01"},
|
||||
{"power": 0, "coeff": "0x01"}
|
||||
],
|
||||
"bits": 409,
|
||||
"poly": {
|
||||
"m": 409,
|
||||
"e1": 87
|
||||
}
|
||||
"degree": 409
|
||||
},
|
||||
"params": {
|
||||
"a": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
||||
@@ -333,11 +350,13 @@
|
||||
"oid": "",
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"poly": [
|
||||
{"power": 409, "coeff": "0x01"},
|
||||
{"power": 87, "coeff": "0x01"},
|
||||
{"power": 0, "coeff": "0x01"}
|
||||
],
|
||||
"bits": 409,
|
||||
"poly": {
|
||||
"m": 409,
|
||||
"e1": 87
|
||||
}
|
||||
"degree": 409
|
||||
},
|
||||
"params": {
|
||||
"a": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
|
||||
@@ -362,13 +381,15 @@
|
||||
"oid": "",
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"poly": [
|
||||
{"power": 571, "coeff": "0x01"},
|
||||
{"power": 10, "coeff": "0x01"},
|
||||
{"power": 5, "coeff": "0x01"},
|
||||
{"power": 2, "coeff": "0x01"},
|
||||
{"power": 0, "coeff": "0x01"}
|
||||
],
|
||||
"bits": 571,
|
||||
"poly": {
|
||||
"m": 571,
|
||||
"e1": 10,
|
||||
"e2": 5,
|
||||
"e3": 2
|
||||
}
|
||||
"degree": 571
|
||||
},
|
||||
"params": {
|
||||
"a": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
|
||||
@@ -393,13 +414,15 @@
|
||||
"oid": "",
|
||||
"field": {
|
||||
"type": "Binary",
|
||||
"poly": [
|
||||
{"power": 571, "coeff": "0x01"},
|
||||
{"power": 10, "coeff": "0x01"},
|
||||
{"power": 5, "coeff": "0x01"},
|
||||
{"power": 2, "coeff": "0x01"},
|
||||
{"power": 0, "coeff": "0x01"}
|
||||
],
|
||||
"bits": 571,
|
||||
"poly": {
|
||||
"m": 571,
|
||||
"e1": 10,
|
||||
"e2": 5,
|
||||
"e3": 2
|
||||
}
|
||||
"degree": 571
|
||||
},
|
||||
"params": {
|
||||
"a": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
|
||||
|
||||
Reference in New Issue
Block a user