sect571r1
571-bit binary field Weierstrass curve.Also known as: B-571ansit571r1
Parameters
Characteristics
- OID:
1.3.132.0.39 - Seed:
2AA058F73A0E33AB486B0F610410C53A7F132310 - j-invariant:
4214501753546941913223695905024629172637342244349568219783929342383426637975668846684512012478218604779111370893214803288669006084397110899225485839234972840008396689070376 - Trace of Frobenius:
99534385013609758659469819150465382236412396452349171016760770327496674607579419075443 - Discriminant:
2853329245261343535560086964181551296889298776106832980891560850944180011701123307905326019642652653533003482753023669016842884108172514870944140611113679225347419720217210 - Anomalous:
false - Supersingular:
false
SAGE
F.<x> = GF(2)[]K = GF(2^571, name="x", modulus= x^571 + x^10 + x^5 + x^2 + 1)E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a)))E.set_order(0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 * 0x2)G = E(K.fetch_int(0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19), K.fetch_int(0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b))
JSON
{"name": "sect571r1","desc": "","oid": "1.3.132.0.39","form": "Weierstrass","field": {"type": "Binary","bits": 571,"degree": 571,"poly": [{"coeff": "0x01","power": 571},{"coeff": "0x01","power": 10},{"coeff": "0x01","power": 5},{"coeff": "0x01","power": 2},{"coeff": "0x01","power": 0}],"basis": "poly"},"params": {"a": {"raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"},"b": {"raw": "0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a"}},"generator": {"x": {"raw": "0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19"},"y": {"raw": "0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b"}},"order": "0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47","cofactor": "0x2","aliases": ["nist/B-571","x963/ansit571r1"],"characteristics": {"seed": "2AA058F73A0E33AB486B0F610410C53A7F132310","j_invariant": "4214501753546941913223695905024629172637342244349568219783929342383426637975668846684512012478218604779111370893214803288669006084397110899225485839234972840008396689070376","anomalous": false,"discriminant": "2853329245261343535560086964181551296889298776106832980891560850944180011701123307905326019642652653533003482753023669016842884108172514870944140611113679225347419720217210","supersingular": false,"trace_of_frobenius": "99534385013609758659469819150465382236412396452349171016760770327496674607579419075443"}}