此页面列出的是由环智中诚团队通过查阅资料和网页整理的常用的标准(通用)椭圆曲线算法(ECC Cure)数据库,包含了详细的参数和运算法则。可供用于开发和学习、研究密码。

ANSI x9.62

由美国国家标准协会(ANSI)制定发布的 ANSI x9.62 标准, 金融服务行业的公钥密码术:椭圆曲线数字签名算法(ECDSA)。

prime192v1

192位素数韦氏曲线算法

基本信息

名称
别名secp192r1、P-192
OID1.2.840.10045.3.1.1.1

参数

名称
p0xfffffffffffffffffffffffffffffffeffffffffffffffff
a0xfffffffffffffffffffffffffffffffefffffffffffffffc
b0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
G(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811)
n0xffffffffffffffffffffffff99def836146bc9b1b4d22831
h0x1

JSON

{
  "name": "prime192v1",
  "desc": "",
  "oid": "1.2.840.10045.3.1.1.1",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
    },
    "b": {
      "raw": "0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1"
    }
  },
  "generator": {
    "x": {
      "raw": "0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012"
    },
    "y": {
      "raw": "0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"
    }
  },
  "order": "0xffffffffffffffffffffffff99def836146bc9b1b4d22831",
  "cofactor": "0x1",
  "aliases": [
    "secg/secp192r1",
    "nist/P-192"
  ],
  "characteristics": {
    "j_invariant": "6234286251230310114240839169629130138801351179850969208331",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692799058262018920874353817167917",
    "conductor": "1",
    "discriminant": "5525402385154848923235289274741921730185152131202286251655",
    "embedding_degree": "627710173538668076383578942317605901376719477318284228408",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 20,
        "least": 4,
        "r": 5
      },
      {
        "full": 48,
        "least": 48,
        "r": 7
      },
      {
        "full": 55,
        "least": 5,
        "r": 11
      },
      {
        "full": 12,
        "least": 4,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "31607402316713927207482677199"
  }
}

prime192v2

192位素数韦氏曲线算法

基本信息

名称
OID1.2.840.10045.3.1.1.2

参数

名称
p0xfffffffffffffffffffffffffffffffeffffffffffffffff
a0xfffffffffffffffffffffffffffffffefffffffffffffffc
b0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953
G(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, 0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15)
n0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31
h0x1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953)
E = EllipticCurve(K, (a, b))
G = E(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, 0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15)
E.set_order(0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31 * 0x1)

JSON

{
  "name": "prime192v2",
  "desc": "",
  "oid": "1.2.840.10045.3.1.1.2",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
    },
    "b": {
      "raw": "0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953"
    }
  },
  "generator": {
    "x": {
      "raw": "0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a"
    },
    "y": {
      "raw": "0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15"
    }
  },
  "order": "0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "2188073006583539552141688552564683396860111048461359479401",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692701825184443826638755359939885",
    "conductor": "1",
    "discriminant": "3136318742261921876063208570368096687049382158828912127687",
    "embedding_degree": "1569275433846670190958947355769706484048025134396096264012",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 20,
        "least": 4,
        "r": 5
      },
      {
        "full": 6,
        "least": 2,
        "r": 7
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "128840479891808162805939905231"
  }
}

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