RFC7836

Parameters

Characteristics

• j-invariant:
  2850514806025719070145724293578244494155992500562074285019380556682599199784707862702432619340199207468768980481671624645560499531743272474439893330387268
• Trace of Frobenius:
  97744483583712349266929640403245629889151353128602905529915952558174263790419
• Discriminant:
  12198408522911213052632489093057402109612720640096098688583378894786958412526782601142507389753258425683973521245032174347351331325939929127804416473292375
• Supersingular:
  false
• Embedding degree:
  13407807929942597099574024998205846127479365820592393377723561443721764030073449232318290585817636498049628612556596899500625279906416653993875474742293108

SAGE

p = 0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7
K = GF(p)
a = K(0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4)
b = K(0x00E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760)
E = EllipticCurve(K, (a, b))
G = E(0x03, 0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4)
E.set_order(0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275 * 0x1)

PARI/GP

p = 0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7
a = Mod(0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4, p)
b = Mod(0x00E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760, p)
E = ellinit([a, b])
E[16][1] = 0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275 * 0x1
G = [Mod(0x03, p), Mod(0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4, p)]

JSON

{
  "name": "id-tc26-gost-3410-12-512-paramSetA",
  "desc": "RFC7836",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4"
    },
    "b": {
      "raw": "0x00E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760"
    }
  },
  "generator": {
    "x": {
      "raw": "0x03"
    },
    "y": {
      "raw": "0x7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4"
    }
  },
  "order": "0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "2850514806025719070145724293578244494155992500562074285019380556682599199784707862702432619340199207468768980481671624645560499531743272474439893330387268",
    "discriminant": "12198408522911213052632489093057402109612720640096098688583378894786958412526782601142507389753258425683973521245032174347351331325939929127804416473292375",
    "embedding_degree": "13407807929942597099574024998205846127479365820592393377723561443721764030073449232318290585817636498049628612556596899500625279906416653993875474742293108",
    "supersingular": false,
    "trace_of_frobenius": "97744483583712349266929640403245629889151353128602905529915952558174263790419"
  }
}