RFC5832

Parameters

Characteristics

• j-invariant:
  610900649669533983695054775734306011088557592049408816983490905302782604532556561056354879375964032515423415363590524121501491460792551618405795037507769
• Trace of Frobenius:
  33317690176989408428354063686744165122149707869071609401230178415964786752661
• Discriminant:
  2354030499938796080455685465248118319217198068927486418321815690157012200907763643687518461996694967111330756661917773558875004226725808279081784408642042

SAGE

p = 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15df1d852741af4704a0458047e80e4546d35b8336fac224dd81664bbf528be6373
K = GF(p)
a = K(0x7)
b = K(0x1cff0806a31116da29d8cfa54e57eb748bc5f377e49400fdd788b649eca1ac4361834013b2ad7322480a89ca58e0cf74bc9e540c2add6897fad0a3084f302adc)
E = EllipticCurve(K, (a, b))
G = E(0x24d19cc64572ee30f396bf6ebbfd7a6c5213b3b3d7057cc825f91093a68cd762fd60611262cd838dc6b60aa7eee804e28bc849977fac33b4b530f1b120248a9a, 0x2bb312a43bd2ce6e0d020613c857acddcfbf061e91e5f2c3f32447c259f39b2c83ab156d77f1496bf7eb3351e1ee4e43dc1a18b91b24640b6dbb92cb1add371e)
E.set_order(0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15da82f2d7ecb1dbac719905c5eecc423f1d86e25edbe23c595d644aaf187e6e6df * 0x1)

PARI/GP

p = 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15df1d852741af4704a0458047e80e4546d35b8336fac224dd81664bbf528be6373
a = Mod(0x7, p)
b = Mod(0x1cff0806a31116da29d8cfa54e57eb748bc5f377e49400fdd788b649eca1ac4361834013b2ad7322480a89ca58e0cf74bc9e540c2add6897fad0a3084f302adc, p)
E = ellinit([a, b])
E[16][1] = 0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15da82f2d7ecb1dbac719905c5eecc423f1d86e25edbe23c595d644aaf187e6e6df * 0x1
G = [Mod(0x24d19cc64572ee30f396bf6ebbfd7a6c5213b3b3d7057cc825f91093a68cd762fd60611262cd838dc6b60aa7eee804e28bc849977fac33b4b530f1b120248a9a, p), Mod(0x2bb312a43bd2ce6e0d020613c857acddcfbf061e91e5f2c3f32447c259f39b2c83ab156d77f1496bf7eb3351e1ee4e43dc1a18b91b24640b6dbb92cb1add371e, p)]

JSON

{
  "name": "gost512",
  "desc": "RFC5832",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15df1d852741af4704a0458047e80e4546d35b8336fac224dd81664bbf528be6373",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0x7"
    },
    "b": {
      "raw": "0x1cff0806a31116da29d8cfa54e57eb748bc5f377e49400fdd788b649eca1ac4361834013b2ad7322480a89ca58e0cf74bc9e540c2add6897fad0a3084f302adc"
    }
  },
  "generator": {
    "x": {
      "raw": "0x24d19cc64572ee30f396bf6ebbfd7a6c5213b3b3d7057cc825f91093a68cd762fd60611262cd838dc6b60aa7eee804e28bc849977fac33b4b530f1b120248a9a"
    },
    "y": {
      "raw": "0x2bb312a43bd2ce6e0d020613c857acddcfbf061e91e5f2c3f32447c259f39b2c83ab156d77f1496bf7eb3351e1ee4e43dc1a18b91b24640b6dbb92cb1add371e"
    }
  },
  "order": "0x4531acd1fe0023c7550d267b6b2fee80922b14b2ffb90f04d4eb7c09b5d2d15da82f2d7ecb1dbac719905c5eecc423f1d86e25edbe23c595d644aaf187e6e6df",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "610900649669533983695054775734306011088557592049408816983490905302782604532556561056354879375964032515423415363590524121501491460792551618405795037507769",
    "discriminant": "2354030499938796080455685465248118319217198068927486418321815690157012200907763643687518461996694967111330756661917773558875004226725808279081784408642042",
    "trace_of_frobenius": "33317690176989408428354063686744165122149707869071609401230178415964786752661"
  }
}