A binary-field curve in optimal normal basis

Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.15
• Seed:
  2C04F44D696E676875615175C586B41F6CA150C9

SAGE

F.<x> = GF(2)[]
K.<z> = GF(2^239, name="z", modulus=u^239 +  u^238 +  u^236 +  u^232 +  u^224 +  u^208 +  u^207 +  u^206 +  u^204 +  u^200 +  u^192 +  u^144 +  u^143 +  u^142 +  u^140 +  u^136 +  u^128 +  u^16 +  u^15 +  u^14 +  u^12 +  u^8 + 1)
def from_integer(K, h):
	return sum(map(lambda ix: K(Integer(ix[1]) * z^(2^ix[0])), enumerate(h.binary())), K(0))
E = EllipticCurve(K, (1, from_integer(K, 0x1ECF1B9D28D8017505E17475D3DF2982E243CA5CB5E9F94A3F36124A486E), 0, 0, from_integer(K, 0x3EE257250D1A2E66CEF23AA0F25B12388DE8A10FF9554F90AFBAA9A08B6D)))
E.set_order(0x1555555555555555555555555555558CF77A5D0589D2A9340D963B7AD703 * 0x06)
G = E(from_integer(K, 0x02193279FC543E9F5F7119189785B9C60B249BE4820BAF6C24BDFA2813F8B8), from_integer(K, ))

JSON

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      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
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    "degree": 239,
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