A binary-field curve in optimal normal basis

Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.14
• Seed:
  F851638CFA4D696E67687561517556513841BFAC

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, 0x182DD45F5D470239B8983FEA47B8B292641C57F9BF84BAECDE8BB3ADCE30), 0, 0, from_integer(K, 0x147A9C1D4C2CE9BE5D34EC02797F76667EBAD5A3F93FA2A524BFDE91EF28)))
E.set_order(0x200000000000000000000000000000474F7E69F42FE430931D0B455AAE8B * 0x04)
G = E(from_integer(K, 0x034912AD657F1D1C6B32EDB9942C95E226B06FB012CD40FDEA0D72197C8104), 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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