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Fp384BN

384-bit prime field Weierstrass curve.

Curve described in https://www.iso.org/standard/80241.html


y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b
a0x00
b0x03
G(0x01, 0x02)
n0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775
h0x01

Characteristics

  • j-invariant:
    0
  • Trace of Frobenius:
    6277101735386680763835754795021643429033562911502587034007
  • Discriminant:
    39402006196394479212278605372068645601647601647604977711041989197213181721117185302456933847594895764913993728967131
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    12

SAGE

p = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b
K = GF(p)
a = K(0x00)
b = K(0x03)
E = EllipticCurve(K, (a, b))
G = E(0x01, 0x02)
E.set_order(0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775 * 0x01)

PARI/GP

p = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b
a = Mod(0x00, p)
b = Mod(0x03, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775 * 0x01
G = [Mod(0x01, p), Mod(0x02, p)]

JSON

{
"name": "Fp384BN",
"desc": "Curve described in https://www.iso.org/standard/80241.html",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b",
"bits": 384
},
"params": {
"a": {
"raw": "0x00"
},
"b": {
"raw": "0x03"
}
},
"generator": {
"x": {
"raw": "0x01"
},
"y": {
"raw": "0x02"
}
},
"order": "0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775",
"cofactor": "0x01",
"characteristics": {
"j_invariant": "0",
"anomalous": false,
"discriminant": "39402006196394479212278605372068645601647601647604977711041989197213181721117185302456933847594895764913993728967131",
"embedding_degree": "12",
"supersingular": false,
"trace_of_frobenius": "6277101735386680763835754795021643429033562911502587034007"
}
}

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