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BLS24-477

477-bit prime field Weierstrass curve.

Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.


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

Parameters

NameValue
p0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b
a0x00
b0x04
G(0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD, 0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E)
n0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001
h0x41550AAAC04B3FD5000015AB


SAGE

p = 0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b
K = GF(p)
a = K(0x00)
b = K(0x04)
E = EllipticCurve(K, (a, b))
G = E(0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD, 0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E)
E.set_order(0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001 * 0x41550AAAC04B3FD5000015AB)

PARI/GP

p = 0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b
a = Mod(0x00, p)
b = Mod(0x04, p)
E = ellinit([a, b])
E[16][1] = 0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001 * 0x41550AAAC04B3FD5000015AB
G = [Mod(0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD, p), Mod(0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E, p)]

JSON

{
"name": "BLS24-477",
"desc": "Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b",
"bits": 477
},
"params": {
"a": {
"raw": "0x00"
},
"b": {
"raw": "0x04"
}
},
"generator": {
"x": {
"raw": "0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD"
},
"y": {
"raw": "0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E"
}
},
"order": "0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001",
"cofactor": "0x41550AAAC04B3FD5000015AB"
}

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