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Curve67254

382-bit prime field Weierstrass curve.

Curve from https://github.com/relic-toolkit/relic


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

Parameters

NameValue
p0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97
a0x2E32419A32377AF8E7F03148A106D112C8C2E26D31A89F46B743DEED322C7ADC3024AFE4B5AFD8DB7180281586549F4A
b0x22F6EF3BE72A67FDC236D7173727CD2AF6D02A195753C44BDF451369B02EA0F963D9A775CAE6DC3AE9CCABB7F183C1AD
G(0x141946416199FDDA96EC1F1AC80058AA3F0CE96B1BCD023E97BAE542FE3404B4738DB9B81A13698339387672ECA360C0, 0xD51BF79D968F4A076022E750F821058E2B5073697B639EDD355EBF8AD32352B1EFA9478DE7EB5662EF0D26EF6EEA795)
n0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD5FB21F21E95EEE17C5E69281B102D2773E27E13FD3C9719
h0x04


SAGE

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97
K = GF(p)
a = K(0x2E32419A32377AF8E7F03148A106D112C8C2E26D31A89F46B743DEED322C7ADC3024AFE4B5AFD8DB7180281586549F4A)
b = K(0x22F6EF3BE72A67FDC236D7173727CD2AF6D02A195753C44BDF451369B02EA0F963D9A775CAE6DC3AE9CCABB7F183C1AD)
E = EllipticCurve(K, (a, b))
G = E(0x141946416199FDDA96EC1F1AC80058AA3F0CE96B1BCD023E97BAE542FE3404B4738DB9B81A13698339387672ECA360C0, 0xD51BF79D968F4A076022E750F821058E2B5073697B639EDD355EBF8AD32352B1EFA9478DE7EB5662EF0D26EF6EEA795)
E.set_order(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD5FB21F21E95EEE17C5E69281B102D2773E27E13FD3C9719 * 0x04)

PARI/GP

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97
a = Mod(0x2E32419A32377AF8E7F03148A106D112C8C2E26D31A89F46B743DEED322C7ADC3024AFE4B5AFD8DB7180281586549F4A, p)
b = Mod(0x22F6EF3BE72A67FDC236D7173727CD2AF6D02A195753C44BDF451369B02EA0F963D9A775CAE6DC3AE9CCABB7F183C1AD, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD5FB21F21E95EEE17C5E69281B102D2773E27E13FD3C9719 * 0x04
G = [Mod(0x141946416199FDDA96EC1F1AC80058AA3F0CE96B1BCD023E97BAE542FE3404B4738DB9B81A13698339387672ECA360C0, p), Mod(0xD51BF79D968F4A076022E750F821058E2B5073697B639EDD355EBF8AD32352B1EFA9478DE7EB5662EF0D26EF6EEA795, p)]

JSON

{
"name": "Curve67254",
"desc": "Curve from https://github.com/relic-toolkit/relic",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97",
"bits": 382
},
"params": {
"a": {
"raw": "0x2E32419A32377AF8E7F03148A106D112C8C2E26D31A89F46B743DEED322C7ADC3024AFE4B5AFD8DB7180281586549F4A"
},
"b": {
"raw": "0x22F6EF3BE72A67FDC236D7173727CD2AF6D02A195753C44BDF451369B02EA0F963D9A775CAE6DC3AE9CCABB7F183C1AD"
}
},
"generator": {
"x": {
"raw": "0x141946416199FDDA96EC1F1AC80058AA3F0CE96B1BCD023E97BAE542FE3404B4738DB9B81A13698339387672ECA360C0"
},
"y": {
"raw": "0xD51BF79D968F4A076022E750F821058E2B5073697B639EDD355EBF8AD32352B1EFA9478DE7EB5662EF0D26EF6EEA795"
}
},
"order": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD5FB21F21E95EEE17C5E69281B102D2773E27E13FD3C9719",
"cofactor": "0x04"
}

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