This page describes the constants, fields, and groups associated with the MNT6-753 curve.
r
:
Integer
=
0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
q
:
Integer
=
0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
π½q
is the field of integers mod
q
Binary representation
Array(uint64, 12)
π½q3 is constructed as \(\mathbb{F}_q[x] / (x^{3} = \alpha)\) where \(\alpha\) is 11.
Concretely, each element has the form \(a_0 + a_1 \sqrt[3]{\alpha} + a_2 \sqrt[3]{\alpha}^{2}\) and is represented as the tuple \((a_0, a_1, a_2)\).
Binary representation
Array(Array(uint64, 12), 3)
b
:
π½q
=
0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
\(G_1\)
=
{ (x, y) β π½qβ¨―π½qο½y2=x3 + ax + b}
Binary representation
-
x
:
Array(uint64, 12)
-
y
:
Array(uint64, 12)