This page describes the constants, fields, and groups associated with the MNT4-753 curve.
r
:
Integer
=
0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
q
:
Integer
=
0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
π½q
is the field of integers mod
q
Binary representation
Array(uint64, 12)
π½q2 is constructed as \(\mathbb{F}_q[x] / (x^{2} = \alpha)\) where \(\alpha\) is 13.
Concretely, each element has the form \(a_0 + a_1 \sqrt{\alpha}\) and is represented as the tuple \((a_0, a_1)\).
Binary representation
Array(Array(uint64, 12), 2)
b
:
π½q
=
0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
\(G_1\)
=
{ (x, y) β π½qβ¨―π½qο½y2=x3 + ax + b}
Binary representation
-
x
:
Array(uint64, 12)
-
y
:
Array(uint64, 12)