Coda Home Prover Intro MNT4753

MNT4753

This page describes the constants, fields, and groups associated with the MNT4-753 curve.

r : Integer = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
q : Integer = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
e : Integer = 2
𝔽q is the field of integers mod q

Binary representation

Array(uint64, 12)
𝔽q2 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)
\(\sigma\) : 𝔽r = 17
a : 𝔽q = 2
b : 𝔽q = 0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
\(G_1\) = { (x, y) ∈ 𝔽q⨯𝔽q|y2=x3 + ax + b}

Binary representation

  • x : Array(uint64, 12)
  • y : Array(uint64, 12)
\(\tilde{a}\) : 𝔽q2 = (13β‹…a, 0)
\(\tilde{b}\) : 𝔽q2 = (0, 13β‹…b)
\(G_2\) = { (x, y) ∈ 𝔽q2⨯𝔽q2|y2=x3 + \(\tilde{a}\)x + \(\tilde{b}\)}

Binary representation

  • x : Array(Array(uint64, 12), 2)
  • y : Array(Array(uint64, 12), 2)