Lib.rs

This library implements the MNT4_753 curve generated in [BCTV14]. The name denotes that it is a Miyaji--Nakabayashi--Takano curve of embedding degree 4, defined over a 753-bit (prime) field. The main feature of this curve is that its scalar field and base field respectively equal the base field and scalar field of MNT6_753.

Curve information:

• Base field: q = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
• Scalar field: r = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
• valuation(q - 1, 2) = 15
• valuation(r - 1, 2) = 30
• G1 curve equation: y^2 = x^3 + ax + b, where
  • a = 2
  • b = 0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
• G2 curve equation: y^2 = x^3 + Ax + B, where
  • A = Fq2 = (a * NON_RESIDUE, 0)
  • B = Fq2(0, b * NON_RESIDUE)
  • NON_RESIDUE = 13 is the quadratic non-residue used to construct the extension field Fq2