#elliptic-curve #finite-fields #math

no-std dev ark-mnt6-753

The MNT6-753 pairing-friendly elliptic curve

7 unstable releases

0.5.0 Oct 28, 2024
0.5.0-alpha.0 Jun 20, 2024
0.4.0 Jan 17, 2023
0.4.0-alpha.2 Dec 28, 2022
0.2.0 Mar 25, 2021

#2710 in Cryptography

Download history 2824/week @ 2024-08-17 3857/week @ 2024-08-24 4816/week @ 2024-08-31 4753/week @ 2024-09-07 4667/week @ 2024-09-14 4837/week @ 2024-09-21 4794/week @ 2024-09-28 3509/week @ 2024-10-05 2999/week @ 2024-10-12 1691/week @ 2024-10-19 565/week @ 2024-10-26 178/week @ 2024-11-02 135/week @ 2024-11-09 244/week @ 2024-11-16 341/week @ 2024-11-23 145/week @ 2024-11-30

889 downloads per month
Used in 7 crates

MIT/Apache

650KB
13K SLoC

This library implements the MNT6_753 curve generated in [BCTV14]. The name denotes that it is a Miyaji--Nakabayashi--Takano curve of embedding degree 6, 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 MNT4_753.

Curve information:

  • Base field: q = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
  • Scalar field: r = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
  • valuation(q - 1, 2) = 30
  • valuation(r - 1, 2) = 15
  • G1 curve equation: y^2 = x^3 + ax + b, where
    • a = 11
    • b = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
  • G2 curve equation: y^2 = x^3 + Ax + B, where
    • A = Fq3(0, 0, a)
    • B = Fq3(b * NON_RESIDUE, 0, 0)
    • NON_RESIDUE = 11 is the cubic non-residue used to construct the extension field Fq3

Dependencies

~3.5–5MB
~88K SLoC