constantine/constantine/curves/jubjub_sqrt.nim
Mamy Ratsimbazafy 53f9708c2b
Initial support for Twisted Edwards curves (#167)
* Point decoding: optimized sqrt for p ≡ 5 (mod 8) (Curve25519)

* Implement fused sqrt(u/v) for twisted edwards point deserialization

* Introduce twisted edwards affine

* Allow declaration of curve field elements (and fight against recursive dependencies

* Twisted edwards group law + tests

* Add support for jubjub and bandersnatch #162

* test twisted edwards scalar mul
2021-12-29 01:54:17 +01:00

20 lines
943 B
Nim

# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
../config/[curves, type_bigint, type_ff],
../io/[io_bigints, io_fields],
../arithmetic/finite_fields
const
# with e = 2adicity
# p == s * 2^e + 1
# root_of_unity = smallest_quadratic_nonresidue^s
# exponent = (p-1-2^e)/2^e / 2
Jubjub_TonelliShanks_exponent* = BigInt[222].fromHex"0x39f6d3a994cebea4199cec0404d0ec02a9ded2017fff2dff7fffffff"
Jubjub_TonelliShanks_twoAdicity* = 32
Jubjub_TonelliShanks_root_of_unity* = Fp[Jubjub].fromHex"0x212d79e5b416b6f0fd56dc8d168d6c0c4024ff270b3e0941b788f500b912f1f"