def s0_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/psign.bend:98

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as SO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarpow.bend as SP
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pscal.bend as SQ

98def s0_r(+one: Nat, +h1: {one == 1n : Nat}, +z: List<&2, Nat>, +hz: {FS.reduced(one, FS.order(one), z) == True{} : Bool}, +d: List<&2, Nat>, +hd: {FS.reduced(one, FS.order(one), d) == True{} : Bool}, +k: List<&2, Nat>, +hk: {FS.reduced(one, FS.order(one), k) == True{} : Bool}, +x: List<&2, Nat>, +hx: {FS.limbs16(one, 16n, x) == True{} : Bool}) -> {FS.reduced(one, FS.order(one), S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d)))) == True{} : Bool}:
99  +hr = SQ.sred_r(one, h1, x, hx)
100  SO.mul_r(one, h1, S.inv(k), S.add(z, S.mul(S.reduce(x), d)), SP.inv_r(one, h1, k, hk), SO.add_r(one, h1, z, S.mul(S.reduce(x), d), hz, SO.mul_r(one, h1, S.reduce(x), d, hr, hd)))