def s0_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/psign.bend:102

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

102def s0_v(+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.value(one, S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}:
103  +hr = SQ.sred_r(one, h1, x, hx)
104  +hm = SO.mul_r(one, h1, S.reduce(x), d, hr, hd)
105  %Equal.sym(Nat, FS.value(one, S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d)))), FS.mmul(FS.order(one), FS.value(one, S.inv(k)), FS.value(one, S.add(z, S.mul(S.reduce(x), d)))), SO.mul_v(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, hm))) : {_ == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
106  %Equal.sym(Nat, FS.value(one, S.inv(k)), FS.minv(FS.order(one), FS.value(one, k)), SP.inv_v(one, h1, k, hk)) : {FS.mmul(FS.order(one), _, FS.value(one, S.add(z, S.mul(S.reduce(x), d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
107  %Equal.sym(Nat, FS.value(one, S.add(z, S.mul(S.reduce(x), d))), FS.madd(FS.order(one), FS.value(one, z), FS.value(one, S.mul(S.reduce(x), d))), SO.add_v(one, h1, z, S.mul(S.reduce(x), d), hz, hm)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), _) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
108  %Equal.sym(Nat, FS.value(one, S.mul(S.reduce(x), d)), FS.mmul(FS.order(one), FS.value(one, S.reduce(x)), FS.value(one, d)), SO.mul_v(one, h1, S.reduce(x), d, hr, hd)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), _)) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
109  %Equal.sym(Nat, FS.value(one, S.reduce(x)), Nat.mod(FS.value(one, x), FS.order(one)), SQ.sred_v(one, h1, x, hx)) : {FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), _, FS.value(one, d)))) == FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))) : Nat}
110  {==}