def lbits

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/pmul.bend:36

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/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsrel.bend as BR

36# the bits of a scalar's limbs are the specification's bits of its value
37def lbits(+one: Nat, +h1: {one == 1n : Nat}, +ks: List<&2, Nat>, +hk: {FS.limbs16(one, 16n, ks) == True{} : Bool}) -> {L.bits(ks) == CV.bits(256n, FS.value(one, ks)) : List<&2, Nat>}:
38  %Equal.sym(List<&2, Nat>, L.bits(ks), BR.sb(256n, 0n, LV.ev(ks)), BR.bits_sb(one, h1, 16n, ks, hk)) : {_ == CV.bits(256n, FS.value(one, ks)) : List<&2, Nat>}
39  %Equal.sym(List<&2, Nat>, CV.bits(256n, FS.value(one, ks)), CV.bits_go(256n, FS.value(one, ks)), bits_is(256n, FS.value(one, ks))) : {BR.sb(256n, 0n, LV.ev(ks)) == _ : List<&2, Nat>}
40  %Equal.sym(List<&2, Nat>, CV.bits_go(256n, FS.value(one, ks)), BR.sb(256n, 0n, FS.value(one, ks)), go_sb(256n, FS.value(one, ks))) : {BR.sb(256n, 0n, LV.ev(ks)) == _ : List<&2, Nat>}
41  %Equal.sym(Nat, FS.value(one, ks), LV.ev(ks), LV.ev_value(one, h1, ks)) : {BR.sb(256n, 0n, LV.ev(ks)) == BR.sb(256n, 0n, _) : List<&2, Nat>}
42  {==}