Psign.drbg_sign: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend as Psign
Lines 219-225 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&start_line=219&end_line=225

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/ecdsa.bend as ES
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend as E

def drbg_sign(+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}, g: E.Drbg) -> {msig(E.sign_drbg(z, d, g)) == ES.sign_drbg(one, FS.value(one, z), FS.value(one, d), dr(g)) : Maybe<&2, List<&2, U32>>}:
  match g:
    case E.Drbg{+k, +v}:
      %Equal.sym(List<&2, U32>, E.hmac(k, v), ES.hmac(k, v), hm(k, v)) : {msig(E.sign_loop(16n, z, d, k, _, E.attempt(z, d, E.hmac(k, v)))) == ES.sign_loop(16n, one, FS.value(one, z), FS.value(one, d), k, ES.hmac(k, v), ES.attempt(one, FS.value(one, z), FS.value(one, d), ES.hmac(k, v))) : Maybe<&2, List<&2, U32>>}
      %Equal.sym(List<&2, U32>, E.hmac(k, v), ES.hmac(k, v), hm(k, v)) : {msig(E.sign_loop(16n, z, d, k, ES.hmac(k, v), E.attempt(z, d, _))) == ES.sign_loop(16n, one, FS.value(one, z), FS.value(one, d), k, ES.hmac(k, v), ES.attempt(one, FS.value(one, z), FS.value(one, d), ES.hmac(k, v))) : Maybe<&2, List<&2, U32>>}
      %Equal.sym(ES.Attempt, ES.attempt(one, FS.value(one, z), FS.value(one, d), ES.hmac(k, v)), matt(E.attempt(z, d, ES.hmac(k, v))), Equal.sym(ES.Attempt, matt(E.attempt(z, d, ES.hmac(k, v))), ES.attempt(one, FS.value(one, z), FS.value(one, d), ES.hmac(k, v)), att_v(one, h1, z, hz, d, hd, ES.hmac(k, v), hlen(k, v)))) : {msig(E.sign_loop(16n, z, d, k, ES.hmac(k, v), E.attempt(z, d, ES.hmac(k, v)))) == ES.sign_loop(16n, one, FS.value(one, z), FS.value(one, d), k, ES.hmac(k, v), _) : Maybe<&2, List<&2, U32>>}
      sl(16n, one, h1, z, hz, d, hd, k, ES.hmac(k, v), E.attempt(z, d, ES.hmac(k, v)))

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=att_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=dr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=hlen
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=hm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=matt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=msig
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/psign.bend&name=sl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=Attempt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=attempt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=hmac
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=sign_drbg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend&name=sign_loop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=order
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=reduced
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=Drbg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=attempt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=hmac
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=sign_drbg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend&name=sign_loop