LAWS.xor_involution: law of bend-osdev-crypto@0.1.0.0
Import: import bend-osdev-crypto@0.1.0.0/LAWS.bend as LAWS
Lines 80-87 of bend-osdev-crypto@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-crypto@0.1.0.0/LAWS.bend&start_line=80&end_line=87

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-crypto@0.1.0.0/stream.bend as St

# the cipher is its own inverse: from one state, applied twice, the data
# comes back
law xor_involution:
  for ~S: Data
  for ~next: S -> St.CrKsStep<S>
  for +s: S
  for +m: B.Octets
  {St.CrXor.out_data(~S, St.CrXor.update(~S, ~next, s, St.CrXor.out_data(~S, St.CrXor.update(~S, ~next, s, m)))) == m : B.Octets}

Uses (17):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/LAWS.bend&name=octets_of_list_idempotent
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/LAWS.bend&name=octets_of_to
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/LAWS.bend&name=octets_to_of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.of_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.to_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/PROOF.bend&name=ks_mask_xs
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/PROOF.bend&name=ks_xs_xs
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/PROOF.bend&name=xor_update_ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=CrKsStep
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=CrXor.out_data
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=CrXor.update
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-crypto@0.1.0.0/stream.bend&name=cr.ks.xs