LAWS.cbc_round_trip: law of bend-osdev-cipher-modes@0.1.0.0
Import: import bend-osdev-cipher-modes@0.1.0.0/LAWS.bend as LAWS
Lines 30-42 of bend-osdev-cipher-modes@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-cipher-modes@0.1.0.0/LAWS.bend&start_line=30&end_line=42

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend as M
import bend-osdev-cipher-modes@0.1.0.0/cbc.bend as C

# CBC on bytes: for every 16-byte IV and every message of whole blocks,
# encryption succeeds and decryption gives the message back
law cbc_round_trip:
  for ~K: Data
  for ~enc: K -> M.CmBlock -> M.CmBlock
  for ~dec: K -> M.CmBlock -> M.CmBlock
  for ~inv: @k: K -> @b: M.CmBlock -> {dec(k, enc(k, b)) == b : M.CmBlock}
  for +k: K
  for +iv: B.Octets
  for +m: B.Octets
  for hi: {B.Octets.len(iv) == 16n : Nat}
  for hm: {Nat.mod(B.Octets.len(m), 16n) == 0n : Nat}
  {Result.bind(&2, &2, M.CmError, B.Octets, B.Octets, C.Cbc.encrypt(~K, ~enc, k, iv, m), c => C.Cbc.decrypt(~K, ~dec, k, iv, c)) == Done{m} : Result<&2, &2, M.CmError, B.Octets>}

Uses (46):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result.bind
  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_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.len
  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=len
  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-cipher-modes@0.1.0.0/PROOF.bend&name=cbcp.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=cbcp.iv
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=oc.masked
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=oc.mod
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.eta
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.join_split
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.mask_join
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.mod_tail
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.split_join
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=tr.bind_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=tr.cbc_decrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=tr.cbc_encrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=Cbc.decrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=Cbc.decrypt.ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=Cbc.encrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=Cbc.encrypt.ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.d1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.d2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.dec
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.e1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.e2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.enc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cbc.bend&name=cbc.iv
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=CmBlock
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=CmError
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=CmSplit
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.block_of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.join_onto
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split.blocks
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split.tail