LAWS.xts_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 68-82 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=68&end_line=82

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/xts.bend as T

# XTS on bytes, with ciphertext stealing: for every 16-byte sequence number
# and every data unit of at least 16 bytes, encryption succeeds and
# decryption gives the data unit back
law xts_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 +k1: K
  for +k2: K
  for +i: B.Octets
  for +p: B.Octets
  for hi: {B.Octets.len(i) == 16n : Nat}
  for hp: {Nat.is_le(16n, B.Octets.len(p)) == True{} : Bool}
  {Result.bind(&2, &2, M.CmError, B.Octets, B.Octets, T.Xts.encrypt(~K, ~enc, k1, k2, i, p), c => T.Xts.decrypt(~K, ~enc, ~dec, k1, k2, i, c)) == Done{p} : Result<&2, &2, M.CmError, B.Octets>}

Uses (70):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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=li.init_last
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=li.len_enc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=oc.le16
  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=sp.eta
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.hd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.join_append
  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_onto
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.nonempty
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.split_join_short
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.tail_masked
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.tail_short
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.tl
  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.xts_decrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=tr.xts_encrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.d2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.mask_steal_t
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.split_steal_t
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.steal
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=xtsp.tweak
  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.bytes_onto
  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
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=Xts.decrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=Xts.decrypt.ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=Xts.encrypt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=Xts.encrypt.ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.alpha_n
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.d1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.d2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.dec
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.dout
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.dsteal
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.e1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.e2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.enc
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.init
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.last
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.steal_c
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.steal_t
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/xts.bend&name=xts.tweak