Copyright | (c) Austin Seipp |
---|---|

License | BSD3 |

Maintainer | erkokl@gmail.com |

Stability | experimental |

Safe Haskell | None |

Language | Haskell2010 |

An implementation of RC4 (AKA Rivest Cipher 4 or Alleged RC4/ARC4), using SBV. For information on RC4, see: http://en.wikipedia.org/wiki/RC4.

We make no effort to optimize the code, and instead focus on a clear implementation. In fact, the RC4 algorithm relies on in-place update of its state heavily for efficiency, and is therefore unsuitable for a purely functional implementation.

- type S = STree Word8 Word8
- initS :: S
- type Key = [SWord8]
- type RC4 = (S, SWord8, SWord8)
- swap :: SWord8 -> SWord8 -> S -> S
- prga :: RC4 -> (SWord8, RC4)
- initRC4 :: Key -> S
- keySchedule :: Key -> [SWord8]
- keyScheduleString :: String -> [SWord8]
- encrypt :: String -> String -> [SWord8]
- decrypt :: String -> [SWord8] -> String
- rc4IsCorrect :: IO ThmResult

# Types

type S = STree Word8 Word8 Source

RC4 State contains 256 8-bit values. We use the symbolically accessible
full-binary type `STree`

to represent the state, since RC4 needs
access to the array via a symbolic index and it's important to minimize access time.

Construct the fully balanced initial tree, where the leaves are simply the numbers `0`

through `255`

.

type RC4 = (S, SWord8, SWord8) Source

Represents the current state of the RC4 stream: it is the `S`

array
along with the `i`

and `j`

index values used by the PRGA.

# The PRGA

prga :: RC4 -> (SWord8, RC4) Source

Implements the PRGA used in RC4. We return the new state and the next key value generated.

# Key schedule

keySchedule :: Key -> [SWord8] Source

The key-schedule. Note that this function returns an infinite list.

keyScheduleString :: String -> [SWord8] Source

Generate a key-schedule from a given key-string.

# Encryption and Decryption

encrypt :: String -> String -> [SWord8] Source

RC4 encryption. We generate key-words and xor it with the input. The following test-vectors are from Wikipedia http://en.wikipedia.org/wiki/RC4:

`>>>`

"bbf316e8d940af0ad3"`concatMap hex $ encrypt "Key" "Plaintext"`

`>>>`

"1021bf0420"`concatMap hex $ encrypt "Wiki" "pedia"`

`>>>`

"45a01f645fc35b383552544b9bf5"`concatMap hex $ encrypt "Secret" "Attack at dawn"`

decrypt :: String -> [SWord8] -> String Source

RC4 decryption. Essentially the same as decryption. For the above test vectors we have:

`>>>`

"Plaintext"`decrypt "Key" [0xbb, 0xf3, 0x16, 0xe8, 0xd9, 0x40, 0xaf, 0x0a, 0xd3]`

`>>>`

"pedia"`decrypt "Wiki" [0x10, 0x21, 0xbf, 0x04, 0x20]`

`>>>`

"Attack at dawn"`decrypt "Secret" [0x45, 0xa0, 0x1f, 0x64, 0x5f, 0xc3, 0x5b, 0x38, 0x35, 0x52, 0x54, 0x4b, 0x9b, 0xf5]`

# Verification

rc4IsCorrect :: IO ThmResult Source

Prove that round-trip encryption/decryption leaves the plain-text unchanged. The theorem is stated parametrically over key and plain-text sizes. The expression performs the proof for a 40-bit key (5 bytes) and 40-bit plaintext (again 5 bytes).

Note that this theorem is trivial to prove, since it is essentially establishing
xor'in the same value twice leaves a word unchanged (i.e., `x `

).
However, the proof takes quite a while to complete, as it gives rise to a fairly
large symbolic trace.`xor`

y `xor`

y = x