/*

MKRAND - A Digital Random Bit Generator

    The MIT License (MIT)

    Copyright (c) 2014, TAG Universal Machine.

    Permission is hereby granted, free of charge, to any person
    obtaining a copy of this software and associated documentation
    files (the "Software"), to deal in the Software without
    restriction, including without limitation the rights to use, copy,
    modify, merge, publish, distribute, sublicense, and/or sell copies
    of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be
    included in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.

   --

   USAGE

   Create a 128 bit seed:

   seed = seedUnit

   Once the seed is created, you may use it to generate a stream of random bits:

   take `{100} (randBytes seed)

   Here a string is encoded with seedUnit, using the deterministic random stream as a
   one-time pad against which to XOR the string:

     Encode:
       randXOR seedUnit "Deus Ex Machina"
       [0x28, 0x2b, 0x2c, 0xfa, 0x92, 0xca, 0xb3, 0xcb, 0xed, 0x50, 0xc2,v0x1b, 0x11, 0x0e, 0x70]

     Decode:
       :set ascii=on
       randXOR seedUnit [0x28, 0x2b, 0x2c, 0xfa, 0x92, 0xca, 0xb3, 0xcb, 0xed, 0x50, 0xc2,0x1b, 0x11, 0x0e, 0x70]
       "Deus Ex Machina"

*/

module MKRAND where

type Seg   = [0x80]
type Field = [0x80]Seg

/* Canonical seed - a segment with a single True bit in the center */
seedUnit:Seg
seedUnit = (0 :[63]) # (1:[1]) # (0:[64])


/*
 *  Field - Unfold an application of Rule 30 to a seed
 */
field: Seg -> [inf]Seg
field s = new
  where
    new = [s] # [ rule30 row | row <- new]
    rule30 r = [ a ^ (b || c) | a <- r >>> 1
                              | b <- r
                              | c <- r <<< 1
               ]


/* SHA30 - Use the input segment as the seed, generate two square fields,
 * keep the center column of the second.
 */
sha30: Seg -> Seg
sha30 s = take`{0x80} (drop`{0x80} [ r @ ((((length r) / 2)-1):[8]) | r <- field s])


/*
 * RAND - Seed XOR (SHA30 Seed)
 */
rands : Seg -> [inf]Seg
rands s = rest
  where
     rand p = p ^ (sha30 p)
     rest = [rand s] # [rand x | x <- rest]


/* Break segments into bytes */
randBytes : Seg -> [inf][8]
randBytes s = groupBy`{8} (join (rands s))


/* XOR a byte string into a random byte string, using the given seed */
randXOR : {n} Seg ->  String n -> String n
randXOR seed src = [s ^ r | s <- src
                          | r <- randBytes seed
                   ]

/* OTP example */

property otp_encdec =
     randXOR seedUnit "Deus Ex Machina" == c
  /\ randXOR seedUnit c == "Deus Ex Machina"
  where c = [ 0x28, 0x2b, 0x2c, 0xfa
            , 0x92, 0xca, 0xb3, 0xcb
            , 0xed, 0x50, 0xc2, 0x1b
            , 0x11, 0x0e, 0x70]

otp_involutive : {len} (fin len) => String len -> Bit
otp_involutive msg = randXOR seedUnit (randXOR seedUnit msg) == msg

property otp_involutive_32 msg = otp_involutive (msg : String 32)