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119 lines
3.4 KiB
Plaintext
119 lines
3.4 KiB
Plaintext
/*
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MKRAND - A Digital Random Bit Generator
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The MIT License (MIT)
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Copyright (c) 2014, TAG Universal Machine.
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Permission is hereby granted, free of charge, to any person
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obtaining a copy of this software and associated documentation
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files (the "Software"), to deal in the Software without
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restriction, including without limitation the rights to use, copy,
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modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be
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included in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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DEALINGS IN THE SOFTWARE.
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--
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USAGE
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Create a 128 bit seed:
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seed = seedUnit
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Once the seed is created, you may use it to generate a stream of random bits:
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take `{100} (randBytes seed)
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Here a string is encoded with seedUnit, using the deterministic random stream as a
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one-time pad against which to XOR the string:
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Encode:
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randXOR seedUnit "Deus Ex Machina"
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[0x28, 0x2b, 0x2c, 0xfa, 0x92, 0xca, 0xb3, 0xcb, 0xed, 0x50, 0xc2,v0x1b, 0x11, 0x0e, 0x70]
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Decode:
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:set ascii=on
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randXOR seedUnit [0x28, 0x2b, 0x2c, 0xfa, 0x92, 0xca, 0xb3, 0xcb, 0xed, 0x50, 0xc2,0x1b, 0x11, 0x0e, 0x70]
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"Deus Ex Machina"
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*/
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module MKRAND where
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type Seg = [0x80]
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type Field = [0x80]Seg
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/* Canonical seed - a segment with a single True bit in the center */
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seedUnit:Seg
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seedUnit = (0 :[63]) # (1:[1]) # (0:[64])
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/*
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* Field - Unfold an application of Rule 30 to a seed
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*/
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field: Seg -> [inf]Seg
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field s = new
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where
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new = [s] # [ rule30 row | row <- new]
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rule30 r = [ a ^ (b || c) | a <- r >>> 1
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| b <- r
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| c <- r <<< 1
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]
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/* SHA30 - Use the input segment as the seed, generate two square fields,
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* keep the center column of the second.
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*/
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sha30: Seg -> Seg
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sha30 s = take`{0x80} (drop`{0x80} [ r @ ((((length r) / 2)-1):[8]) | r <- field s])
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/*
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* RAND - Seed XOR (SHA30 Seed)
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*/
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rands : Seg -> [inf]Seg
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rands s = rest
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where
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rand p = p ^ (sha30 p)
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rest = [rand s] # [rand x | x <- rest]
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/* Break segments into bytes */
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randBytes : Seg -> [inf][8]
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randBytes s = groupBy`{8} (join (rands s))
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/* XOR a byte string into a random byte string, using the given seed */
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randXOR : {n} Seg -> String n -> String n
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randXOR seed src = [s ^ r | s <- src
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| r <- randBytes seed
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]
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/* OTP example */
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property otp_encdec =
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randXOR seedUnit "Deus Ex Machina" == c
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/\ randXOR seedUnit c == "Deus Ex Machina"
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where c = [ 0x28, 0x2b, 0x2c, 0xfa
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, 0x92, 0xca, 0xb3, 0xcb
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, 0xed, 0x50, 0xc2, 0x1b
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, 0x11, 0x0e, 0x70]
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otp_involutive : {len} (fin len) => String len -> Bit
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otp_involutive msg = randXOR seedUnit (randXOR seedUnit msg) == msg
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property otp_involutive_32 msg = otp_involutive (msg : String 32) |