Implementing GIFT-COFB algorithm using Cryptol- list problem - list

Question

I'm already new to Haskell with Cryptol dialect, also I'm irritated because I can't use loops...
I would like to implement array like this one... Initialization Matrix but I have the only idea to get every 4th element starting by [0] index and load this new list to S0. Similarly starting by 1 index of the list and load to new S1 array every 4th element.

Answer 1

Cryptol's type system is designed so that these sorts of bit splits that you find in crypto algorithms is almost trivial to express. And in fact, lack of loops is a plus, not a detriment, once you get used to that style.
There could be multiple ways to code your "initialization" code. But here's how I would go about it:
load : {a} [128][a] -> [4][32][a]
load(elts) = reverse (transpose cols)
where cols : [32][4][a]
cols = split elts
Note that the type here is more general than what you need, but it allows for easier testing. Here's what I get at the cryptol prompt:
Main> :set base=10
Main> load [127, 126 .. 0]
Showing a specific instance of polymorphic result:
* Using '7' for type argument 'a' of 'Main::load'
[[124, 120, 116, 112, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72,
68, 64, 60, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4,
0],
[125, 121, 117, 113, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69,
65, 61, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5, 1],
[126, 122, 118, 114, 110, 106, 102, 98, 94, 90, 86, 82, 78, 74, 70,
66, 62, 58, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2],
[127, 123, 119, 115, 111, 107, 103, 99, 95, 91, 87, 83, 79, 75, 71,
67, 63, 59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3]]
This is a little hard to read, so here it is formatted:
[[124, 120, 116, 112, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72, 68, 64, 60, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0],
[125, 121, 117, 113, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69, 65, 61, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5, 1],
[126, 122, 118, 114, 110, 106, 102, 98, 94, 90, 86, 82, 78, 74, 70, 66, 62, 58, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2],
[127, 123, 119, 115, 111, 107, 103, 99, 95, 91, 87, 83, 79, 75, 71, 67, 63, 59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3]]
which is exactly the structure you wanted. Now we can specialize:
loadBits : [128] -> [4][32]
loadBits(vector) = reverse (transpose cols)
where cols : [32][4]
cols = split vector
Note that the code is exactly the same as before, we just made it specific to the type you wanted.
Hope this gets you started!