Require Recdef.
Require Coq.Strings.String.
Require Coq.Strings.Ascii.
(* LINEAR-TIME FUNCTIONAL VERSION OF SHA256 *)
Function zeros (n : Z) {measure Z.to_nat n} : list Int.int :=
if Z.gtb n 0 then Int.zero :: zeros (n-1) else nil.
Hint Rewrite length_zeros : norm.
Local Open Scope Z.
Definition padlen' (n: Z) : list Int.int :=
let q := (n+8)/64*16 + 15 - (n+8)/4   (* number of zero-pad words *)
in zeros q ++ [Int.repr (n * 8 / Int.modulus); Int.repr (n * 8)].
Transparent generate_word.
Definition nthB (b: list int) (i: nat) (n: Z) :=
nth (Z.to_nat (Z.of_nat i - 16 + n)) (rev (generate_word (rev b) 48)) Int.zero.

Lemma nth_rev_generate_word:
forall i b,
length b = 16%nat ->
(16 <= i < 64)%nat ->
nth i (rev (generate_word (rev b) 48)) Int.zero =
Int.add (nthB b i 0)
(Int.add (Int.add (sigma_0 (nthB b i 1)) (sigma_1 (nthB b i 14)))
(nthB b i 9)).