(* Module SHAHF <: Hashfunction. (* TODO use neater definition with conversion functions *)
(* TODO split out of HMAC_spec_pad *)
Definition c := (32 * 8)%nat.
Definition p := (32 * 8)%nat.
Definition b := (c + p)%nat.
Definition BlockSize := 64.
Definition sha_iv : Blist :=
intsToBits SHA256.init_registers.
Definition sha_h (regs : Blist) (block : Blist) : Blist :=
intsToBits (SHA256.hash_block (bitsToInts regs) (bitsToInts block)).
Definition sha_splitandpad (msg : Blist) : Blist :=
bytesToBits (sha_padding_lemmas.pad (bitsToBytes msg)).
(* artifact of app_fpad definition *)
Definition fpad_inner (msg : list Z) : list Z :=
(let n := BlockSize + Zlength msg in
[128%Z]
++ list_repeat (Z.to_nat (-(n + 9) mod 64)) 0
++ intlist_to_Zlist ([Int.repr (n * 8 / Int.modulus); Int.repr (n * 8)]))%list.
Definition fpad (msg : Blist) : Blist :=
bytesToBits (fpad_inner (bitsToBytes msg)).

(* Specifications: *)
Lemma fold_left_iv_length: forall k (HK: forall iv x, length iv = k -> length (sha_h iv x) = k) l iv x ,
length iv = k ->
length (fold_left sha_h l (sha_h iv x)) = k.