(*Variant of Gen_loop_bvec that uses list byte instead of Bvector 256*)
Fixpoint Gen_loop_Zlist (k : list byte) (v : list byte) (n : nat)
: list (list byte) * (list byte) :=
match n with
| O => (nil, v)
| S n' =>
let v' := HMAC256 v k in
let (bits, v'') := Gen_loop_Zlist k v' n' in
(List.app bits (List.cons v' List.nil), v'')
end.

(* Specifications: *)
Lemma Gen_loop_Zlist_ZlengthBlocks k: forall n v blocks u,
Gen_loop_Zlist k v n = (blocks,u) -> Zlength blocks = Z.of_nat n.
Lemma Gen_loop_Zlist_Blist k:
forall n v,
match Gen_loop_Zlist k v n with (blocks,u) =>
Gen_loop_Blist (bytesToBits k) (bytesToBits v) n
= (map bytesToBits blocks, bytesToBits u)
end.
Lemma Gen_loop_Zlist_nestedV k: forall n v blocks u blocks' u',
Gen_loop_Zlist k (HMAC256 v k) n = (blocks, u) ->
Gen_loop_Zlist k v n = (blocks', u') ->
u = HMAC256 u' k /\
blocks = map (fun z => HMAC256 z k) blocks'.
Lemma Gen_loop_Zlist_nestedV' k: forall n v blocks u,
Gen_loop_Zlist k (HMAC256 v k) n = (blocks, u) ->
exists blocks' u',
Gen_loop_Zlist k v n = (blocks', u') /\
u = HMAC256 u' k /\
blocks = map (fun z => HMAC256 z k) blocks'.