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

(* Specifications: *)
(*Relationship between Gen_loop_Blist and Gen_loop_bvec*)
Lemma Gen_loop_Blist_Bvec k: forall n v blocks u,
Gen_loop_Blist (to_list k) (to_list v) n = (blocks, u) ->
forall blocks' u', Gen_loop_Bvec k v n = (blocks', u') ->
u = to_list u' /\ blocks = map (@Vector.to_list _ 256) blocks'.