val f (t: size_t{v t <= 79}) (x y z: word SHA1) : Tot (word SHA1)
let f (t: size_t {v t <= 79}) (x y z: word SHA1) : Tot (word SHA1) =
  if t <. 20ul
  then
    (x &. y) ^. (~. x &. z)
  else if 39ul <. t && t <. 60ul
  then
    (x &. y) ^. (x &. z) ^. (y &. z)
  else
    x ^. y ^. z
val f (t: size_t{v t <= 79}) (x y z: word SHA1) : Tot (word SHA1)
let f (t: size_t{v t <= 79}) (x y z: word SHA1) : Tot (word SHA1) =
if t <. 20ul
then (x &. y) ^. (~.x &. z)
else if 39ul <. t && t <. 60ul then (x &. y) ^. (x &. z) ^. (y &. z) else x ^. y ^. z
Spec.SHA1.fst.checked
Spec.Loops.fst.checked Spec.Hash.Definitions.fst.checked prims.fst.checked Lib.IntTypes.fsti.checked FStar.UInt32.fsti.checked FStar.Seq.fst.checked FStar.Pervasives.fsti.checked FStar.List.Tot.fst.checked FStar.Classical.fsti.checked
Spec.SHA1.fst
Lib.IntTypes.size_t Prims.b2t Prims.op_LessThanOrEqual Lib.IntTypes.v Lib.IntTypes.U32 Lib.IntTypes.PUB Spec.Hash.Definitions.word Spec.Hash.Definitions.SHA1 Lib.IntTypes.op_Less_Dot FStar.UInt32.__uint_to_t Lib.IntTypes.op_Hat_Dot Spec.Hash.Definitions.word_t Lib.IntTypes.SEC Lib.IntTypes.op_Amp_Dot Lib.IntTypes.op_Tilde_Dot Prims.bool Prims.op_AmpAmp
module Spec.SHA1

open Lib.IntTypes
module H = Spec.Hash.Definitions
module Seq = FStar.Seq

open Spec.Hash.Definitions
(* Source: https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf *)

(* Section 5.3.1 *)

inline_for_extraction
let init_as_list : list uint32 = [
  u32 0x67452301;
  u32 0xefcdab89;
  u32 0x98badcfe;
  u32 0x10325476;
  u32 0xc3d2e1f0;
]

let init : words_state SHA1 = Seq.seq_of_list init_as_list

(* Section 6.1.2 Step 1: message schedule *)

let rec w' (mi: Seq.lseq (word SHA1) (block_word_length SHA1)) (t: nat {t <= 79}) : GTot (word SHA1) (decreases (t)) =
  if t < 16
  then Seq.index mi (t)
  else (w' mi (t - 3) ^. w' mi (t - 8) ^. w' mi (t - 14) ^. w' mi (t - 16)) <<<. 1ul

let w (mi: Seq.lseq (word SHA1) (block_word_length SHA1)) (t: size_t {v t <= 79}) : GTot (word SHA1) = w' mi (v t)

let compute_w_post
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat)
  (res: Seq.lseq (word SHA1) n)
: GTot Type0
= (n <= 80 /\ (
    forall (i: nat) . i < n ==> Seq.index res i == w' mi i
  ))

let compute_w_post_intro
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat)
  (res: Seq.lseq (word SHA1) n)
  (u: squash (n <= 80))
  (f: (i: nat) -> Lemma
      (requires (i < n))
      (ensures (i < n /\ Seq.index res i == w' mi i)))
: Lemma
  (compute_w_post mi n res)
= Classical.forall_intro (Classical.move_requires f)

inline_for_extraction
let compute_w_n'
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat { n <= 79 } )
  (w: ((i: nat {i < n}) -> Tot (y: word SHA1 {y == w' mi i})))
: Tot (y: word SHA1 {y == w' mi n})
= let r =
      if n < 16
      then Seq.index mi n
      else (w (n - 3) ^. w (n - 8) ^. w (n - 14) ^. w (n - 16)) <<<. 1ul
  in
  r

inline_for_extraction
let compute_w_n
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat { n <= 79 } )
  (accu: Seq.lseq (word SHA1) n)
: Pure (word SHA1)
  (requires (compute_w_post mi n accu))
  (ensures (fun y -> n <= 79 /\ y == w' mi n))
= [@inline_let]
  let w (i: nat {i < n}) : Tot (y: word SHA1 {y == w' mi i}) = Seq.index accu i in
  compute_w_n' mi n w

inline_for_extraction
let compute_w_next
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat { n <= 79 } )
  (accu: Seq.lseq (word SHA1) n)
: Pure (Seq.lseq (word SHA1) (n + 1))
  (requires (compute_w_post mi n accu))
  (ensures (fun accu' -> compute_w_post mi (n + 1) accu'))
= let wn = compute_w_n mi n accu in
  let accu' = Seq.snoc accu wn in
  assert (n + 1 <= 80);
  let g
    (i: nat)
  : Lemma
    (requires (i < n + 1))
    (ensures (i < n + 1 /\ Seq.index accu' i == w' mi i))
  = if i = n
    then ()
    else ()
  in
  compute_w_post_intro mi (n + 1) accu' () g;
  accu'

let rec compute_w
  (mi: Seq.lseq (word SHA1) (block_word_length SHA1))
  (n: nat)
  (accu: Seq.lseq (word SHA1) n)
: Pure (Seq.lseq (word SHA1) 80)
  (requires (compute_w_post mi n accu))
  (ensures (fun res -> compute_w_post mi 80 res))
  (decreases (80 - n))
= assert (n <= 80); // this assert is necessary for Z3 to prove that n <= 79 in the else branch
  if n = 80
  then accu
  else compute_w mi (n + 1) (compute_w_next mi n accu)

(* Section 4.1.1: logical functions *)

inline_for_extraction
val f (t: size_t{v t <= 79}) (x y z: word SHA1) : Tot (word SHA1)

    t: Lib.IntTypes.size_t{Lib.IntTypes.v t <= 79} ->
    x: Spec.Hash.Definitions.word Spec.Hash.Definitions.SHA1 ->
    y: Spec.Hash.Definitions.word Spec.Hash.Definitions.SHA1 ->
    z: Spec.Hash.Definitions.word Spec.Hash.Definitions.SHA1
  -> Spec.Hash.Definitions.word Spec.Hash.Definitions.SHA1