val step3_body (mi: word_block) (w: step3_body_w_t mi) (st: words_state SHA1) (t: nat{t < 80})
    : Tot (words_state SHA1)
let step3_body
  (mi: word_block)
  (w: step3_body_w_t mi)
  (st: words_state SHA1)
  (t: nat {t < 80})
: Tot (words_state SHA1)
= step3_body' mi st (size t) (w t)
val step3_body (mi: word_block) (w: step3_body_w_t mi) (st: words_state SHA1) (t: nat{t < 80})
    : Tot (words_state SHA1)
let step3_body (mi: word_block) (w: step3_body_w_t mi) (st: words_state SHA1) (t: nat{t < 80})
    : Tot (words_state SHA1) =
step3_body' mi st (size t) (w t)
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
Spec.SHA1.word_block Spec.SHA1.step3_body_w_t Spec.Hash.Definitions.words_state Spec.Hash.Definitions.SHA1 Prims.nat Prims.b2t Prims.op_LessThan Spec.SHA1.step3_body' Lib.IntTypes.size
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
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

(* Section 4.2.1 *)

inline_for_extraction
let k (t: size_t { v t <= 79 } ) : Tot (word SHA1) =
  if t <. 20ul
  then u32 0x5a827999
  else if t <. 40ul
  then u32 0x6ed9eba1
  else if t <. 60ul
  then u32 0x8f1bbcdc
  else u32 0xca62c1d6

(* Section 6.1.2 Step 3 *)

let word_block = Seq.lseq (word SHA1) (block_word_length SHA1)

let step3_body'_aux
  (mi: word_block)
  (st: words_state SHA1)
  (t: size_t {v t < 80})
  (wt: word SHA1 { wt == w mi t } )
: Tot (words_state SHA1)
= let sta = Seq.index st 0 in
  let stb = Seq.index st 1 in
  let stc = Seq.index st 2 in
  let std = Seq.index st 3 in
  let ste = Seq.index st 4 in
  let _T = (sta <<<. 5ul) +. f t stb stc std +. ste +. k t +. wt in
  let e = std in
  let d = stc in
  let c = stb <<<. 30ul in
  let b = sta in
  let a = _T in
  let l : list uint32 = [
    a;
    b;
    c;
    d;
    e;
  ] in
  assert_norm (List.Tot.length l = 5);
  Seq.seq_of_list l

[@"opaque_to_smt"]
let step3_body' = step3_body'_aux

#reset-options "--z3rlimit 50"
[@unifier_hint_injective]
inline_for_extraction
let step3_body_w_t
  (mi: word_block)
: Tot Type
= (t: nat { t < 80 }) -> Tot (wt: word SHA1 { wt == w' mi t } )

let step3_body
  (mi: word_block)
  (w: step3_body_w_t mi)
  (st: words_state SHA1)
  (t: nat {t < 80})
val step3_body (mi: word_block) (w: step3_body_w_t mi) (st: words_state SHA1) (t: nat{t < 80})
    : Tot (words_state SHA1)

    mi: Spec.SHA1.word_block ->
    w: Spec.SHA1.step3_body_w_t mi ->
    st: Spec.Hash.Definitions.words_state Spec.Hash.Definitions.SHA1 ->
    t: Prims.nat{t < 80}
  -> Spec.Hash.Definitions.words_state Spec.Hash.Definitions.SHA1