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Addressing Alex's review
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@pennyannn
pennyannn committed Sep 19, 2024
1 parent cc420c4 commit 53024ec
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Showing 2 changed files with 21 additions and 39 deletions.
10 changes: 3 additions & 7 deletions Arm/BitVec.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -311,10 +311,8 @@ def reverse (x : BitVec n) : BitVec n :=
match i with
| 0 => acc
| j + 1 =>
have h1 : i - 1 - (i - 1) + 1 = 1 := by omega
let xi : BitVec 1 := BitVec.cast h1 $ extractLsb (i - 1) (i - 1) x
have h2 : 1 = (n - i) - (n - i) + 1 := by omega
let acc := BitVec.partInstall (n - i) (n - i) (BitVec.cast h2 xi) acc
let xi : BitVec 1 := extractLsb' (i - 1) 1 x
let acc := BitVec.partInstall (n - i) (n - i) (xi.cast (by omega)) acc
reverseTR x j acc
reverseTR x n $ BitVec.zero n

Expand All @@ -328,9 +326,7 @@ def split (x : BitVec n) (e : Nat) (h : 0 < e): List (BitVec e) :=
| 0 => acc
| j + 1 =>
let lo := (n / e - i) * e
let hi := lo + e - 1
have h₀ : hi - lo + 1 = e := by simp only [hi, lo]; omega
let part : BitVec e := BitVec.cast h₀ (extractLsb hi lo x)
let part : BitVec e := extractLsb' lo e x
let newacc := part :: acc
splitTR x e h j newacc
splitTR x e h (n / e) []
Expand Down
50 changes: 18 additions & 32 deletions Specs/GCMV8.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -41,10 +41,10 @@ def pmult (x: BitVec (m + 1)) (y : BitVec (n + 1)) : BitVec (m + n + 1) :=
| 0 => acc
| j + 1 =>
let acc := acc <<< 1
have h : m + n + 1 = n + (m + 1) := by omega
let tmp := if getMsbD y (n + 1 - i)
then (BitVec.zero n) ++ x
else BitVec.cast h (BitVec.zero (m + n + 1))
else BitVec.zero (n + (m + 1))
have h : m + n + 1 = n + (m + 1) := by omega
let acc := (BitVec.cast h acc) ^^^ tmp
pmultTR x y j (BitVec.cast h.symm acc)
pmultTR x y (n + 1) (BitVec.zero (m + n + 1))
Expand All @@ -66,29 +66,23 @@ private def reduce (x : BitVec n) (y : BitVec n) : BitVec n :=
if getLsbD y (GCMV8.degree x) then y ^^^ x else y

/-- Performs division of polynomials over GF(2). -/
def pdiv (x: BitVec n) (y : BitVec m) (h : 0 < m): BitVec n :=
def pdiv (x: BitVec n) (y : BitVec m): BitVec n :=
let rec pdivTR (x : BitVec n) (y : BitVec m) (i : Nat) (z : BitVec m)
(acc : BitVec n) : BitVec n :=
match i with
| 0 => acc
| j + 1 =>
have h2 : (i - 1) - (i - 1) + 1 = 1 := by omega
let xi : BitVec 1 := BitVec.cast h2 (extractLsb (i - 1) (i - 1) x)
have h3 : m - 1 - 0 + 1 = m := by omega
let zi : BitVec m :=
BitVec.cast h3 (extractLsb (m - 1) 0 ((GCMV8.reduce y z) ++ xi))
have h1 : GCMV8.degree y - GCMV8.degree y + 1 = 1 := by omega
let bit : BitVec 1 :=
BitVec.cast h1 $ extractLsb (GCMV8.degree y) (GCMV8.degree y) zi
have h4 : 1 = (i - 1) - (i - 1) + 1 := by omega
let xi := extractLsb' (i - 1) 1 x
let zi := extractLsb' 0 m ((GCMV8.reduce y z) ++ xi)
let bit := extractLsb' (GCMV8.degree y) 1 zi
let newacc : BitVec n :=
partInstall (i - 1) (i - 1) (BitVec.cast h4 bit) acc
partInstall (i - 1) (i - 1) (bit.cast (by omega)) acc
pdivTR x y j zi newacc
pdivTR x y n (BitVec.zero m) (BitVec.zero n)

example : pdiv 0b1101#4 0b10#2 (by omega) = 0b110#4 := by rfl
example : pdiv 0x1a#5 0b10#2 (by omega) = 0b1101#5 := by rfl
example : pdiv 0b1#1 0b10#2 (by omega) = 0b0#1 := by rfl
example : pdiv 0b1101#4 0b10#2 = 0b110#4 := by rfl
example : pdiv 0x1a#5 0b10#2 = 0b1101#5 := by rfl
example : pdiv 0b1#1 0b10#2 = 0b0#1 := by rfl

/-- Performs modulus of polynomials over GF(2). -/
def pmod (x : BitVec n) (y : BitVec (m + 1)) (H : 0 < m) : BitVec m :=
Expand All @@ -98,13 +92,10 @@ def pmod (x : BitVec n) (y : BitVec (m + 1)) (H : 0 < m) : BitVec m :=
| 0 => r
| j + 1 =>
let xi := getLsbD x (n - i)
have h : m - 1 + 1 = m := by omega
let tmp : BitVec (m - 1 + 1) :=
if xi
then extractLsb (m - 1) 0 p
else BitVec.cast h.symm (BitVec.zero m)
let r := (BitVec.cast h.symm r) ^^^ tmp
pmodTR x y (GCMV8.reduce y (p <<< 1)) j (BitVec.cast h r) H
let tmp :=
if xi then extractLsb' 0 m p else BitVec.zero m
let r := r ^^^ tmp
pmodTR x y (GCMV8.reduce y (p <<< 1)) j r H
if y = 0 then 0 else pmodTR x y (GCMV8.reduce y 1) n (BitVec.zero m) H

example: pmod 0b011#3 0b00#2 (by omega) = 0b0#1 := by rfl
Expand Down Expand Up @@ -187,8 +178,7 @@ def GCMInitV8 (H : BitVec 128) : (List (BitVec 128)) :=
[H0_rev, H1, H2_rev, H3_rev, H4, H5_rev, H6_rev,
H7, H8_rev, H9_rev, H10, H11_rev]

set_option maxRecDepth 20000 in
set_option maxHeartbeats 200000 in
set_option maxRecDepth 8000 in
example : GCMInitV8 0x66e94bd4ef8a2c3b884cfa59ca342b2e#128 ==
[ 0x1099f4b39468565ccdd297a9df145877#128,
0x62d81a7fe5da3296dd4b631a4b7c0e2b#128,
Expand All @@ -213,8 +203,7 @@ def GCMGmultV8 (H : BitVec 128) (Xi : List (BitVec 8)) (h : 8 * Xi.length = 128)
let H := (lo H) ++ (hi H)
split (GCMV8.gcm_polyval H (BitVec.cast h (BitVec.flatten Xi))) 8 (by omega)

set_option maxRecDepth 20000 in
set_option maxHeartbeats 200000 in
set_option maxRecDepth 8000 in
example : GCMGmultV8 0x1099f4b39468565ccdd297a9df145877#128
[ 0x10#8, 0x54#8, 0x43#8, 0xb0#8, 0x2c#8, 0x4b#8, 0x1f#8, 0x24#8,
0x3b#8, 0xcd#8, 0xd4#8, 0x87#8, 0x16#8, 0x65#8, 0xb3#8, 0x2b#8 ] (by decide) =
Expand Down Expand Up @@ -242,9 +231,7 @@ def GCMGhashV8 (H : BitVec 128) (Xi : List (BitVec 8))
| 0 => Xi
| j + 1 =>
let lo := (i - 1) * 128
let hi := lo + 127
have h2 : hi - lo + 1 = 128 := by omega
let inpi : BitVec 128 := BitVec.cast h2 $ extractLsb hi lo inp
let inpi := extractLsb' lo 128 inp
let Xj := GCMV8.gcm_ghash_block H Xi inpi
GCMGhashV8TR H Xj inp j h1
have h3 : 128 ∣ 8 * inp.length := by omega
Expand All @@ -253,8 +240,7 @@ def GCMGhashV8 (H : BitVec 128) (Xi : List (BitVec 8))
let flat_inp := BitVec.flatten inp
split (GCMGhashV8TR H flat_Xi flat_inp (8 * inp.length / 128) h3) 8 (by omega)

set_option maxRecDepth 20000 in
set_option maxHeartbeats 200000 in
set_option maxRecDepth 8000 in
example : GCMGhashV8 0x1099f4b39468565ccdd297a9df145877#128
[ 0xa2#8, 0xc9#8, 0x9c#8, 0x56#8, 0xeb#8, 0xa7#8, 0x91#8, 0xf6#8,
0x9e#8, 0x15#8, 0xa6#8, 0x00#8, 0x67#8, 0x29#8, 0x7e#8, 0x0f#8 ]
Expand Down

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