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Diffstat (limited to 'src/Assembly/WordBounds.v')
| -rw-r--r-- | src/Assembly/WordBounds.v | 122 |
1 files changed, 0 insertions, 122 deletions
diff --git a/src/Assembly/WordBounds.v b/src/Assembly/WordBounds.v deleted file mode 100644 index e05fcb1d4..000000000 --- a/src/Assembly/WordBounds.v +++ /dev/null @@ -1,122 +0,0 @@ -Require Import Bedrock.Word. -Import BinNums PArith.BinPos NArith.BinNat NArith.Ndigits. - -Definition wordUn (f : N -> N) {sz : nat} (x : word sz) := - NToWord sz (f (wordToN x)). -Definition wshr {l} n := @wordUn (fun x => N.shiftr x n) l. -Lemma wshr_test : (wordToN (wshr 3 (NToWord 32 (128- 19)))) = 13%N. - reflexivity. -Qed. - -Module WordBoundsExamples. - Definition u31 := word 31. - Definition U31 := NToWord 31. - Definition u64 := word 64. - Definition U64 := NToWord 64. - - Definition c2 : u64 := NToWord _ 2. - Definition c19_31 : u31 := NToWord _ 19. - Definition c19 : u64 := NToWord _ 19. - Definition c38 : u64 := NToWord _ 38. - Definition t25_31 : u31 := NToWord _ (Npos (2^25)). - Definition t26_31 : u31 := NToWord _ (Npos (2^26)). - Definition t25 : u64 := NToWord _ (Npos (2^25)). - Definition t26 : u64 := NToWord _ (Npos (2^26)). - Definition t27 : u64 := NToWord _ (Npos (2^26)). - Definition m25 : u64 := t25^-(NToWord _ 1). - Definition m26 : u64 := t26^-(NToWord _ 1). - Definition r25 (hSk hk:u64) : (u64 * u64) := (hSk ^+ wshr 25 hk, wand m25 hk). - Definition r26 (hSk hk:u64) : (u64 * u64) := (hSk ^+ wshr 26 hk, wand m26 hk). - Definition r25mod (hSk hk:u64) : (u64 * u64) := (hSk ^+ c19^*wshr 25 hk, wand m25 hk). - - Lemma simple_add_rep : forall (a b c d:N), - (a < Npos(2^29) -> b < Npos(2^29) -> c < Npos(2^29) -> d < Npos(2^29))%N -> - wordToN(U31 a ^+ U31 b ^+ U31 c ^+ U31 d) = (a + b + c + d)%N. - Admitted. - - Lemma simple_add_bound : forall (a b c d:u64), - a < t25 -> b < t25 -> c < t25 -> d < t25 -> - (a ^+ b ^+ c ^+ d) < t27. - Admitted. - - (* the bounds can as well be stated in N if the _rep lemma works. - I am not sure whether it is a better idea to propagate the bounds in word or - in N, though -- proving rep requires propagating bounds for the subexpressions. - *) - - Lemma simple_linear_rep : forall (a b:N), (a < Npos(2^25) + Npos(2^26) -> b < Npos(2^25))%N -> - wordToN((U31 a)^*c19_31 ^+ U31 b) = (a*19 + b)%N. - Admitted. - - Lemma simple_linear_bound : forall (a b:u31), a < t25_31 ^+ t26_31 -> b < t25_31 -> - a^*c19_31 ^+ b < (NToWord _ 1946157056). (* (2**26+2**25)*19 + 2**25 = 1946157056 *) - Admitted. - - Lemma simple_mul_carry_rep : forall (a b c:N), (a < Npos(2^26) -> b < Npos(2^26) -> c < Npos(2^26))%N -> - wordToN(wshr 26 (U64 a ^* U64 b) ^+ U64 c) = ((a*b)/(2^26) + c)%N. - Admitted. - - Lemma simple_mul_carry_bound : forall (a b c:u64), a < t26 -> b < t26 -> c < t26 -> - wshr 26 (a ^* b) ^+ c < t27. - Admitted. - - Lemma simple_mul_reduce_rep : forall (a b c:N), (a < Npos(2^26) -> b < Npos(2^26))%N -> - wordToN(wand m26 (U64 a ^* U64 b)) = ((a*b) mod (2^26) + c)%N. - Admitted. - - Lemma sandy2x_bound : forall - (* this example is transcribed by hand from <https://eprint.iacr.org/2015/943.pdf> section 2.2. - it is very representative of the bounds check / absence-of-overflow proofs we actually - want to do. However, given its size, presence of transcription errors is totally plausible. - A corresponding _rep proof will also necessary.*) - (f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 : u64) - (g0 g1 g2 g3 g4 g5 g6 g7 g8 g9 : u64), - f0 < t26 -> g0 < t26 -> - f1 < t25 -> g1 < t25 -> - f2 < t26 -> g2 < t26 -> - f3 < t25 -> g3 < t25 -> - f4 < t26 -> g4 < t26 -> - f5 < t25 -> g5 < t25 -> - f6 < t26 -> g6 < t26 -> - f7 < t25 -> g7 < t25 -> - f8 < t26 -> g8 < t26 -> - f9 < t25 -> g9 < t25 -> - - let h0 := f0^*g0 ^+ c38^*f1^*g9 ^+ c19^*f2^*g8 ^+ c38^*f3^*g7 ^+ c19^*f4^*g6 ^+ c38^*f5^*g5 ^+ c19^*f6^*g4 ^+ c38^*f7^*g3 ^+ c19^*f8^*g2 ^+ c38^*f9^*g1 in - let h1 := f0^*g1 ^+ f1^*g0 ^+ c19^*f2^*g9 ^+ c19^*f3^*g8 ^+ c19^*f4^*g7 ^+ c19^*f5^*g6 ^+ c19^*f6^*g5 ^+ c19^*f7^*g4 ^+ c19^*f8^*g3 ^+ c19^*f9^*g2 in - let h2 := f0^*g2 ^+ c2^* f1^*g1 ^+ f2^*g0 ^+ c38^*f3^*g9 ^+ c19^*f4^*g8 ^+ c38^*f5^*g7 ^+ c19^*f6^*g6 ^+ c38^*f7^*g5 ^+ c19^*f8^*g4 ^+ c38^*f9^*g3 in - let h3 := f0^*g3 ^+ f1^*g2 ^+ f2^*g1 ^+ f3^*g0 ^+ c19^*f4^*g9 ^+ c19^*f5^*g8 ^+ c19^*f6^*g7 ^+ c19^*f7^*g6 ^+ c19^*f8^*g5 ^+ c19^*f9^*g4 in - let h4 := f0^*g4 ^+ c2^* f1^*g3 ^+ f2^*g2 ^+ c2^* f3^*g1 ^+ f4^*g0 ^+ c38^*f5^*g9 ^+ c19^*f6^*g8 ^+ c38^*f7^*g7 ^+ c19^*f8^*g6 ^+ c38^*f9^*g5 in - let h5 := f0^*g5 ^+ f1^*g4 ^+ f2^*g3 ^+ f3^*g2 ^+ f4^*g1 ^+ f5^*g0 ^+ c19^*f6^*g9 ^+ c19^*f7^*g8 ^+ c19^*f8^*g7 ^+ c19^*f9^*g6 in - let h6 := f0^*g6 ^+ c2^* f1^*g5 ^+ f2^*g4 ^+ c2^* f3^*g3 ^+ f4^*g2 ^+ c2^* f5^*g1 ^+ f6^*g0 ^+ c38^*f7^*g9 ^+ c19^*f8^*g8 ^+ c38^*f9^*g7 in - let h7 := f0^*g7 ^+ f1^*g6 ^+ f2^*g5 ^+ f3^*g4 ^+ f4^*g3 ^+ f5^*g2 ^+ f6^*g1 ^+ f7^*g0 ^+ c19^*f8^*g9 ^+ c19^*f9^*g8 in - let h8 := f0^*g8 ^+ c2^* f1^*g7 ^+ f2^*g6 ^+ c2^* f3^*g5 ^+ f4^*g4 ^+ c2^* f5^*g3 ^+ f6^*g2 ^+ c2^* f7^*g1 ^+ f8^*g0 ^+ c38^*f9^*g9 in - let h9 := f0^*g9 ^+ f1^*g8 ^+ f2^*g7 ^+ f3^*g6 ^+ f4^*g5 ^+ f5^*g4 ^+ f6^*g3 ^+ f7^*g2 ^+ f8^*g1 ^+ f9^*g0 in - - let (h1_1, h0_1) := r26 h1 h0 in - let (h2_1, h1_2) := r25 h2 h1_1 in - let (h3_1, h2_2) := r26 h3 h2_1 in - let (h4_1, h3_2) := r25 h4 h3_1 in - - let (h6_1, h5_1) := r25 h6 h5 in - let (h7_1, h6_2) := r26 h7 h6_1 in - let (h8_1, h7_2) := r25 h8 h7_1 in - let (h9_1, h8_2) := r26 h9 h8_1 in - let (h0_2, h9_2) := r25mod h0_1 h9_1 in - let (h1_3, h0_2) := r26 h1_2 h0_1 in - - let (h5_2, h4_2) := r26 h5_1 h4_1 in - let (h6_2, h5_3) := r25 h6_1 h5_2 in - - h0_2 < t26 /\ - h1_3 < t27 /\ - h2_2 < t26 /\ - h3_2 < t25 /\ - h4_2 < t26 /\ - h5_3 < t25 /\ - h6_2 < t27 /\ - h7_2 < t25 /\ - h8_2 < t26 /\ - h9_2 < t25. - Admitted. -End WordBoundsExamples. |