diff options
Diffstat (limited to 'src/Specific/GF1305.v')
| -rw-r--r-- | src/Specific/GF1305.v | 37 |
1 files changed, 29 insertions, 8 deletions
diff --git a/src/Specific/GF1305.v b/src/Specific/GF1305.v index b004a60d1..02ef714d9 100644 --- a/src/Specific/GF1305.v +++ b/src/Specific/GF1305.v @@ -15,6 +15,7 @@ Local Open Scope Z. Definition modulus : Z := 2^130 - 5. Lemma prime_modulus : prime modulus. Admitted. +Definition int_width := 32%Z. Instance params1305 : PseudoMersenneBaseParams modulus. construct_params prime_modulus 5%nat 130. @@ -26,16 +27,22 @@ Instance subCoeff : SubtractionCoefficient modulus params1305. apply Build_SubtractionCoefficient with (coeff := mul2modulus); cbv; auto. Defined. +Definition freezePreconditions1305 : freezePreconditions params1305 int_width. +Proof. + constructor; compute_preconditions. +Defined. + (* END PseudoMersenneBaseParams instance construction. *) (* Precompute k and c *) Definition k_ := Eval compute in k. Definition c_ := Eval compute in c. +Definition c_subst : c = c_ := eq_refl c_. (* Makes Qed not take forever *) Opaque Z.shiftr Pos.iter Z.div2 Pos.div2 Pos.div2_up Pos.succ Z.land Z.of_N Pos.land N.ldiff Pos.pred_N Pos.pred_double Z.opp Z.mul Pos.mul - Let_In digits Z.add Pos.add Z.pos_sub. + Let_In digits Z.add Pos.add Z.pos_sub andb Z.eqb Z.ltb. Local Open Scope nat_scope. Lemma GF1305Base26_mul_reduce_formula : @@ -45,8 +52,9 @@ Lemma GF1305Base26_mul_reduce_formula : -> rep ls (f*g)%F}. Proof. eexists; intros ? ? Hf Hg. - pose proof (carry_mul_opt_correct k_ c_ (eq_refl k) (eq_refl c_) [0;4;3;2;1;0]_ _ _ _ Hf Hg) as Hfg. + pose proof (carry_mul_opt_rep k_ c_ (eq_refl k) c_subst _ _ _ _ Hf Hg) as Hfg. compute_formula. + exact Hfg. Defined. Lemma GF1305Base26_add_formula : @@ -58,17 +66,30 @@ Proof. eexists; intros ? ? Hf Hg. pose proof (add_opt_rep _ _ _ _ Hf Hg) as Hfg. compute_formula. + exact Hfg. Defined. -Lemma GF25519Base25Point5_sub_formula : - forall f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 - g0 g1 g2 g3 g4 g5 g6 g7 g8 g9, - {ls | forall f g, rep [f0;f1;f2;f3;f4;f5;f6;f7;f8;f9] f - -> rep [g0;g1;g2;g3;g4;g5;g6;g7;g8;g9] g +Lemma GF1305Base26_sub_formula : + forall f0 f1 f2 f3 f4 g0 g1 g2 g3 g4, + {ls | forall f g, rep [f0;f1;f2;f3;f4] f + -> rep [g0;g1;g2;g3;g4] g -> rep ls (f - g)%F}. Proof. eexists. intros f g Hf Hg. pose proof (sub_opt_rep _ _ _ _ Hf Hg) as Hfg. compute_formula. -Defined.
\ No newline at end of file + exact Hfg. +Defined. + +Lemma GF1305Base26_freeze_formula : + forall f0 f1 f2 f3 f4, + {ls | forall x, rep [f0;f1;f2;f3;f4] x + -> rep ls x}. +Proof. + eexists. + intros x Hf. + pose proof (freeze_opt_preserves_rep _ c_subst freezePreconditions1305 _ _ Hf) as Hfreeze_rep. + compute_formula. + exact Hfreeze_rep. +Defined. |