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stdlib: basic commutative algebra #602

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stdlib: basic commutative algebra
strub Aug 21, 2024
7ad5f04
CommAlgebra: witness-level (comax) CRT layer
strub Jul 17, 2026
2d510c3
CommAlgebra: stack as Base / Euclidean; guard dvdw
strub Jul 17, 2026
d1603dc
Poly: evaluation lemma library; tighten the peval definition
strub Jul 17, 2026
1696643
Poly, ZModP: keep instance members as aliases; export IDPoly
strub Jul 17, 2026
fdd2dcb
Poly: evaluation of polynomial products
strub Jul 17, 2026
bfd7ee8
Poly: rename peval_big to peval_sum
strub Jul 17, 2026
f3fbf4e
Poly: products of monic linear factors
strub Jul 17, 2026
d263dec
Poly: mprod does not vanish outside its roots
strub Jul 17, 2026
3c6febe
Poly: simplify the monic-linear-factor lemmas
strub Jul 17, 2026
9b347d0
Poly: PolyField, polynomials over a field; Lagrange interpolation
strub Jul 17, 2026
b55d7a6
Poly: package Lagrange interpolation in a sub-theory; tidy proofs
strub Jul 17, 2026
4d3f588
CommAlgebra: Base owns its big operators and pushes them into Ideal
strub Jul 17, 2026
bbb6cb1
Ring, ZModP: delta-only mixins for IDomain and Field (pilot)
strub Jul 18, 2026
e6b9ba1
Ring, ZModP: reference-bundles for domains and fields
strub Jul 18, 2026
93e2b90
Poly: mixin architecture for the IDomain and Field levels
strub Jul 18, 2026
538159e
ZModP: remove the bundled ZModpField clone
strub Jul 18, 2026
5734cf6
Ideal, CommAlgebra: mixin parameters; BigPoly's CR slot as alias
strub Jul 18, 2026
95b5855
CommAlgebra: generic congruence modulo an element (eqm)
strub Jul 18, 2026
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4 changes: 2 additions & 2 deletions examples/SchnorrPK.ec
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Expand Up @@ -15,7 +15,7 @@ clone G.PowZMod as GP with

clone GP.FDistr as FD.

clone GP.ZModE.ZModpField as ZPF.
clone GP.ZModE.ZModpFieldBd as ZPF.

import G GP GP.ZModE FD.

Expand Down Expand Up @@ -145,7 +145,7 @@ section SchnorrPKSecurity.
auto; rewrite /R /R_DL /oget => &hr /> hne 2!-> /=.
rewrite expM !expB accepting_transcript_1 accepting_transcript_2.
rewrite invM (mulcC m{hr}) -mulcA (mulcA m{hr}) mulcV mulcA mulc1 -expB -expM.
by rewrite ZPF.divrr ?ZPF.subr_eq0 // exp1.
by rewrite ZPF.F.divff ?ZPF.R.subr_eq0 // exp1.
qed.

(* Special honest verifier zero knowledge *)
Expand Down
4 changes: 2 additions & 2 deletions examples/UC/dh_enc.ec
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Expand Up @@ -328,7 +328,7 @@ require DiffieHellman.
clone DiffieHellman as DH.
import DH.DDH DH.G DH.GP DH.FD DH.GP.ZModE.

clone DH.GP.ZModE.ZModpField as ZPF.
clone DH.GP.ZModE.ZModpFieldBd as ZPF.

(* Such statements make no sense when we don't restrict to a
complexity class
Expand Down Expand Up @@ -897,7 +897,7 @@ wp;call (_: ={glob HybFChan.F2Auth.F2Auth,
); last first.

(* Init *)
by auto => /> &2; rewrite expM /= -expM ZPF.mulrC expM.
by auto => /> &2; rewrite expM /= -expM ZPF.R.mulrC expM.
(* Now the call *)
+ by proc;inline *; auto => /> /#.
+ by sim />.
Expand Down
8 changes: 4 additions & 4 deletions examples/cramer-shoup/cramer_shoup.ec
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Expand Up @@ -9,7 +9,7 @@ require DiffieHellman.
clone DiffieHellman as DH.
import DH.DDH DH.G DH.GP DH.FD DH.GP.ZModE.

clone DH.GP.ZModE.ZModpField as ZPF.
clone DH.GP.ZModE.ZModpFieldBd as ZPF.

lemma gt1_q : 1 < order by smt(ge2_p).

Expand Down Expand Up @@ -576,7 +576,7 @@ section Security_Aux.
move=> kL _ xL _ x2L _ yL _ y2L _ zL _ resu bL _.
have H1 : (-uL) * wL + u'L * wL = wL * (u'L - uL) by ring.
have H2 : (-uL) * wL + u'L * wL <> zero.
+ rewrite H1 ZPF.mulf_eq0 negb_or HwL /=.
+ rewrite H1 ZPF.F.mulf_eq0 negb_or HwL /=.
by move: Hu'L;apply: contra => H;ring H.
split => [? _ | _ ]; 1: by field.
move=> z2L _; split => [ | _]; 1: by field.
Expand Down Expand Up @@ -605,7 +605,7 @@ section Security_Aux.
move=> kL _ yL _ y2L _ zL _ r'L _ xL _.
have H1 : (-uL) * wL + u'L * wL = wL * (u'L - uL) by ring.
have H2 : (-uL) * wL + u'L * wL <> zero.
+ rewrite H1 ZPF.mulf_eq0 negb_or HwL /=.
+ rewrite H1 ZPF.F.mulf_eq0 negb_or HwL /=.
by move: Hu'L;apply: contra => H;ring H.
split => [? _ | _ ]; 1: by field.
move=> z2L _; split => [ | _]; 1: by field.
Expand Down Expand Up @@ -751,7 +751,7 @@ section Security_Aux.
move=> yL _ y2L _ zL _ r'L _ xL _ rL _.
have H1 : (-uL) * wL + u'L * wL = wL * (u'L - uL) by ring.
have H2 : (-uL) * wL + u'L * wL <> zero.
+ rewrite H1 ZPF.mulf_eq0 negb_or HwL0 /=.
+ rewrite H1 ZPF.F.mulf_eq0 negb_or HwL0 /=.
by move: HuL;apply: contra => H;ring H.
split => [ | _ /#].
rewrite log_bij !(logg1, logrzM, logDr); field.
Expand Down
6 changes: 3 additions & 3 deletions examples/elgamal.ec
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Expand Up @@ -11,7 +11,7 @@ pragma +implicits.
clone DiffieHellman as DH.
import DH.DDH DH.G DH.GP DH.FD DH.GP.ZModE.

clone DH.GP.ZModE.ZModpField as ZPF.
clone DH.GP.ZModE.ZModpFieldBd as ZPF.

(** Construction: a PKE **)
type pkey = group.
Expand Down Expand Up @@ -107,8 +107,8 @@ section Security.
(fun z, z - loge (if b then m1 else m0){2}).
auto; call (_:true).
auto; progress.
- by rewrite ZPF.addrAC -ZPF.addrA ZPF.subrr ZPF.addr0.
- by rewrite -ZPF.addrA ZPF.subrr ZPF.addr0.
- by rewrite ZPF.R.addrAC -ZPF.R.addrA ZPF.R.subrr ZPF.R.addr0.
- by rewrite -ZPF.R.addrA ZPF.R.subrr ZPF.R.addr0.
- by rewrite expD expgK.
qed.

Expand Down
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