saymrwulf/dalek-ed25519-verified
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dalek-ed25519-verified/verification/Proofs
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mrwulf ee739ed1f6 PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT 
(verify_accepts_iff_decompress, button-enforced)

THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and

    verifier accepts   <=>   Pt = [k]*(-A) + [s]*B    (as points)

- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).

Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
  d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
  of valid on-curve points decompress to them - from_bytes recovers the
  y-residue exactly (sign bit discarded), Q's own x witnesses the
  square so sqrt_ratio_i returns the even root, the sign bit (Q's
  x-parity, from byte 31) selects +/-root, and the parity-injectivity
  argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
  ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.

Full button green fresh. Remaining: replicate x3, coherence pass 4.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-06 00:05:55 +02:00
..
AddSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
Basic.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
CompressSpec.lean Phase 2, brick 1 complete: ed_compress_spec - compress emits the canonical 2026-07-05 13:33:58 +02:00
ConstSpecs.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
DecompressMain.lean PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT 2026-07-06 00:05:55 +02:00
DecompressSpec.lean Phase 2, decompress part 2b: THE SQUARE-ROOT WALK PROVEN 2026-07-05 22:03:57 +02:00
Denote.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
DsmLoopSpec.lean Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop 2026-07-04 15:30:18 +02:00
DsmMulSpec.lean NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex 2026-07-04 16:52:06 +02:00
DsmNafLoadSpec.lean NAF campaign stages 1-2: LE load walks + the digit loop's arithmetic core 2026-07-04 15:30:18 +02:00
DsmNafLoopSpec.lean NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex 2026-07-04 16:52:06 +02:00
DsmNafMath.lean NAF campaign stages 1-2: LE load walks + the digit loop's arithmetic core 2026-07-04 15:30:18 +02:00
DsmNafSpec.lean NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex 2026-07-04 16:52:06 +02:00
DsmStepSpec.lean Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop 2026-07-04 15:30:18 +02:00
DsmTableSpec.lean Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop 2026-07-04 15:30:18 +02:00
EdAddAffNiels.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdAddProjNiels.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdConvert.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdCurve.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdDenote.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdDouble.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
EdMain.lean group-law layer: complete twisted Edwards addition law proven 2026-07-02 14:50:42 +02:00
FeQ.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
Field.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
FieldMain.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
FromBytesSpec.lean Phase 2, decompress step 2: THE BYTE PARSER PROVEN (from_bytes_spec, 2026-07-05 22:55:18 +02:00
InvertSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
MulSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
P25519.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
PointEqSpec.lean THE POINT-LEVEL VERIFICATION EQUATION: verify_accepts_iff_point_eq, 2026-07-05 18:27:25 +02:00
PointLiftSpec.lean PHASE 2 HALF-LIFT PROVEN: verify_accepts_iff_point, button-enforced 2026-07-05 16:06:23 +02:00
ReduceSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
ScalarAddSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarBytesSpec.lean Hash-to-scalar PROVEN: from_bytes_wide_spec - Scalar::from_hash's reduction is exact mod l 2026-07-04 10:31:32 +02:00
ScalarDenote.lean Merge scalar into CurveField; integrate the verify glue against the model 2026-07-04 18:13:58 +02:00
ScalarFromBytesSpec.lean Hash-to-scalar PROVEN: from_bytes_wide_spec - Scalar::from_hash's reduction is exact mod l 2026-07-04 10:31:32 +02:00
ScalarFullMulSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarLoop.lean scalar: generic loop-combinator lemmas (loop_step, range_next_lt/ge_spec) 2026-07-02 21:47:47 +02:00
ScalarMain.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarMontSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarMulSpec.lean scalar layer: mul_internal proven — Montgomery frontier phase A down 2026-07-03 18:56:04 +02:00
ScalarPackSpec.lean Phase 2, half-lift prerequisite: the hash-to-scalar entry is canonical 2026-07-05 14:10:09 +02:00
ScalarReduceSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarSubSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
ScalarUnpackSpec.lean Hash-to-scalar PROVEN: from_bytes_wide_spec - Scalar::from_hash's reduction is exact mod l 2026-07-04 10:31:32 +02:00
ScalarWideSpec.lean Signature layer, first bricks: canonicity closure + hash-to-scalar foundation 2026-07-03 23:18:29 +02:00
SigApexSpec.lean THE SIGNATURE APEX: the EdDSA verification equation, proven and audited 2026-07-04 19:45:55 +02:00
Square2Spec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
SquareSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
SubNegSpec.lean field layer: 14 proofs pass, fieldImplementation axiom-clean 2026-07-02 14:17:44 +02:00
ToBytesMath.lean Phase 2, half-lift prerequisite: the hash-to-scalar entry is canonical 2026-07-05 14:10:09 +02:00
ToBytesSpec.lean Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited) 2026-07-05 13:10:43 +02:00