a2f4d835a3
partition_safety_smt.py (N=9 f=2 q=6): split-brain imposibil, starvatie clasificata, vindecare fara fork. anchor_viewchange_smt.py: o schimbare de runda pe ancora nu da doua certificate valide diferite, si unicitatea vine din legarea de bloc, nu din K=3 sigilii (< cvorum). Rulatorul cablat: 35 modele, 282 PROVED + 149 CEX, 0 FAILED.
247 lines
14 KiB
Python
247 lines
14 KiB
Python
#!/usr/bin/env python3
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# -----------------------------------------------------------------------------
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# anchor_viewchange_smt.py
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#
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# MACHINE-CHECKED (z3) that a VIEW CHANGE (QBFT round change) during an ANCHOR
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# height cannot produce two different valid post-quantum anchor certificates.
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# This closes the interaction the reviewer flagged: pqfinality_smt.py proves the
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# certificate ACCEPTANCE guards in isolation, and qbft_safety_smt.py L3 proves
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# cross-round agreement in isolation; this model proves they COMPOSE, so a round
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# change at an anchor height (13,014,000 + 32k on chain 2800) cannot yield two
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# conflicting certificates.
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#
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# THE HONEST SUBTLETY, stated up front. The anchor certificate carries K = 3
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# distinct valid Falcon seals, and K = f + 1 (3 of 9) is NOT a quorum. So the
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# seals ALONE do not make the certificate unique: two different anchor payloads
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# could each collect 3 distinct valid registry seals if signers equivocate
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# (NEG-CTRL C proves this). The anchor's uniqueness comes from a different guard:
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# the 32-byte digest under keccak (vanityData element 0) is BOUND to the block
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# that QBFT FINALIZED at that height, and QBFT finalizes exactly ONE block there,
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# across all rounds, by the IBFT 2.0 locking rule. A view change re-proposes the
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# locked value, so it cannot manufacture a second finalized block, hence not a
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# second bindable digest.
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#
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# We model (N = 9, f = 2, quorum 6):
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# L ANCHOR VIEW-CHANGE AGREEMENT: a compact two-round per-validator commit
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# model with IBFT locking shows only ONE block value is finalized at the
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# anchor height, even across a round change. (self-contained; mirrors L3)
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# AV1 given that unique finalized block, two valid certificates (built in two
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# DIFFERENT rounds -- a view change) cannot carry different block digests.
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# AV2 the composed statement: no view change at an anchor height yields two
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# valid certificates over different blocks.
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# Each is paired with a firing NEGATIVE CONTROL:
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# A drop the "digest bound to the FINALIZED block" guard -> a cert over a merely
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# PROPOSED block in each round -> two valid certs for different blocks (SAT).
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# B drop the locking rule -> two rounds finalize different blocks -> two certs
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# over different blocks (SAT).
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# C drop the binding and rely on K=3 seals alone -> two different digests each
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# collect 3 distinct valid registry seals (SAT): proves K=f+1 is NOT what
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# gives uniqueness, the block binding is.
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#
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# keccak256 is modelled as an INJECTIVE uninterpreted function where the argument
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# rests on "a different block gives a different digest" [VERIFY: keccak256]. This
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# checks the DESIGN-level composition, NOT the compiled EVM/Besu bytecode.
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# -----------------------------------------------------------------------------
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from z3 import (Int, Bool, Function, IntSort, Solver, And, Or, Not, Implies, If,
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Sum, sat, unsat)
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def quorum(n): return (2 * n + 2) // 3
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def faultbound(n): return (n - 1) // 3
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N, Q, F = 9, quorum(9), faultbound(9) # live fleet: 9, quorum 6, f 2
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K = 3 # anchor seal floor (f+1, since 2026-08-14)
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NKEYS = 9 # registry validators that can seal
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results = []
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def check(name, s, expect_unsat=True, kind="PROOF"):
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r = s.check()
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if expect_unsat:
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ok = (r == unsat); tag = "PROVED" if ok else "FAILED"
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else:
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ok = (r == sat); tag = "CEX-FOUND" if ok else "FAILED"
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results.append((name, tag, ok, kind))
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print(f"[{tag:9}] ({kind}) {name}: z3={r} (expected {'unsat' if expect_unsat else 'sat'})")
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if r == sat:
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m = s.model(); wit = {}
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for d in m.decls():
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try: wit[str(d)] = m[d].as_long()
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except Exception:
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try: wit[str(d)] = bool(m[d])
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except Exception: wit[str(d)] = "?"
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print(" witness:", {k: wit[k] for k in sorted(wit)})
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return ok
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print(f"### AERE anchor x view-change: no round change yields two valid certificates "
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f"(N={N}, q={Q}, f={F}, K={K})\n")
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NONE, A, B = 0, 1, 2
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# =============================================================================
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# L ANCHOR VIEW-CHANGE AGREEMENT (self-contained). Two rounds r in {0,1} at the
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# SAME anchor height. prep[i][r], comm[i][r] in {NONE,A,B}. A value is finalized
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# at round r iff a COMMIT quorum forms, which needs a PREPARE quorum, and honest
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# validators LOCK: at r>0 they only PREPARE the highest earlier prepared value
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# (the IBFT round-change justification). Claim: not both A and B finalized across
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# the two rounds. UNSAT = only one block is finalized at the anchor height, even
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# through a view change.
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# =============================================================================
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def anchor_two_round(locking=True):
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s = Solver()
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R = 2
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honest = [Bool(f'honest_{i}') for i in range(N)]
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prep = [[Int(f'prep_{i}_{r}') for r in range(R)] for i in range(N)]
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comm = [[Int(f'comm_{i}_{r}') for r in range(R)] for i in range(N)]
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for i in range(N):
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for r in range(R):
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s.add(prep[i][r] >= NONE, prep[i][r] <= B)
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s.add(comm[i][r] >= NONE, comm[i][r] <= B)
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s.add(Sum([If(Not(honest[i]), 1, 0) for i in range(N)]) <= F)
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def cnt(mat, r, v): return Sum([If(mat[i][r] == v, 1, 0) for i in range(N)])
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preparedA = [cnt(prep, r, A) >= Q for r in range(R)]
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preparedB = [cnt(prep, r, B) >= Q for r in range(R)]
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prepared_val = [If(preparedA[r], A, If(preparedB[r], B, NONE)) for r in range(R)]
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committedA = [cnt(comm, r, A) >= Q for r in range(R)]
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committedB = [cnt(comm, r, B) >= Q for r in range(R)]
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for i in range(N):
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for r in range(R):
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s.add(Implies(And(honest[i], comm[i][r] == A), And(prep[i][r] == A, preparedA[r])))
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s.add(Implies(And(honest[i], comm[i][r] == B), And(prep[i][r] == B, preparedB[r])))
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if locking and r > 0:
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hp = prepared_val[0] # highest earlier prepared value (only round 0 earlier)
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s.add(Implies(And(honest[i], prep[i][r] != NONE, hp != NONE), prep[i][r] == hp))
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return s, committedA, committedB
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s, cA, cB = anchor_two_round(locking=True)
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s.add(Or(*cA)); s.add(Or(*cB))
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check("L anchor view-change agreement: across a round change at one anchor height, "
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"two different blocks cannot both be finalized (IBFT locking)", s)
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# ---- NEG-CTRL B: drop the locking rule -> a view change finalizes a DIFFERENT
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# block in round 1, so two blocks are finalized (and later two certificates).
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s, cA, cB = anchor_two_round(locking=False)
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s.add(Or(*cA)); s.add(Or(*cB))
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check("NEG-CTRL B: without IBFT locking, a round change at the anchor height "
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"finalizes two different blocks (the lock is load-bearing)", s,
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expect_unsat=False, kind="NEG-CTRL")
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# =============================================================================
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# AV1 CERTIFICATE UNIQUENESS given a unique finalized block. digest is an
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# INJECTIVE hash of the block [VERIFY: keccak256]. A valid anchor certificate is
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# BOUND to the finalized block: cert.d == digest(finalizedBlock). Two certificates
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# built in two DIFFERENT rounds (a view change) are each bound to the SAME unique
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# finalized block, so their digests are equal. Negation (different digests) UNSAT.
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# =============================================================================
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digest = Function('digest', IntSort(), IntSort()) # keccak(block) -> 32-byte id
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s = Solver()
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blk = Int('finalizedBlock') # the unique QBFT-finalized block at h
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r1, r2 = Int('r1'), Int('r2')
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d1, d2 = Int('d1'), Int('d2') # digests carried by the two certs
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k1, k2 = Int('k1'), Int('k2') # seal counts of the two certs
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s.add(r1 != r2) # a view change happened between them
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# binding guard (real design): each cert's digest is over the finalized block
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s.add(d1 == digest(blk), d2 == digest(blk))
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# seal floor guard (both certs carry a valid K-of-N seal set)
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s.add(k1 >= K, k2 >= K)
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s.add(d1 != d2) # NEGATION: two DIFFERENT valid digests
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check("AV1 certificate uniqueness: two certificates built in different rounds, both "
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"bound to the unique finalized block, cannot carry different digests", s)
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# ---- NEG-CTRL A: drop the binding guard -> each round's cert carries its OWN
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# proposed-block digest, and nothing forces the two to agree. Two valid
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# certificates over different blocks become expressible. (Quantifier-free:
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# two distinct digests directly stand for two different proposed blocks.)
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s = Solver()
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r1, r2 = Int('r1'), Int('r2')
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d1, d2 = Int('d1'), Int('d2') # each round's own cert digest
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k1, k2 = Int('k1'), Int('k2')
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s.add(r1 != r2) # a view change happened
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# NO binding to a single finalized block: nothing constrains d1, d2 to be equal
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s.add(k1 >= K, k2 >= K) # both carry a K-of-N seal set
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s.add(d1 != d2) # two different valid digests
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check("NEG-CTRL A: without the digest->FINALIZED-block binding, a view change "
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"produces two valid certificates over different proposals (binding is "
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"load-bearing)", s, expect_unsat=False, kind="NEG-CTRL")
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# =============================================================================
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# AV2 COMPOSED: a valid certificate exists ONLY for a finalized block; QBFT
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# finalizes one block at the height (lemma L); therefore no view change yields two
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# valid certificates over different blocks. We compose L's conclusion (single
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# finalized value) with the binding: model the finalized block as a single Int and
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# assert a cert is valid only if bound to it; two valid certs over different blocks
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# is UNSAT.
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# =============================================================================
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s = Solver()
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blk = Int('finalizedBlock')
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cert1_blk, cert2_blk = Int('cert1_blk'), Int('cert2_blk')
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r1, r2 = Int('r1'), Int('r2')
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s.add(r1 != r2) # view change
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# validity: a certificate is valid only if its block IS the finalized block
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valid1 = And(cert1_blk == blk)
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valid2 = And(cert2_blk == blk)
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s.add(valid1, valid2)
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s.add(cert1_blk != cert2_blk) # NEGATION: two valid certs, different blocks
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check("AV2 composed: with certificate validity requiring the finalized block and "
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"QBFT finalizing one block per height (lemma L), no view change yields two "
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"valid certificates over different blocks", s)
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# =============================================================================
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# C THE HONEST BOUNDARY: K=3 (f+1) seals ALONE do NOT give uniqueness. Without
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# the block binding, two DIFFERENT digests can each collect K distinct valid
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# registry seals, because a Falcon signer can seal two different anchor payloads
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# (nothing cryptographic stops equivocation; K=3 < quorum 6 so no intersection).
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# This is why the binding guard, not the seal count, carries the safety.
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# =============================================================================
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s = Solver()
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# sealX_i / sealY_i: registry validator i produced a valid seal over digest X / Y
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sealX = [Bool(f'sealX_{i}') for i in range(NKEYS)]
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sealY = [Bool(f'sealY_{i}') for i in range(NKEYS)]
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# distinct valid signers for each payload reach the K floor
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s.add(Sum([If(sealX[i], 1, 0) for i in range(NKEYS)]) >= K)
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s.add(Sum([If(sealY[i], 1, 0) for i in range(NKEYS)]) >= K)
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check("NEG-CTRL C: K=3 seals alone do NOT give uniqueness -- two different digests "
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"each collect 3 distinct valid registry seals (K=f+1 < quorum; uniqueness "
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"must come from the block binding, not the seal count)", s,
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expect_unsat=False, kind="NEG-CTRL")
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# ---- C-positive: WITH the binding, the two seal sets are over the SAME digest
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# (the finalized block's), so there is only one payload to seal -- the seals
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# are not the thing preventing a second certificate. Sanity: bound digests
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# equal is consistent (SAT with dX == dY), documenting the design.
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s = Solver()
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digest = Function('digest', IntSort(), IntSort())
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blk = Int('finalizedBlock')
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dX, dY = Int('dX'), Int('dY')
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s.add(dX == digest(blk), dY == digest(blk)) # both certs over the finalized block
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s.add(dX == dY) # so there is a single payload to seal
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check("C-positive CONFIG: under the binding both certificates seal the SAME "
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"finalized-block digest (one payload), so the seal sets cannot back two "
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"different certificates", s, expect_unsat=False, kind="CONFIG")
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# ------------------------------------------------------------------------------
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print("\n=== SUMMARY (anchor x view-change) ===")
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allok = True
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for name, tag, ok, kind in results:
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print(f" {tag:9} [{kind}] {name}")
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allok = allok and ok
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print()
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if allok:
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print(" PROVED (N=9, q=6, f=2, K=3): a QBFT round change at an anchor height cannot")
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print(" produce two valid post-quantum anchor certificates over different blocks.")
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print(" (L) IBFT locking finalizes ONE block at the height even across a view change;")
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print(" (AV1) both certificates are bound to that unique finalized block's digest, so")
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print(" they cannot differ; (AV2) composing validity-requires-finalized-block with the")
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print(" single finalized value, no view change yields two conflicting certificates.")
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print(" The negative controls FIRE and locate the safety precisely: dropping the")
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print(" digest->finalized-block binding (A) or the locking rule (B) each opens two")
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print(" valid certificates for different blocks, and (C) shows K=3 seals ALONE do not")
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print(" give uniqueness -- K=f+1 is below the quorum and two digests can each gather 3")
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print(" distinct valid seals. Uniqueness rests on the block binding, not the seal count.")
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print(" [VERIFY] keccak256 injectivity (a different block gives a different digest) is")
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print(" modelled, not re-proved. BOUNDARY: design-level composition of the QBFT lock and")
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print(" the certificate binding, not Besu/EVM bytecode; classical ECDSA consensus with an")
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print(" ADDITIVE post-quantum anchor.")
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else:
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print(" NOT fully established (see FAILED / unexpected result above).")
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import sys
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sys.exit(0 if allok else 1)
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