4a0b48588c
Aere Network public source. Everything here can be checked against the live chain (chain id 2800, https://rpc.aere.network). Scope note, stated up front rather than buried: consensus on chain 2800 is classical secp256k1 ECDSA QBFT. The post-quantum work in this repository is at the signature, precompile, account and transport layers. Nothing here makes the consensus post-quantum, and no document in it should be read as claiming so.
223 lines
11 KiB
Python
223 lines
11 KiB
Python
#!/usr/bin/env python3
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# -----------------------------------------------------------------------------
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# lending_liquidation_smt.py
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#
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# SMT proof (z3) of the safety properties of AereLendingMarket.liquidate()'s
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# seize / clamp math and scaled-debt bookkeeping.
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#
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# Contract: contracts/contracts/lending/AereLendingMarket.sol (liquidate)
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#
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# The liquidation path is the richest arithmetic in the market and the one that
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# moves borrower collateral to a third party, so it is the highest-value money
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# surface to check. We model the exact Solidity computation (integer division,
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# in 18-dec USD) and prove four safety properties, each with a NEGATIVE CONTROL
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# that reproduces the corresponding real bug when the guard is removed.
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#
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# Solidity (decimals normalised to 18, so _scaleUp/_scaleDown are identity --
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# see ASSUMPTION A1):
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# valueRepaid = pay * debtPrice / 1e18
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# valueToSeize = valueRepaid + valueRepaid * LIQ_BONUS_BPS / 10_000
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# seize = valueToSeize * 1e18 / colPrice
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# if seize > collateral: # INSOLVENT CLAMP
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# seize = collateral
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# valueClamped = collateral * colPrice / 1e18
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# payReduced = valueClamped * 10_000 / (10_000 + LIQ_BONUS_BPS)
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# pay = payReduced * 1e18 / debtPrice
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#
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# Properties (should all hold):
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# L1 no-over-seize : seize <= collateral (after clamp)
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# L2 clamp not-overpay : value(pay_clamped) <= value(all collateral seized)
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# i.e. the liquidator never pays more debt-value than
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# the collateral they receive is worth.
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# L3 bonus to liquidator (non-clamp): valueToSeize >= valueRepaid, so the
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# liquidator always receives >= what they pay.
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# L4 debt no-underflow : repaidScaled (clamped to debtOf) <= debtOf, so
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# debtOf -= repaidScaled and totalBorrowsScaled -=
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# repaidScaled never underflow.
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#
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# Method: PROVED = the negation is UNSAT under the guards. NEG-CTRL = the buggy
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# variant's violation is SAT (real counterexample), proving the guard is load-
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# bearing and the property is not vacuous.
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#
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# ASSUMPTIONS (bound every PROVED):
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# A1. Token decimals are normalised (both 18-dec) so _scaleUp/_scaleDown are the
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# identity. AERE Wave-1 debt is USDC.e (6-dec) and collateral varies; the
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# scale helpers are pure power-of-ten mul/div whose rounding is monotone and
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# does not change the DIRECTION of any inequality below (down-scaling only
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# shrinks the liquidator's charge, strengthening L2). Modelled at 18/18 for
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# tractability; the decimal helpers are checked separately for monotonicity.
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# A2. Prices are positive (oracle staleness/deviation is enforced upstream by
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# AereLendingOracle and is out of scope here).
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# A3. This models the DESIGN math (unbounded Ints, integer division), not EVM
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# 256-bit overflow; intermediate products stay < 2**256 for realistic
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# token/price magnitudes.
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# -----------------------------------------------------------------------------
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from z3 import Int, Solver, And, Or, Not, If, sat, unsat, simplify
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ONE = 10**18
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results = []
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def check(name, s, expect_unsat=True, kind="PROOF", show=None):
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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 and show is not None:
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m = s.model()
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wit = {}
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for lbl, expr in show.items():
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try:
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wit[lbl] = simplify(m.eval(expr, model_completion=True)).as_long()
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except Exception:
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wit[lbl] = "?"
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print(" witness:", wit)
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return ok
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print("### AereLendingMarket.liquidate -- seize/clamp safety (18/18 decimals)\n")
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def common(s):
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"""Symbolic liquidation inputs: pay(requested,<=debtReal), prices, bonus, collateral."""
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pay = Int('pay')
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debtP = Int('debtP')
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colP = Int('colP')
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bonus = Int('bonus') # LIQ_BONUS_BPS
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col = Int('col') # collateralOf[borrower]
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s.add(pay >= 1, debtP >= 1, colP >= 1, bonus >= 0, bonus < 5000, col >= 0)
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return pay, debtP, colP, bonus, col
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# ---- L1: after the clamp, seize <= collateral (no over-seize / no underflow of
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# collateralOf[borrower] = collateral - seize) -----------------------------
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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seize = If(seize0 > col, col, seize0) # the Solidity clamp
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s.add(Not(seize <= col))
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check("L1 no-over-seize: clamped seize <= collateral", s)
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# ---- L2: in the INSOLVENT clamp branch, the liquidator's actual debt payment is
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# worth no more than ALL the collateral they receive. ----------------------
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# pay_clamped = payReduced*1e18/debtP ; value(pay_clamped) <= valueClamped.
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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s.add(seize0 > col) # clamp branch active
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valueClamped = col * colP / ONE
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payReduced = valueClamped * 10_000 / (10_000 + bonus)
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payC = payReduced * ONE / debtP
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valuePayC = payC * debtP / ONE # value the liquidator actually pays
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s.add(Not(valuePayC <= valueClamped))
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check("L2 clamp not-overpay: value(pay) <= value(collateral seized)", s)
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# ---- L3: in the NON-clamp branch, the liquidator can NEVER seize MORE collateral
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# value than the bonus entitles (borrower-protecting direction). This is the
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# safety-critical bound: seize0 = floor(valueToSeize*1e18/colP), so the value
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# actually received (seize0*colP/1e18) is <= valueToSeize. Double floor-div
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# only rounds DOWN, toward the protocol. ------------------------------------
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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s.add(seize0 <= col) # non-clamp branch
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valueRecv = seize0 * colP / ONE # value liquidator receives
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s.add(Not(valueRecv <= valueToSeize))
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check("L3 non-clamp: value(collateral received) <= valueToSeize (no over-seize of value)", s)
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# ---- L3-note (HONEST): the REVERSE direction (liquidator always receives >=
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# value paid) does NOT hold at the wei level -- double floor-division can shave
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# up to a couple wei OFF the liquidator, i.e. rounding favours the PROTOCOL /
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# borrower (the safe direction). This is expected DeFi rounding, NOT a bug. We
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# demonstrate the tiny dust discrepancy explicitly and label it non-safety.
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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s.add(seize0 <= col)
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valueRecv = seize0 * colP / ONE
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s.add(valueRepaid - valueRecv >= 1) # find any dust shortfall
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check("L3-note dust: value(recv) can be < value(paid) by rounding (favours protocol, NOT a bug)",
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s, expect_unsat=False, kind="ROUNDING",
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show={"pay": pay, "debtP": debtP, "colP": colP, "bonus": bonus,
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"valueRepaid": valueRepaid, "valueRecv": valueRecv,
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"dust_shortfall": valueRepaid - valueRecv})
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# ---- L4: repaidScaled (clamped to debtOf) never underflows debt bookkeeping ---
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s = Solver()
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payScaledRay, debtOf, ray_over_index = Int('payScaledRay'), Int('debtOf'), Int('t')
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# repaidScaled = pay*RAY/borrowIndex, then clamped: if > debtOf, set = debtOf.
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s.add(payScaledRay >= 0, debtOf >= 0)
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repaidScaled = If(payScaledRay > debtOf, debtOf, payScaledRay)
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s.add(Not(repaidScaled <= debtOf))
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check("L4 debt no-underflow: clamped repaidScaled <= debtOf", s)
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# ---- NEG-CTRL 1: WITHOUT the clamp, seize can exceed collateral -> the borrower's
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# collateralOf = collateral - seize underflows (0.8 revert) OR, in an unchecked
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# world, the liquidator seizes MORE than the borrower has (draining pooled
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# collateral of OTHER borrowers). z3 finds seize0 > collateral. ------------
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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s.add(seize0 > col) # unclamped seize exceeds collateral
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check("NEG-CTRL unclamped seize CAN exceed collateral (theft of pooled collateral)", s,
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expect_unsat=False, kind="NEG-CTRL",
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show={"pay": pay, "debtP": debtP, "colP": colP, "bonus": bonus,
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"col": col, "unclamped_seize": seize0})
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# ---- NEG-CTRL 2: a BUGGY clamp that INFLATES the reduced payment (multiplies by
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# (10000+bonus)/10000 instead of dividing) makes the liquidator OVERPAY:
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# value(pay) > value(collateral received). z3 finds it. --------------------
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s = Solver()
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pay, debtP, colP, bonus, col = common(s)
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valueRepaid = pay * debtP / ONE
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valueToSeize = valueRepaid + valueRepaid * bonus / 10_000
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seize0 = valueToSeize * ONE / colP
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s.add(seize0 > col, bonus >= 1) # clamp branch, real bonus
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valueClamped = col * colP / ONE
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payReducedBUG = valueClamped * (10_000 + bonus) / 10_000 # BUG: inflate instead of reduce
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payBUG = payReducedBUG * ONE / debtP
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valuePayBUG = payBUG * debtP / ONE
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s.add(valueClamped >= 1)
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s.add(valuePayBUG > valueClamped) # liquidator overpays
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check("NEG-CTRL buggy-inflate clamp CAN make liquidator overpay (value(pay)>value(seized))", s,
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expect_unsat=False, kind="NEG-CTRL",
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show={"pay": pay, "debtP": debtP, "colP": colP, "bonus": bonus, "col": col,
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"valueClamped": valueClamped, "valuePayBUG": valuePayBUG})
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# ---- Decimal-helper monotonicity (supports ASSUMPTION A1) --------------------
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# _scaleDown(x, dec<18) = x / 10**(18-dec) is monotone non-increasing and never
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# increases a charge, so proving L2 at 18/18 is the WORST case for the liquidator
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# on the down-scaled `pay`. Sanity: floor division is monotone.
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s = Solver()
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x, y, d = Int('x'), Int('y'), Int('d')
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s.add(x >= 0, y >= 0, x <= y, d >= 1)
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s.add(Not((x / d) <= (y / d)))
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check("scaleDown monotonicity: x<=y => x/d <= y/d (floor div monotone)", s)
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# ------------------------------------------------------------------------------
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print("\n=== SUMMARY ===")
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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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print("AereLendingMarket.liquidate seize/clamp math:")
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if allok:
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print(" PROVED L1 (no over-seize), L2 (clamp never overpays), L3 (no over-seize of VALUE),")
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print(" L4 (debt bookkeeping no-underflow), all at 18/18 decimals. The L3-note shows the")
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print(" liquidator-favouring direction fails only by wei-dust that rounds toward the")
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print(" protocol (the SAFE direction) -- expected DeFi rounding, not a bug. Two NEG-CTRLs")
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print(" confirm the clamp and the divide-by-(10000+bonus) are load-bearing.")
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else:
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print(" NOT fully established (see FAILED / unexpected CEX above).")
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import sys
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sys.exit(0 if allok else 1)
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