© Andrew IrelandDependable Systems Group On the Scalability of Proof Carrying Code for Software Certification Andrew Ireland School of Mathematical & Computer Sciences Heriot-Watt University Edinburgh

© Andrew IrelandDependable Systems Group Outline High integrity software development Evidence based software certificates Scalability problems A planning approach Issues for discussion

© Andrew IrelandDependable Systems Group The SPARK Approach SPARK Examiner SPADE Simplifier SPADE Proof Checker SPARK is a subset of Ada with annotations (Praxis High Integrity Systems Ltd) Supports data & information flow analysis and formal verification - in particular, exception freedom proofs EuroFighter and Hawk projects, advocated by NSA, … VCs Unproven VCs  SPARK code Proofs X Revisions Tactics

© Andrew IrelandDependable Systems Group NuSPADE SPARK Examiner SPADE Simplifier SPADE Proof Checker NuSPADE = proof planning + program analysis Annotation generation motivated by proof-failure analysis VCs Unproven VCs  SPARK code Proofs Annotations X Tactics

© Andrew IrelandDependable Systems Group NuSPADE Unproven VCs Abstract Predicates Annotations Co-operative style of integration, i.e. “productive use of failure” Proof Planner Program Analyzer Tactics

© Andrew IrelandDependable Systems Group Conjecture Proof Plans Plan Theory Proof Planner Proof Checker Tactic Proof Failure

© Andrew IrelandDependable Systems Group SPARK and Certification Z specifications + rigorous proofs Data flow & information analysis Code level proofs: –Exception freedom proofs: automatic + interactive proofs –Functional proofs: significant level of interactive proofs –Proof review files Resource analysis Note: various levels of formal & rigorous evidence

© Andrew IrelandDependable Systems Group Evidence Based Certification Proof-Carrying Code (PCC) – a example of an evidence based approach to certification Code is delivered with a certificate containing a condensed mathematical proof, i.e. a proof that the code satisfies desired safety properties Responsibility for proof construction lies with the code producer, consumer performs proof checking Trusted Computing Base (TCB) for PCC is small, i.e. safety properties, verification condition generator and proof checker

© Andrew IrelandDependable Systems Group Properties, Proofs & Certificates Properties typically simple, e.g. memory safety Proof construction involves advanced type checking, i.e. no theorem proving Certificates: –LF proofs quadratic with respect to program size –LFi proofs 2.5 to 5 times program size –Oracles strings on average 12% program size –Proof tactics have also been used

© Andrew IrelandDependable Systems Group Scalability Problems Need for comprehensive properties, e.g. functional properties MOBIUS: combining type-based and logic- based approaches Need to exploit automated theorem proving techniques Will current PCC architecture scale-up, e.g. oracles strings?

© Andrew IrelandDependable Systems Group Conjecture Proof Plans Plan Theory Proof Planner Proof Checker Tactic Proof Failure

© Andrew IrelandDependable Systems Group Conjecture Proof Plans Plan Theory Proof Planner Proof Checker Tactic Proof Failure

© Andrew IrelandDependable Systems Group Conjecture Proof Plans Plan Theory Proof Planner Proof Checker Tactic Proof Failure Oracle

© Andrew IrelandDependable Systems Group Conjecture Planning Oracles as Certificates Plan Theory Proof Planner Proof Checker Tactic Proof Failure Oracle

© Andrew IrelandDependable Systems Group Conjecture Planning Oracles as Certificates Plan Theory Proof Planner Proof Checker Tactic Proof Failure Oracle Oracle identifies: Proof plans and where they should be used Relevant theories Search control hints, e.g. auxiliary lemmas and generalization steps

© Andrew IrelandDependable Systems Group Certificate Generation Code + Spec Certificate Generation (VCGen + Planner +Checker) Certificate (Oracle) ? ProofFailure Repositories (plans + theories)

© Andrew IrelandDependable Systems Group Certificate Validation Code + Spec Certificate Validation (VCGen + Planner +Checker) Certificate (Oracle) Repositories (plans + theories) ? Proof Failure CPU Note: Certificate transforming compiler

© Andrew IrelandDependable Systems Group Discussion Issues The proposed proof planning approach will add theory repositories (and specifications) to the TCB – is this acceptable? For memory limited devices, proof planning oracles are not an option for on-device certificate validation – how important is on-device validation to certification management in general? More comprehensive properties will require off-device validation – could a dedicated certificate validation device have a role to play? Certificate transforming compiler or trusted compiler?

© Andrew IrelandDependable Systems Group Conclusion The SPARK Approach and proof automation via proof planning The success of PCC as well and the limits of current architectures Proposal for proof planning and proof planning oracles as a technique for addressing limitations