A Deductive System for Contract Satisfaction Proofs

2026-04-10

AI Summary

This work proposes a method for formally verifying that CPUs satisfy hardware–software contracts—thereby ensuring high-level programs are secure against side-channel attacks—without requiring explicit modeling of microarchitectural details. The core insight is to abstract contract satisfaction as relative trace equivalence and introduce relative bisimulation as the underlying proof technique. Building on coinductive reasoning, we develop the first mechanizable, sound, and complete deductive proof system that supports modular and incremental interactive verification, implemented in the Rocq proof assistant. The system has been successfully applied to verify two complex contracts, demonstrating the approach’s effectiveness, scalability, and novelty.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Hardware-aware ML
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Hardware-software contracts are abstract specifications of a CPU's leakage behavior. They enable verifying the security of high-level programs against side-channel attacks without having to explicitly reason about the microarchitectural details of the CPU. Using the abstraction powers of a contract requires proving that the targeted CPU satisfies the contract in the sense that the contract over-approximates the CPU's leakage. Besides pen-and-paper reasoning, proving contract satisfaction has been approached mostly from the model-checking perspective, with approaches based on a (semi-)automated search for the necessary invariants. As an alternative, this paper explores how such proofs can be conducted in interactive proof assistants. We start by observing that contract satisfaction is an instance of a more general problem we call relative trace equality, and we introduce relative bisimulation as an associated proof technique. Leveraging recent advances in the field of coinductive proofs, we develop a deductive proof system for relative trace equality. Our system is provably sound and complete, and it enables a modular and incremental proof style. It also features several reasoning principles to simplify proofs by exploiting symmetries and transitivity properties. We formalized our deductive system in the Rocq proof assistant and applied it to two challenging contract satisfaction proofs.

Problem

• contract satisfaction
• side-channel attacks
• hardware-software contracts
• trace equality
• formal verification

Innovation

• relative trace equality
• relative bisimulation
• coinductive proofs
• contract satisfaction
• deductive proof system