Relational Hoare Logic for Realistically Modelled Machine Code

2025-05-20

AI Summary

This work addresses the challenge of verifying consistency between assembly code and realistic machine models in low-level verification—particularly for security properties requiring multi-trace correlation, such as constant-time behavior and cross-version equivalence. Existing relational verification techniques operate predominantly at high abstraction levels and lack direct support for concrete machine-code semantics. To bridge this gap, we introduce the first relational Hoare logic tailored to realistic machine models, formally defined in HOL Light. It features instruction-level memory and control-flow semantics, along with refinement-based relational specifications. Our approach enables rigorous, compositional verification of multi-trace relational properties. We demonstrate its effectiveness on the large s2n-bignum assembly library, verifying constant-time execution and functional equivalence between optimized and verification-friendly routine variants. The method significantly advances expressiveness, provability, and industrial applicability of low-level system security verification.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a realistic machine model is a challenging task. Furthermore, certain security properties -- such as constant-time behavior -- require relational reasoning that goes beyond traditional correctness by linking multiple execution traces within a single specification. Yet, relational verification has been extensively explored at a higher level of abstraction. In this work, we introduce a Hoare-style logic that provides low-level, expressive relational verification. We demonstrate our approach on the s2n-bignum library, proving both constant-time discipline and equivalence between optimized and verification-friendly routines. Formalized in HOL Light, our results confirm the real-world applicability of relational verification in large assembly codebases.

Problem

• Verifying assembly code against realistic machine models
• Enabling relational reasoning for security properties like constant-time
• Providing low-level expressive relational verification for large codebases

Innovation

• Hoare-style logic for low-level relational verification
• Proves constant-time behavior in assembly code
• Formalized in HOL Light for real-world applicability