Logical Relations for Formally Verified Authenticated Data Structures (2501.10802v1)

Abstract: Authenticated data structures allow untrusted third parties to carry out operations which produce proofs that can be used to verify an operation's output. Such data structures are challenging to develop and implement correctly. This paper gives a formal proof of security and correctness for a library that generates authenticated versions of data structures automatically. The proof is based on a new relational separation logic for reasoning about programs that use collision-resistant cryptographic hash functions. This logic provides a basis for constructing two semantic models of a type system, which are used to justify how the library makes use of type abstraction to enforce security and correctness. Using these models, we also prove the correctness of several optimizations to the library and then show how optimized, hand-written implementations of authenticated data structures can be soundly linked with automatically generated code. All of the results in this paper have been mechanized in the Coq proof assistant using the Iris framework.

• The paper introduces a novel relational separation logic that verifies ADS security and prevents hash collision vulnerabilities.
• It presents semantic models and advanced type systems to ensure correctness and optimize automatically generated authenticated data structures.
• Machine-checked proofs with Iris in Coq validate the secure integration and interoperability of both hand-written and generated ADS implementations.

Overview of "Logical Relations for Formally Verified Authenticated Data Structures"

This paper presents a rigorous mathematical framework for the security and correctness verification of authenticated data structures (ADSs) using logical relations. Authenticated data structures are designed to enable untrusted third parties to perform operations that yield cryptographic proofs, allowing the outcomes to be verified without fully trusting the computing entity. The authors provide a formal proof for a library capable of automatically generating authenticated versions of data structures, with the integrity of these architectures ensured through a novel relational separation logic involving collision-resistant cryptographic functions.

Key Contributions

1. Relational Separation Logic: The paper introduces a tailored program logic for reasoning about ADSs, based on a separation logic that supports relational reasoning while incorporating collision-resistant hash functions. This logic is instrumental in proving properties about programs that might otherwise be vulnerable to hash collision attacks.
2. Semantic Models and Type Systems: The authors construct two semantic models within the confines of a type system that justify the correct use of type abstraction to enforce security and correctness in the library. These models not only affirm the soundness of automatically generated ADSs but also validate specific library optimizations that enhance performance.
3. Verification of Optimizations and Code Interoperability: The research explores various optimizations applied to the ADS library. The paper asserts that these optimizations maintain the correctness and security of ADS operations, particularly focusing on how hand-written, optimized ADS implementations can interoperate seamlessly with automatic code generation.
4. Mechanization with Iris in Coq: All theoretical results are backed by machine-checked proofs using the Coq proof assistant via the Iris framework. This signifies a meticulous verification process, ensuring high confidence in the claims made about security and correctness.

Implications and Future Directions

The implications of this research are notably significant for the domain of secure data outsourcing. By affirming the correctness and security of ADSs, this work paves the way for practical applications in settings where data integrity is paramount, such as database systems, cloud storage, and blockchain technologies. The formal models and proofs developed could serve as a benchmark for future work aiming to optimize or expand upon authenticated data structures.

Future research may build upon this foundation by exploring more complex data structures or operations, integrating further optimizations, and extending other parts of software systems to leverage secure, formally verified data structures. Moreover, adapting the current work to a wider range of programming languages beyond OCaml-like systems might broaden its applicability across different technological stacks.

In summary, this paper provides a precise and comprehensive approach to the formal verification of authenticated data structures, emphasizing the importance of security in cryptographic computations and fostering further innovation in secure data handling technologies.