A Hybrid Approach to Formal Verification of Higher-Order Masked Arithmetic Programs

Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by removing the statistical dependence between secrecy and power consumption via randomization. However, designing efficient and effective masked implementations turns out to be an error-prone task. Current techniques for verifying whether masked programs are secure are limited in their applicability and accuracy, especially when they are applied. To bridge this gap, in this article, we first propose a sound type system, equipped with an efficient type inference algorithm, for verifying masked arithmetic programs against higher-order attacks. We then give novel model-counting based and pattern-matching based methods which are able to precisely determine whether the potential leaky observable sets detected by the type system are genuine or simply spurious. We evaluate our approach on various implementations of arithmetic cryptographicprograms.The experiments confirm that our approach out performs the state-of-the-art base lines in terms of applicability, accuracy and efficiency

Formal Verification of Masking Countermeasures for Arithmetic Programs

Cryptographic algorithms are widely used to protect data privacy in many aspects of daily lives. Unfortunately, programs implementing cryptographic algorithms may be vulnerable to practical power side-channel attacks, which may infer private data via statistical analysis. To thwart these attacks, several masking schemes have been proposed, giving rise to effective countermeasures for reducing the statistical correlation between private data and power consumptions. However, programs that rely on secure masking schemes are not secure a priori. Indeed, designing effective masking programs is a labor intensive and error-prone task. Although some techniques have been proposed for formally verifying masking countermeasures and for quantifying masking strength, they are currently limited to Boolean programs and suffer from low accuracy. In this work, we propose an approach for formally verifying masking countermeasures of arithmetic programs. Our approach is more accurate for arithmetic programs and more scalable for Boolean programs comparing to the existing approaches. It is essentially a synergistic integration of type inference and model-counting based methods, armed with domain specific heuristics. The type inference system allows a fast deduction of leakage-freeness of most intermediate computations, the model-counting based methods accounts for completeness, namely, to eliminate spurious flaws, and the heuristics facilitate both type inference and model-counting based reasoning, which improve scalability and efficiency in practice. In case that the program does contain leakage, we provide a method to quantify its masking strength. A distuiguished feature of our type sytem lies in its support of compositonal reasoning when verifying programs with procedure calls, so the need of inlining procedures can be significantly reduced. We have implemented our methods in a verification tool QMVERIF which has been extensively evaluated on cryptographic benchmarks including full AES, DES and MAC-Keccak. The experimental results demonstrate the effectiveness and efficiency of our approach, especially for compositional reasoning. In particular, our tool is able to automatically prove leakage-freeness of arithmetic programs for which only manual proofs exist so far; it is also significantly faster than the state-of-the-art tools: EasyCrypt on common arithmetic programs, QMSINFER, SC Sniffer and maskVerif on Boolean programs

A hybrid approach to formal verification of higher-order masked arithmetic programs

Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by removing the statistical dependence between secrecy and power consumption via randomization. However, designing efficient and effective masked implementations turns out to be an error-prone task. Current techniques for verifying whether masked programs are secure are limited in their applicability and accuracy, especially when they are applied. To bridge this gap, in this article, we first propose a sound type system, equipped with an efficient type inference algorithm, for verifying masked arithmetic programs against higher-order attacks. We then give novel model-counting-based and pattern-matching-based methods that are able to precisely determine whether the potential leaky observable sets detected by the type system are genuine or simply spurious. We evaluate our approach on various implementations of arithmetic cryptographic programs. The experiments confirm that our approach outperforms the state-of-the-art baselines in terms of applicability, accuracy, and efficiency

Formal Verification of Arithmetic Masking in Hardware and Software

Masking is a popular secret-sharing technique that is used to protect cryptographic implementations against physical attacks like differential power analysis. So far, most research in this direction has focused on finding efficient Boolean masking schemes for well-known symmetric cryptographic algorithms like AES and Keccak. However, especially with the advent of post-quantum cryptography (PQC), arithmetic masking has received increasing attention from the research community. In practice, many PQC algorithms require a combination of arithmetic and Boolean masking, which makes the search for secure and efficient conversion algorithms between these domains (A2B/B2A) an interesting but very challenging research topic. While there already exist lots of tools that can help with the formal verification of Boolean masked implementations, the same cannot be said about arithmetic masking and accompanying mask conversion algorithms. In this work, we demonstrate the first formal verification approach for (any-order) Boolean and arithmetic masking which can be applied to both hardware and software, while considering side-effects such as glitches and transitions. First, we show how a formal verification approach for Boolean masking can be used in the context of arithmetic masking such that we can verify A2B/B2A conversions for arbitrary masking orders. We investigate various conversion algorithms in hardware and software, and point out several new findings such as glitch-based issues for straightforward implementations of [CGV14]-A2B in hardware, transition-based leakage in Goubin-A2B in software, and more general implementation pitfalls when utilizing common optimization techniques in PQC. We provide the first formal analysis of table-based A2Bs from a probing security perspective and point out that they might not be easy to implement securely on processors that use of memory buffers or caches

Armistice: Micro-Architectural Leakage Modelling for Masked Software Formal Verification

Side channel attacks are powerful attacks for retrieving secret data by exploiting physical measurements such as power consumption or electromagnetic emissions. Masking is a popular countermeasure as it can be proven secure against an attacker model. In practice, software masked implementations suffer from a security reduction due to a mismatch between the considered leakage sources in the security proof and the real ones, which depend on the micro-architecture. We present the model of a system comprising an Arm Cortex-M3 obtained from its RTL description and test-vectors, as well as a model of the memory of a STM32F1 board, built exclusively using test-vectors. Based on these models, we propose Armistice, a framework for formally verifying the absence of leakage in first-order masked implementations taking into account the modelled micro-architectural sources of leakage. We show that Armistice enables to pinpoint vulnerable instructions in real world masked implementations and helps design masked software implementations which are practically secure