International Association
for Cryptologic Research

Masking, an effective countermeasure against side-channel attacks, is commonly applied in modern cryptographic implementations. Considering cryptographic algorithms that utilize both Boolean and arithmetic masking, the conversion algorithm between arithmetic masking and Boolean masking is required. Conventional high-order arithmetic masking to Boolean masking conversion algorithms based on Boolean circuits suffer from performance overhead, especially in terms of hardware implementation. In this work, we analyze high latency for the conversion and propose an improved high-order A2B conversion algorithm. For the conversion of 16-bit variables, the hardware latency can be reduced by 47% in the best scenario. For the case study of second-order 32-bit conversion, the implementation results show that the improved scheme reduces the clock cycle latency by 42% in hardware and achieves a 30% speed performance improvement in software. Theoretically, a security proof of arbitrary order is provided for the proposed high-order A2B conversion. Experimental validations are performed to verify the second-order DPA resistance of second-order implementation. The Test Vector Leakage Assessment does not observe side-channel leakage for hardware and software implementations.

SHA-3, the latest hash standard from NIST, is utilized by numerous cryptographic algorithms to handle sensitive information. Consequently, SHA-3 has become a prime target for side-channel attacks, with numerous studies demonstrating successful breaches in unprotected implementations. Masking, a countermeasure capable of providing theoretical security, has been explored in various studies to protect SHA-3. However, masking for hardware implementations may significantly increase area costs and introduce additional delays, substantially impacting the speed and area of higher-level algorithms. In particular, current low-latency first-order masked SHA-3 hardware implementations require more than four times the area of unprotected implementations. To date, the specific structure of SHA-3 has not been thoroughly analyzed for exploitation in the context of masking design, leading to difficulties in minimizing the associated area costs using existing methods. We bridge this gap by conducting detailed leakage path and data dependency analyses on two-share masked SHA-3 implementations. Based on these analyses, we propose a compact and low-latency first-order SHA-3 masked hardware implementation, requiring only three times the area of unprotected implementations and almost no fresh random number demand. We also present a complete theoretical security proof for the proposed implementation in the glitch+register-transition-robust probing model. Additionally, we conduct leakage detection experiments using PROLEAD, TVLA and VerMI to complement the theoretical evidence. Compared to state-of-theart designs, our implementation achieves a 28% reduction in area consumption. Our design can be integrated into first-order implementations of higher-level cryptographic algorithms, contributing to a reduction in overall area costs.

The lattice-based CRYSTALS-Dilithium scheme is one of the three thirdround digital signature finalists in the National Institute of Standards and Technology Post-Quantum Cryptography Standardization Process. Due to the complex calculations and highly individualized functions in Dilithium, its hardware implementations face the problems of large area requirements and low efficiency. This paper proposes several optimization methods to achieve a compact and high-performance hardware architecture for round 3 Dilithium. Specifically, a segmented pipelined processing method is proposed to reduce both the storage requirements and the processing time. Moreover, several optimized modules are designed to improve the efficiency of the proposed architecture, including a pipelined number theoretic transform module, a SampleInBall module, a Decompose module, and three modular reduction modules. Compared with state-of-the-art designs for Dilithium on similar platforms, our implementation requires 1.4×/1.4×/3.0×/4.5× fewer LUTs/FFs/BRAMs/DSPs, respectively, and 4.4×/1.7×/1.4× less time for key generation, signature generation, and signature verification, respectively, for NIST security level 5.