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Physically unclonable functions (PUFs) are crucial for enhancing cybersecurity by providing unique, intrinsic identifiers for electronic devices, thus ensuring their authenticity and preventing unauthorized cloning. The SRAM-PUF, characterized by its simple structure and ease of implementation in various scenarios, has gained widespread usage. The soft-decision Reed–Muller (RM) code, an error correction code, is commonly employed in these designs. This paper introduces the design of an RM code soft-decision attack algorithm to reveal its potential security risks. To address this problem, we propose a soft-decision SRAM-PUF structure based on the elliptic curve digital signature algorithm (ECDSA). To improve the processing speed of the proposed secure SRAM-PUF, we propose a custom ECDSA scheme. Further, we also propose a universal architecture for the critical operations in ECDSA, elliptic curve scalar multiplication (ECSM), and elliptic curve double scalar multiplication (ECDSM) based on the differential addition chain (DAC). For ECSMs, iterations can be performed directly; for ECDSMs, a two-dimensional DAC is constructed through precomputation, followed by iterations. Moreover, due to the high similarity of ECSM and ECDSM data paths, this universal architecture saves hardware resources. Our design is implemented on a field-programmable gate array (FPGA) and an application-specific integrated circuit (ASIC) using a Xilinx Virtex-7 and an TSMC 40 nm process. Compared to existing research, our design exhibits a lower bit error rate (2.7×10−10) and better area–time performance (3902 slices, 6.615 μs ECDSM latency).

Starting from the basic form of GN-authenticated key agreement (GN-AK), the current research proposes an improved protocol by integrating a new scalar multiplication technique based on a dual-base chain representation with bases 1/2 and 3. This representation allows the use of pointwise halving operations, significantly reducing the complexity of elliptic curve calculations. The resulting protocol maintains cryptographic security based on the elliptic curve discrete logarithm problem (ECDLP) while providing improved performance for key establishment in constrained environments.

Scalar multiplication nP is the core operation of elliptic curve public-key cryptosystems. Double bases representation of n is proposed to speed up scalar multiplication. Avanzi et al. presented a recoding algorithm for Koblitz curves which works in all cases with optimal constants [ 1 ]. However, their algorithm may be expensive to implement because it requires many divisions in ℤ[τ]. In this paper, we show that divisions in ℤ[τ] can be replaced by divisions in ℤ. Our improved version of the algorithm runs in about 33% of the time of the Avanzi et al. algorithm on the Koblitz curve K-163, with larger improvements as the size of the curve increases.