A Universal Single and Double Point Multiplications Architecture for ECDSA Based on Differential Addition Chains

Abstract

In the 5G and beyond networks, low-latency digital signatures are essential to ensure the security, integrity, and non-repudiation of massive data in communication processes. The binary finite field-based elliptic curve digital signature algorithm (ECDSA) is particularly suitable for achieving low-latency digital signatures due to its carry-free characteristics. This paper proposes a low-latency and universal architecture for point multiplication (PM) and double point multiplication (DPM) based on the differential addition chain (DAC) designed for signing and verification in ECDSA. By employing the DAC, the area-time product of DPM can be decreased, and throughput efficiency can be increased. Besides, the execution pattern of the proposed architecture is uniform to resist simple power analysis and high-order power analysis. Based on the data dependency, two Karatsuba–Ofman multipliers and four non-pipeline squarers are utilized in the architecture to achieve a compact timing schedule without idle cycles for multipliers during the computation process. Consequently, the calculation latency of DPM is minimized to five clock cycles in each loop. The proposed architecture is implemented on Xilinx Virtex-7, performing DPM in 3.584, 5.656, and $7.453~\mu s$ with 8135, 13372, and 17898 slices over GF(2163), GF(2233), GF(2283), respectively. In the existing designs that are resistant to high-order analysis, our architecture demonstrates throughput efficiency improvements of 36.7% over GF(2233) and 9.8% over GF(2283), respectively.

Keywords

• Elliptic curve cryptosystems
• differential addition chain
• point multiplication
• double point multiplication
• field-programmable gate array