A Novel JSF-Based Fast Implementation Method for Multiple-Point Multiplication

Abstract

ECC is a popular public-key cryptographic algorithm, but it lacks an effective solution to multiple-point multiplication. This paper proposes a novel JSF-based fast implementation method for multiple-point multiplication. The proposed method requires a small storage space and has high performance, making it suitable for resource-constrained IoT application scenarios. This method stores and encodes the required coordinates in the pre-computation phase and uses table lookup operations to eliminate the conditional judgment operations in JSF-5, which improves the efficiency by about 70% compared to the conventional JSF-5 in generating the sparse form. This paper utilizes Co-Z combined with safegcd to achieve low computational complexity for curve coordinate pre-computation, which further reduces the complexity of multiple-point multiplication in the execution phase of the algorithm. The experiments were performed with two short Weierstrass elliptic curves, nistp256r1 and SM2. In comparison to the various CPU architectures used in the experiments, our proposed method showed an improvement of about 3% over 5-NAF.

Keywords

• elliptic curve
• ECDSA
• JSF
• scalar multiplication