Montgomery Algorithm over a Prime Field?

• 作者: LI Bao TIAN Song WANG Kunpeng YU Wei
• 来源期刊: 中国电子杂志（英文版）
• 年，卷（期）: 2019,（1）
• 页码范围: 39-44
• 页数: 6页
• 语种: 英文
• DOI: 10.1049/cje.2018.11.006

摘要

New formulae for point addition and point doubling on elliptic curves over prime fields are presented. Based on these formulae, an improved Montgomery algorithm is proposed. The theoretical analysis indicates that it is about 13.4％ faster than Brier and Joye's Montgomery algorithm. Experiments on the elliptic curve over a 256-bit prime field recommended by the National Institute of Standards and Technology and over a 256-bit prime field in Chinese elliptic curve standard SM2 support the theoretical analysis.