密码学报2018，Vol.5Issue(3)：315-323,9.DOI:10.13868/j.cnki.jcr.000242
二元域上椭圆曲线的Weierstrass形式到Edwards形式的转换算法
Algorithm of Converting Weierstrass Form into Edwards Form for Elliptic Curves over Binary Fields
摘要
Abstract
Elliptic curves over finite fields have found many applications in public key cryptography, such as elliptic curve cryptosystems (ECC), identity-based encryption, isogeny-based Diffie-Hellman key exchange, etc. Elliptic curves have a variety of algebraic equations including Weierstrass form, Edwards form, Huff form, Hessian form, etc. Different forms of elliptic curves have their own merits. Compared with the classical Weierstrass form, the Edwards form has more advantages with respect to efficiency and security. However, the parameters of traditional ECC used in standards are given in the Weierstrass form. It is inconvenient for engineers to implement cryptographic algorithms in the Edwards form. This paper gives an algorithm of converting the Weierstrass form into the Edwards form for elliptic curves over binary fields. The converting process makes use of the Shallue-Woestijne algorithm and the halving a rational point algorithm. The proposed algorithm has a deterministic polynomial time complexity and does not require any additional condition compared with the previous results. In addition, only a small amount of computation is required in the proposed algorithm. An example is illustrated explicitly for the conversion process from the Weierstrass form into the Edwards form in the Appendix.关键词
椭圆曲线/半分有理点算法/Edwards形式/Weierstrass形式Key words
elliptic curves/algorithm of halving a rational point/Edwards form/Weierstrass form分类
信息技术与安全科学引用本文复制引用
张婧炜,赵昌安..二元域上椭圆曲线的Weierstrass形式到Edwards形式的转换算法[J].密码学报,2018,5(3):315-323,9.基金项目
国家重点研发计划(2017YFB0802503,2017YFB0802504) （2017YFB0802503,2017YFB0802504）
国家自然科学基金(61472457) （61472457）
国家留学基金 （）
广东省自然科学基金(2014A030313609) （2014A030313609）
岭南基金 （）
广东财经大学校级科研项目(14GJPY12001) （14GJPY12001）
National Key Research and Development Program of China (2017YFB0802503, 2017YFB0802504) （2017YFB0802503, 2017YFB0802504）
National Natural Science Foundation of China (61472457) （61472457）
CSC Scholarship （）
Natural Science Foundation of Guangdong (2014A030313609) （2014A030313609）
Lingnan Foudation （）
Foudation of Guangdong University of Finance and Economics (14GJPY12001) （14GJPY12001）
