High-performance implementation approach of elliptic curve cryptosystem for wireless network applications

Abstract

This paper presents a new efficient implementation approach of elliptic curve cryptosystem based on a novel finite field multiplication and a high performance scalar multiplication algorithm for wireless network authentication. In this new finite field multiplication, CLNZ sliding window method is used on the signed-digit multiplier in order to reduce the multiplication steps. In addition, in scalar multiplication algorithm of proposed implementation approach, point addition and point doubling operation compute in parallel. Also window technique and signed-digit representation are used in order to reduce the number of point operation. So the multiplication cost in the proposed implementation approach reduced considerably. Using this new implementation approach, the security of the elliptic curve cryptosystem increased considerably. The results show that the proposed finite field multiplication reduces the number of multiplication steps at about 40%–82.4% for d=2–10 in compare with Montgomery modular multiplication algorithm. In addition, the efficiency of the proposed implementation approach of elliptic curve cryptosystem enhances about 88%-97% in compare with the implementation approach of traditional window NAF elliptic curve scalar multiplication algorithm and enhances about 77% in compare with the implementation approach of window NAF elliptic curve scalar multiplication algorithm (based on interleaving) where w=4 and 8, and d=8.