Curves Arithmetic and Binary Ladders

Curves Arithmetic and Binary Ladders

Dr. Raveen Ravinesh Goundar 

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There has been surge of research in the field of elliptic curve cryptography (ECC) since its discovery by Koblitz and Miller, independently in 1985. It is considered to be a modern cryptography with a vast impact on today's society, where development of mobile technologies having constrained memory space is on the rise. This is due to the fact that a small key size of 160bits in ECC can provide a comparable level of security as RSA, which has a large key size of 1064 bits. The efficiency of ECC depends on the computation called scalar multiplication. Our research focus on improving  the efficiency of scalar multiplication algorithms and protecting it against side channel attacks.
Recently, Meloni introduced an efficient arithmetic on elliptic curves when adding projective points sharing the same Z-coordinate. We present  further co-Z addition formulae for various point additions on Weierstrass elliptic curves. Also, we show how the use of conjugate point addition and other implementation tricks allow one to develop efficient scalar multiplication algorithms making use of efficient co-Z arithmetic. Specifically, our  work describes implementations of efficient co-Z based versions of Montgomery ladder and Joye's double-add algorithm. Furthermore, our algorithms are protected against some implementation attacks, such as SPA, DPA and faults attack.

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Raveen Ravinesh Goundar is originally from Fiji. He has obtained Bachelors of Science and Masters of Science degrees from the University of the South Pacific in Fiji. He has obtained his PhD degree in information science from Kochi University in Japan on March, 2008. He achieved gold medal twice for being an outstanding student in mathematics during his undergraduate and graduate studies. In past he has worked at the University of the South Pacific as an assistant lecturer and at Japan Advanced Institute of Science and Technology as a post doctoral researcher. Currently he is an assistant professor at Fiji National University. His research area focuses on designing of efficient and secure algorithms in elliptic curve cryptography.