Naive implementations of crypto-algorithms are susceptible to side-channel analysis. This paper surveys the known methods for preventing side-channel analysis in elliptic curve cryptosystems.

Naive implementations of crypto-algorithms are susceptible to side-channel analysis. This talk surveys the known methods for preventing side-channel analysis in elliptic curve cryptosystems.

In 1976, Diffie and Hellman introduced the revolutionary concept of public-key cryptography, also known as asymmetric cryptography. Today, asymmetric cryptography is routinely used to secure the Internet. The most famous and most widely used asymmetric cryptosystem is RSA, invented by Rivest, Shamir and Adleman. Surprisingly, there are very few alternatives known, and most of them are also base...

Scalar multiplication is the most important and expensive operation in elliptic curve cryptosystems. In this paper we improve the efficiency of the Elliptic Net algorithm to compute scalar multiplication by using the equivalence of elliptic nets. The proposed method saves four multiplications in each iteration loop. Experimental results also indicates that our algorithm will be more efficient t...

This survey discusses algorithmsand explicitcalculationsfor curves of genus at least 2 and their Jacobians, mainly over number elds and nite elds. Miscellaneous examples and a list of possible future projects are given at the end. 1. Introduction An enormous number of people have performed an enormous number of computations on elliptic curves, as one can see from even a perfunctory glance at 29...

Since the seminal note published by M. Somos in 1989, a great deal of attention specialists number theory and adjacent areas are attracted nonlinear sequences that satisfy quadratic recurrence relation. At same time, special is paid to construction integer their Laurent property with respect initial values coefficients recurrence. In fundamental works Robinson, Fomin Zelevinsky Somos-k sequence...

During the last few years, a considerable effort has been devoted to the development of reconfigurable computers, machines that are based on the close interoperation of traditional microprocessors and Field Programmable Gate Arrays (FPGAs). Several prototype machines of this type have been designed, and demonstrated significant speedups compared to conventional workstations for computationally ...

Elliptic Curve Cryptography (ECC) is fast becoming a viable alternative to traditional public-key cryptosystems (RSA, DSA, DH). Although ECC algorithms have been available for quite some time, most of the work in this field has been theoretical in nature, with few actual implementations. This situation has changed because of two factors. One is that processing power itself is increasing and hac...