Arithmetic on elliptic curves with use of graphic calculators (Q2857916)

Elliptic curve algorithms play an important role in modern cryptography. These algorithms use calculations over the group of rational points of an elliptic curve over a finite field \(K=\mathbb F_q\). It is a known fact that these calculations require a very high amount of computational time, if the underlying finite field \(K\) is large (for instance if \(p\) is a prime with more than 200 bits).NEWLINENEWLINEThe aim of this paper is to investigate the performanc of some graphic processors for making arithmetic calculations on an elliptic curve over a finite field with 128-bits prime \(p\). The chosen platform was NVIDIA CUDA with 16-bits and 32-bits architecture, namely NVIDIA GTX 280 and GTX 580. When it is compared with the Intel Core i7-920 processor, the authors are able to show 2 up to 15 times better performance of graphical NVIDIA processors for algorithm calculations on elliptic curves.