Hard problems in elliptic curve scalar multiplication
Vijayarangan Natarajan · Journal of Discrete Mathematical Sciences and Cryptography · 2010
Number Theory and Cryptography are based on mathematical problems that are considered difficult to solve. “Difficult” in this case refers more to the computational requirements in finding a solution than to the conception of the problem. These problems are formally called “hard” problems. Some of the most well known examples are factoring large numbers, finding the discrete logarithms, theorem-proving, and the Traveling Salesman Problem. In the theory of Double Base Number System (DBNS)/Multiple Base Number System (MBNS), finding the best approximation for a given integer is a hard problem. This approximation can be used to compute Elliptic curve scalar multiplication in an efficient way. In this paper, we have come up with an algorithm for DBNS, which expresses any integer n in the form of DBNS with decreasing order of exponents.