Accelerated precomputation points–based scalar reduction on elliptic curve cryptography for wireless sensor networks

Abstract

SummarySensor devices are limited resource power and energy, thus providing security services for sensor networks is very difficult. Elliptic curve cryptography (ECC) is one of the most famous asymmetric cryptographic schemes, which offers the same level of security with much shorter keys compared to the other widely used asymmetric cryptographic algorithm, RSA (Rivest, Shamir, and Adleman). In ECC, the main and most‐heavily used operation is the scalar multiplication kP, where the scalar value k is a private integer and must be secured. In this work, we present a new approach to accelerate the main scalar multiplication on ECC over prime fields for sensor networks. This approach uses an equivalent representation of points and can act as a support for existing schemes in a selected interval. The simulation results showed that the proposed technique increases the efficiency of the computation time. For example, on this scalar multiplication, we obtain a gain of 4 bits in 161 bits for 6.25% of the scalars. This gain can sometimes reach 100% in some cases. After this significant reduction of the scalar k, we present a fast precomputation algorithm in a distributed scalar multiplication on kP to avoid storage of precomputation points, which requires extra memory.