Fast Scalar Multiplication Algorithm Using Constrained Triple-Base Number System and Its Applications

Abstract

With the rapid development of embedded devices, wireless sensor network and Internet of Things, elliptic curve cryptography as a public key cryptography plays an important role to solve the security challenges. How to improve the efficiency of scalar multiplication is a challenging work for future deployment of these new technologies. Because of its sparsity, triple-base number system is used to accelerate the scalar multiplication in elliptic curve cryptography. Instead of using triple base chain, we introduce the concept of constrained tripe-base number system, which sets maximums for exponents of bases 2, 3 and 5. On this basis, we propose two fast scalar multiplication algorithms for the situations with and without precomputations. Our experiments show that the two algorithms are more efficient than 4-NAF, double-base chain and triple-base chain approaches. The improvement of efficiency makes the two scalar multiplication algorithms more suit for wireless sensor network.