Energy-efficient elliptic curve cryptography for MSP430-based wireless sensor nodes

Abstract

The Internet is rapidly evolving from a network of personal computers and servers to a network of smart objects (“things”) able to communicate with each other and with central resources. This evolution has created a demand for lightweight implementations of cryptographic algorithms suitable for resource-constrained devices such as RFID tags and wireless sensor nodes. In this paper we describe a highly optimized software implementation of Elliptic Curve Cryptography (ECC) for the MSP430 series of ultra-low-power 16-bit microcontrollers. Our software is scalable in the sense that it supports prime fields and elliptic curves of different order without recompilation, which allows for flexible tradeoffs between execution time (i.e. energy consumption) and security. The low-level modular arithmetic is optimized for pseudo-Mersenne primes of the form p = 2n − c where n is a multiple of 16 minus 1 and c fits in a 16-bit register. All prime-field arithmetic functions are parameterized with respect to the length of operands (i.e. the number of 16-bit words they consist of) and written in Assembly language, whereby we avoided conditional jumps and branches that could leak information about the secret key. Our ECC implementation can perform scalar multiplication on two types of elliptic curves, namely Montgomery curves and twisted Edwards curves. A full scalar multiplication using a Montgomery curve over a 159-bit field requires about 3.86 · 106 clock cycles when executed on an MSP430F1611 microcontroller.