Petrel: Power and Timing Attack Resistant Elliptic Curve Scalar Multiplier Based on Programmable ${\rm GF}(p)$ Arithmetic Unit

Abstract

This paper proposes a programmable GF(p) arithmetic unit for elliptic curve cryptography. The proposed unit can perform modular addition, subtraction, multiplication, inversion, and division. A suitable countermeasure against differential power analysis attack and doubling attack is proposed. An elliptic curve scalar multiplication hardware is subsequently designed for the curves defined over GF(p) using two cores of programmable GF(p) arithmetic unit. It performs point doubling and point addition in each iteration concurrently on two cores. The proposed scalar multiplication hardware is implemented on the Xilinx Virtex-2 Pro FPGA platform. The proposed parallel architecture is inherently programmable, memoryless, and resistant against timing and power attacks. It efficiently optimizes area × time per bit value for elliptic curve scalar multiplication.