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

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.