Low-Cost Hardware Implementation of Elliptic Curve Cryptography for General Prime Fields

Abstract

In resource-constrained applications, elliptic curve cryptography (ECC) is preferable for the property of shorter key size with comparable security. Binary extension fields are usually used for area-optimized implementations, since the complex carry-propagation logics are avoided over these fields. However, efficient ECC implementations over (general) prime fields are still challenging for low-area constraint. As a popular implementation platform for cryptographic algorithms, Field Programmable Gate Array (FPGA) attracts more and more attentions for these applications due to its nice properties of flexibility and short development cycle. In this paper, we propose a compact and efficient arithmetic logical unit (ALU) by highly integrating the functions of Montgomery modular multiplications, additions and subtractions over general prime fields. Then we design a low-cost hardware architecture for generic elliptic curve point multiplications for FPGA platforms. Experimental results indicate that the implementation only occupies 105 Slices, 2 DSP blocks and 2 BRAMs in Spartan-6 FPGA. To the best of our knowledge, our implementation is the smallest for general prime fields in FPGAs.