FourQ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Large Prime Characteristic Fields B Kimmo J¨arvinen1, Andrea Miele2, Reza Azarderakhsh3, and Patrick Longa4( ) 1 Department of Computer Science, Aalto University, Espoo, Finland
[email protected] 2 Intel Corporation, Santa Clara, USA
[email protected] 3 Department of Computer Engineering, Rochester Institute of Technology, Rochester, USA
[email protected] 4 Microsoft Research, Redmond, USA
[email protected] Abstract. We present fast and compact implementations of FourQ (ASIACRYPT 2015) on field-programmable gate arrays (FPGAs), and demonstrate, for the first time, the high efficiency of this new ellip- tic curve on reconfigurable hardware. By adapting FourQ’s algorithms to hardware, we design FPGA-tailored architectures that are sig- nificantly faster than any other ECC alternative over large prime characteristic fields. For example, we show that our single-core and multi-core implementations can compute at a rate of 6389 and 64730 scalar multiplications per second, respectively, on a Xilinx Zynq-7020 FPGA, which represent factor-2.5 and 2 speedups in comparison with the corresponding variants of the fastest Curve25519 implementation on the same device. These results show the potential of deploying FourQ on hardware for high-performance and embedded security applications. All the presented implementations exhibit regular, constant-time execution, protecting against timing and simple side-channel attacks. Keywords: Elliptic curves · FourQ · FPGA · Efficient hardware imple- mentation · Constant-time · Simple side-channel attacks 1 Introduction With the growing deployment of elliptic curve cryptography (ECC) [15,24]in place of traditional cryptosystems such as RSA, compact, high-performance ECC-based implementations have become crucial for embedded systems and hardware applications.