Efficient Elliptic-Curve Cryptography Using Curve25519 on Reconfigurable Devices

Abstract

Elliptic curve cryptography (ECC) has become the predominant asymmetric cryptosystem found in most devices during the last years. Despite significant progress in efficient implementations, computations over standardized elliptic curves still come with enormous complexity, in particular when implemented on small, embedded devices. In this context, Bernstein proposed the highly efficient ECC instance Curve25519 that was shown to achieve new ECC speed records in software providing a high security level comparable to AES with 128-bit key. These very tempting results from the software domain have led to adoption of Curve25519 by several security-related applications, such as the NaCl cryptographic library or in anonymous routing networks (nTor). In this work we demonstrate that even better efficiency of Curve25519 can be realized on reconfigurable hardware, in particular by employing their Digital Signal Processor blocks (DSP). In a first proposal, we present a DSP-based single-core architecture that provides high-performance despite moderate resource requirements. As a second proposal, we show that an extended architecture with dedicated inverter stage can achieve a performance of more than 32,000 point multiplications per second on a (small) Xilinx Zynq 7020 FPGA. This clearly outperforms speed results of any software-based and most hardware-based implementations known so far, making our design suitable for cheap deployment in many future security applications.