Smaller Keys for Code-Based Cryptography: QC-MDPC McEliece Implementations on Embedded Devices

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Abstract

In the last years code-based cryptosystems were established as promising alternatives for asymmetric cryptography since they base their security on well-known NP-hard problems and still show decent performance on a wide range of computing platforms. The main drawback of code-based schemes, including the popular proposals by McEliece and Niederreiter, are the large keys whose size is inherently determined by the underlying code. In a very recent approach, Misoczki et al. proposed to use quasi-cyclic MDPC (QC-MDPC) codes that allow for a very compact key representation. In this work, we investigate novel implementations of the McEliece scheme using such QC-MDPC codes tailored for embedded devices, namely a Xilinx Virtex-6 FPGA and an 8-bit AVR microcontroller. In particular, we evaluate and improve different approaches to decode QC-MDPC codes. Besides competitive performance for encryption and decryption on the FPGA, we achieved a very compact implementation on the microcontroller using only 4,800 and 9,600 bits for the public and secret key at 80 bits of equivalent symmetric security.