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Cryptographic Hardware and Embedded Systems - CHES 2013

Volume 8086 of the series Lecture Notes in Computer Science pp 273-292

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

  • Stefan HeyseAffiliated withHorst Görtz Institute for IT-Security, Ruhr-Universität Bochum
  • , Ingo von MaurichAffiliated withHorst Görtz Institute for IT-Security, Ruhr-Universität Bochum
  • , Tim GüneysuAffiliated withHorst Görtz Institute for IT-Security, Ruhr-Universität Bochum

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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.

Keywords

MDPC LDPC FPGA microcontroller McEliece code-based public key cryptography