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

Abstract

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.

Overview of the Mceliece Cryptosystem and its Security

“…H e y s e et al in [32] report an 8-bit AVR implementation of QC-MDPC McEliece variant along with a Xilinx Virtex-6 XC6VLX240T FPGA implementation. Their compact implementation uses only 4,800 and 9,600 bits for the public and secret key at 80 bits of equivalent symmetric security.…”

Stream Cipher by Reed-Solomon Codes

“…By contrast, people also seek approaches to implement more secure code by public key cryptography. Code based cryptography [11] with Goppa codes [12] or MDPC codes [13], for example, can be applied to realize McEliece system . Meanwhile, generalized RS code can also be used to implement asymmetric cryptography [6], which brings out short keys compared with that obtained by Goppa code.…”

An Improved Zero-knowledge Identification Scheme based on Quasi-Dyadic Codes

“…Unfortunately, Niederreiter's proposal was proved to be insecure subsequently. In the following years, a number of cryptosystems [5][6][7][8][9][10] were proposed by using different codes such as MDPC, QD-Goppa codes, etc. And the public key size can be reduced much more by exploiting the Toeplitz structure [11].…”