Polar codes discovered by Arikan form a very powerful family of codes attaining many information theoretic limits in the fields of error correction and source coding. They have in particular much better decoding capabilities than Goppa codes which places them as a serious alternative in the design of both a public-key encryption schemeà la McEliece and a very efficient signature scheme. Shrestha and Kim proposed in 2014 to use them in order to come up with a new code-based public key cryptosystem. We present a key-recovery attack that makes it possible to recover a description of the permuted polar code providing all the information required for decrypting any message.
Abstract-QC-MDPC-McEliece is a recent variant of theMcEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost implementations on embedded devices.Decoding MDPC codes is achieved with the (iterative) bit flipping algorithm, as for LDPC codes. Variable time decoders might leak some information on the code structure (that is on the sparse parity check equations) and must be avoided. A constant time decoder is easy to emulate, but its running time depends on the worst case rather than on the average case. So far implementations were focused on minimizing the average cost. We show that the tuning of the algorithm is not the same to reduce the maximal number of iterations as for reducing the average cost. This provides some indications on how to engineer the QC-MDPC-McEliece scheme to resist a timing side-channel attack.
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