Improving the efficiency of the LDPC code-based McEliece cryptosystem through irregular codes

We consider the framework of the McEliece cryptosystem based on LDPC codes, which is a promising post-quantum alternative to classical public key cryptosystems. The use of LDPC codes in this context allows to achieve good security levels with very compact keys, which is an important advantage over the classical McEliece cryptosystem based on Goppa codes. However, only regular LDPC codes have been considered up to now, while some further improvement can be achieved by using irregular LDPC codes, which are known to achieve better error correction performance than regular LDPC codes. This is shown in this paper, for the first time at our knowledge. The possible use of irregular transformation matrices is also investigated, which further increases the efficiency of the system, especially in regard to the public key size.Comment: 6 pages, 3 figures, presented at ISCC 201

Variations of the McEliece Cryptosystem

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed

Worst case QC-MDPC decoder for McEliece cryptosystem

McEliece 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.Comment: 5 pages, conference ISIT 201

LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes

This work presents a new code-based key encapsulation mechanism (KEM) called LEDAkem. It is built on the Niederreiter cryptosystem and relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known statistical attacks, and takes advantage of a new decoding algorithm that provides faster decoding than the classical bit-flipping decoder commonly adopted in this kind of systems. The main attacks against LEDAkem are investigated, taking into account quantum speedups. Some instances of LEDAkem are designed to achieve different security levels against classical and quantum computers. Some performance figures obtained through an efficient C99 implementation of LEDAkem are provided.Comment: 21 pages, 3 table

On Decoding Schemes for the MDPC-McEliece Cryptosystem

Recently, it has been shown how McEliece public-key cryptosystems based on moderate-density parity-check (MDPC) codes allow for very compact keys compared to variants based on other code families. In this paper, classical (iterative) decoding schemes for MPDC codes are considered. The algorithms are analyzed with respect to their error-correction capability as well as their resilience against a recently proposed reaction-based key-recovery attack on a variant of the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New message-passing decoding algorithms are presented and analyzed. Two proposed decoding algorithms have an improved error-correction performance compared to existing hard-decision decoding schemes and are resilient against the GJS reaction-based attack for an appropriate choice of the algorithm's parameters. Finally, a modified belief propagation decoding algorithm that is resilient against the GJS reaction-based attack is presented

Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201