Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other authors/ comment of the author: quotation has been added to Theorem 5.

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

SPHINCS+^+ post-quantum digital signature scheme with Streebog hash function

Many commonly used public key cryptosystems will become insecure once a scalable quantum computer is built. New cryptographic schemes that can guarantee protection against attacks with quantum computers, so-called post-quantum algorithms, have emerged in recent decades. One of the most promising candidates for a post-quantum signature scheme is SPHINCS$^+$, which is based on cryptographic hash functions. In this contribution, we analyze the use of the new Russian standardized hash function, known as Streebog, for the implementation of the SPHINCS$^+$ signature scheme. We provide a performance comparison with SHA-256-based instantiation and give benchmarks for various sets of parameters.Comment: 5 pages, 2 figures, 3 table