4,513 research outputs found
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.
Error Function Attack of chaos synchronization based encryption schemes
Different chaos synchronization based encryption schemes are reviewed and
compared from the practical point of view. As an efficient cryptanalysis tool
for chaos encryption, a proposal based on the Error Function Attack is
presented systematically and used to evaluate system security. We define a
quantitative measure (Quality Factor) of the effective applicability of a chaos
encryption scheme, which takes into account the security, the encryption speed,
and the robustness against channel noise. A comparison is made of several
encryption schemes and it is found that a scheme based on one-way coupled
chaotic map lattices performs outstandingly well, as judged from Quality
Factor
Coding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding
theory and algebraic combinatorics, with most of the focus on the interaction
of codes with combinatorial designs, finite geometries, simple groups, sphere
packings, kissing numbers, lattices, and association schemes. In particular,
special interest is devoted to the relationship between codes and combinatorial
designs. We describe and recapitulate important results in the development of
the state of the art. In addition, we give illustrative examples and
constructions, and highlight recent advances. Finally, we provide a collection
of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in
Information and Coding Theory", ed. by I. Woungang et al., World Scientific,
Singapore, 201
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