39,190 research outputs found
Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations
Ideas from Fourier analysis have been used in cryptography for the last three
decades. Akavia, Goldwasser and Safra unified some of these ideas to give a
complete algorithm that finds significant Fourier coefficients of functions on
any finite abelian group. Their algorithm stimulated a lot of interest in the
cryptography community, especially in the context of `bit security'. This
manuscript attempts to be a friendly and comprehensive guide to the tools and
results in this field. The intended readership is cryptographers who have heard
about these tools and seek an understanding of their mechanics and their
usefulness and limitations. A compact overview of the algorithm is presented
with emphasis on the ideas behind it. We show how these ideas can be extended
to a `modulus-switching' variant of the algorithm. We survey some applications
of this algorithm, and explain that several results should be taken in the
right context. In particular, we point out that some of the most important bit
security problems are still open. Our original contributions include: a
discussion of the limitations on the usefulness of these tools; an answer to an
open question about the modular inversion hidden number problem
Proving knowledge of isogenies – A survey
Isogeny-based cryptography is an active area of research in post-quantum public key cryptography. The problem of proving knowledge of an isogeny is a natural problem that has several applications in isogeny-based cryptography, such as allowing users to demonstrate that they are behaving honestly in a protocol. It is also related to isogeny-based digital signatures. Over the last few years, there have been a number of advances in this area, but there are still many open problems. This paper aims to give an overview of the topic and highlight some open problems and directions for future research
A Comparison of Cryptography Courses
The author taught two courses on cryptography, one at Duke University aimed
at non-mathematics majors and one at Rose-Hulman Institute of Technology aimed
at mathematics and computer science majors. Both tried to incorporate technical
and societal aspects of cryptography, with varying emphases. This paper will
discuss the strengths and weaknesses of both courses and compare the
differences in the author's approach.Comment: 14 pages; to appear in Cryptologi
Using quantum key distribution for cryptographic purposes: a survey
The appealing feature of quantum key distribution (QKD), from a cryptographic
viewpoint, is the ability to prove the information-theoretic security (ITS) of
the established keys. As a key establishment primitive, QKD however does not
provide a standalone security service in its own: the secret keys established
by QKD are in general then used by a subsequent cryptographic applications for
which the requirements, the context of use and the security properties can
vary. It is therefore important, in the perspective of integrating QKD in
security infrastructures, to analyze how QKD can be combined with other
cryptographic primitives. The purpose of this survey article, which is mostly
centered on European research results, is to contribute to such an analysis. We
first review and compare the properties of the existing key establishment
techniques, QKD being one of them. We then study more specifically two generic
scenarios related to the practical use of QKD in cryptographic infrastructures:
1) using QKD as a key renewal technique for a symmetric cipher over a
point-to-point link; 2) using QKD in a network containing many users with the
objective of offering any-to-any key establishment service. We discuss the
constraints as well as the potential interest of using QKD in these contexts.
We finally give an overview of challenges relative to the development of QKD
technology that also constitute potential avenues for cryptographic research.Comment: Revised version of the SECOQC White Paper. Published in the special
issue on QKD of TCS, Theoretical Computer Science (2014), pp. 62-8
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.
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