2,265 research outputs found
Cryptanalysis of some protocols using matrices over group rings
We address a cryptanalysis of two protocols based on the supposed difficulty
of discrete logarithm problem on (semi) groups of matrices over a group ring.
We can find the secret key and break entirely the protocols
Public Key Exchange Using Matrices Over Group Rings
We offer a public key exchange protocol in the spirit of Diffie-Hellman, but
we use (small) matrices over a group ring of a (small) symmetric group as the
platform. This "nested structure" of the platform makes computation very
efficient for legitimate parties. We discuss security of this scheme by
addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman
(CDH) problems for our platform.Comment: 21 page
Quantum computation of discrete logarithms in semigroups
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks.
In contrast, we show that some generalizations of the discrete logarithm problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete logarithm problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to k ≥ 2 generators in a black-box abelian semigroup of order N requires
Θ˜(N12-12k) quantum queries
Using graphic methods to challenge cryptographic performance
Block and stream ciphers have formed the traditional basis for the standardisation of commercial ciphers in the DES, AES, RC4, and so on. More recently alternative graphic methods such as Elliptic Curve Cryptography (ECC) have been adopted for performance gains. In this research we reviewed a range of graphic and non-graphic methods and then designed our own cipher system based on several graphic methods, including Visual Cryptography (VC). We then tested our cipher against RC4 and the AES algorithms for performance and security. The results showed that a graphics based construct may deliver comparable or improved security and performance in many of the required areas. These findings offer potential alternative avenues for post-quantum cryptographic research
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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