•Journal•ISSN: 1930-5338
Advances in Mathematics of Communications
American Institute of Mathematical Sciences
About: Advances in Mathematics of Communications is an academic journal published by American Institute of Mathematical Sciences. The journal publishes majorly in the area(s): Computer science & Linear code. It has an ISSN identifier of 1930-5338. It is also open access. Over the lifetime, 776 publications have been published receiving 6847 citations.
Papers published on a yearly basis
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TL;DR: A new family of linear maximum rank distance (MRD) codes for all parameters is constructed, which contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the Gabdulin codes.
Abstract: In this article we construct a new family of linear maximum rank distance (MRD) codes for all parameters. This family contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the Gabidulin codes. This family also contains the well-known family of semifields known as Generalised Twisted Fields. We also calculate the automorphism group of these codes, including the automorphism group of the Gabidulin codes.
211 citations
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TL;DR: In this article, the authors recall why linear codes with complementary duals (LCD codes) play a role in countermeasures to passive and active side-channel analyses on embedded cryptosystems.
Abstract: We recall why linear codes with complementary duals (LCD codes) play a role in counter-measures to passive and active side-channel analyses on embedded cryptosystems. The rate and the minimum distance of such LCD codes must be as large as possible. We investigate constructions.
182 citations
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TL;DR: This work proposes a public-key encryption scheme and key agreement protocols based on a group action on a set and introduces a novel way of using elliptic curves for constructing asymmetric cryptography.
Abstract: We propose a public-key encryption scheme and key agreement protocols based on a group action on a set. We construct an implementation of these schemes for the action of the class group $\mathcal{CL}(\mathcal{O}_K)$ of an imaginary quadratic field $K$ on the set $\mathcal{ELL}$p,n$(\mathcal{O}_K)$ of isomorphism classes of elliptic curves over $\mathbb{F}_p$ with $n$ points and the endomorphism ring $\mathcal{O}_K$.
This introduces a novel way of using elliptic curves for constructing asymmetric cryptography.
136 citations
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TL;DR: In this paper, a non-quadratic APN function has been constructed, which is in remarkable contrast to all recently constructed APN functions which have all been quadratic.
Abstract: Following an example in [12],
we show how to change one coordinate function of an
almost perfect nonlinear
(APN) function in order to obtain new examples. It turns out that
this is a very powerful method to construct new
APN functions. In particular, we show that our approach can
be used to construct a ''non-quadratic'' APN function.
This new example
is in remarkable contrast to all recently constructed functions which
have all been quadratic.
An equivalent function has been found
independently
by Brinkmann and Leander [8]. However, they
claimed that their function is CCZ equivalent to a quadratic one. In this
paper we give several reasons
why this new function is not equivalent to a quadratic one.
135 citations
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TL;DR: It is shown that skew constacyclic self-dual codes over GR(4, 2) are constructed using Galois rings instead of finite fields as coefficients, and the resulting non commutative rings are no longer left and right Euclidean.
Abstract: We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4, 2) are constructed. Euclidean self-dual codes give self-dual Z(4)-codes. Hermitian self-dual codes yield 3-modular lattices and quasi-cyclic self-dual Z(4)-codes.
118 citations