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Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography
[article]
2022
arXiv
pre-print
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To be specific, we introduce the so-called semilinear transformation in coding theory, which is defined through an 𝔽_q-linear automorphism of 𝔽_q^m, then apply them to construct a public key encryption ...
This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. ...
Semilinear transformations In this section, we first introduce the concept of semilinear transformations and investigate their properties when acting on linear codes. ...
arXiv:2107.03157v5
fatcat:sa3sz4cplfd5li4op3vlp67kpq
The Hardness of Code Equivalence over $\mathbb{F}_q$ and Its Application to Code-Based Cryptography
[chapter]
2013
Lecture Notes in Computer Science
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In this paper, we review the hardness of code equivalence over Fq due to some recent negative results and argue on the possible implications in code-based cryptography. ...
In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem. ...
This Programme is supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission. ...
doi:10.1007/978-3-642-38616-9_14
fatcat:eufpaexm7nhcdbh7xxbee7iiqi
On (2n/3-1)-resilient (n,2)-functions
[article]
2019
arXiv
pre-print
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We suggest constructions of such functions and corresponding partitions, show connections with Latin hypercubes and binary 1-perfect codes, characterize the non-full-rank and the reducible functions from ...
the considered class, and discuss the possibility to make a complete characterization of the class. ...
Multifold perfect codes In this subsection, we discuss equitable partitions with the quotient matrix (8) and their connections with perfect codes. ...
arXiv:1902.00022v1
fatcat:wvnufop7wzbnpgculkhzb2umry
LESS is More: Code-Based Signatures Without Syndromes
[chapter]
2020
Lecture Notes in Computer Science
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Devising efficient and secure signature schemes based on coding theory is still considered a challenge by the cryptographic community. ...
In this paper, we construct a signature scheme by exploring a new approach to the area. ...
Codes that are contained in their dual, i.e. C ⊆ C ⊥ , are called weakly self-dual, and codes that are equal to their dual, i.e. C = C ⊥ , are called simply self-dual. ...
doi:10.1007/978-3-030-51938-4_3
fatcat:5hw4o4loifcyfcofwjmehpns5u
Book Review: Finite element methods: Fifty years of the Courant element
1996
Mathematics of Computation
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Various applications are also discussed in these papers, which include compressible flows, convection-diffusion problems, elasticity and viscoelasticity, the Helmholtz equation, Maxwell equations, Navier-Stokes ...
To commemorate the fiftieth anniversary of the publication of this paper, a conference was held at the University of Jyväskylä, Finland in 1993. ...
Transforms related to the DFT, such as the Laplace transform, the z-transform, the Chebyshev transform, and the Hartley transform, are treated in Chapter 8. ...
doi:10.1090/s0025-5718-96-00755-7
fatcat:cmmgtlmdtvelpey5ntju5iizo4
Fourier's Method of Linear Programming and Its Dual
1986
The American mathematical monthly
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also 11G50, 37P30]
14G50
Applications to coding theory and cryptography [See also 94A60,
94B27, 94B40]
14G99
None of the above, but in this section
14Hxx
Curves
14H05
Algebraic functions; function ...
, economics 46N20 Applications to differential and integral equations 46N30 Applications in probability theory and statistics 46N40 Applications in numerical analysis [See also 65Jxx] 46N50 Applications ...
82D80 Nanostructures and nanoparticles 82D99 None of the above, but in this section
83-XX RELATIVITY AND GRAVITATIONAL THEORY
83-00 General reference works (handbooks, dictionaries, bibliographies, ...
doi:10.2307/2322281
fatcat:yvhgyh2epbcwdoqdhuaopkcrue
Reference list of indexed articles
1999
Theoretical Computer Science
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Zalcstein, The complexity of Grigorchuk groups with application to cryptography 88 (1) (1991) 83-98 1643. S. Cho and D.T. ...
Warmuth, Applications of scheduling theory to formal language theory 37 (2) (1985) 217-243 732. R. De Simone, Higher-level synchronizing devices in MEIJE-SCCS 37 (3) (1985) 245-267 733. A. ...
doi:10.1016/s0304-3975(98)00320-x
fatcat:bdgg2ekzdjahdo7g2gtwbdye6m
Book report
2004
Computers and Mathematics with Applications
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Bayesian Predictive Profiles with Applications to Retail Transaction Data (Igor V. Padhraic Smyth). 169. ...
Starting the Segmentation Gene Cascade in Insects (Urs Schmidt-Ott and Ernst A. Wimmer). 18. The Evolution of Nematode Development: How Cells and Genes Change their Function (Ralf J. ...
doi:10.1016/j.camwa.2004.06.021
fatcat:vi5ps7eddza7hfba726v3epvtq
Ring geometries, two-weight codes, and strongly regular graphs
2008
Designs, Codes and Cryptography
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Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homogeneous weights and multisets of points in an associated projective ring geometry. ...
It is known that a linear two-weight code C over a finite field F q corresponds both to a multiset in a projective space over F q that meets every hyperplane in either a or b points for some integers a ...
Acknowledgement The authors feel indebted to the reviewers for a variety of remarks and corrections which helped to improve the quality of the published paper. ...
doi:10.1007/s10623-007-9136-8
fatcat:3i7b3d6zhrfwxbhywmmleadq6q
Systematic encoders for generalized Gabidulin codes and the q-analogue of Cauchy matrices
[article]
2020
arXiv
pre-print
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In addition, our results allow to give a new efficient criterion to verify whether a rank metric code of dimension k and length n is a generalized Gabidulin code. ...
In particular, as an application, we construct Gabidulin codes whose generator matrix is the concatenation of an identity block and a Toeplitz/Hankel matrix. ...
Acknowledgement The author would like to thank Eimear Byrne for useful comments on the structure of the work and Martino Borello for suggesting to point out Lemma 12. ...
arXiv:1805.06706v2
fatcat:tingb2m6xjaelnux2rmat4cs7u
On a Class of Meromorphic Functions Related to Cho-Kwon-Srivastava Operator
2012
ISRN Applied Mathematics
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by means of an operator given by Ghanim and Darus, in U={z:0<|z|<1}, and investigate a number of inclusion relationships of these classes. ...
We introduce new classes, Σn,λ*,μ,k(α,β,ρ) and Σn,λμ,k(α,β,ρ), of meromorphic functions defined by means of the Hadamard product of Cho-Kwon-Srivastava operator, and we define here a similar transformation ...
Simonis, Some new results on optimal codes over F5,Designs, Codes and Cryptography, vol. 30, 2003, pp. 97-111. цитирана в:M. Araya, M. ...
doi:10.5402/2012/272678
fatcat:kn3oeobqmzh7tgbpns35eeyy4u
On the number of roots of some linearized polynomials
[article]
2020
arXiv
pre-print
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Linearized polynomials appear in many different contexts, such as rank metric codes, cryptography and linear sets, and the main issue regards the characterization of the number of roots from their coefficients ...
Also, we characterize the number of roots of such polynomials directly from their coefficients, dealing with matrices which are much smaller than the relative Dickson matrices and the companion matrices ...
Introduction Linearized polynomials over F q n are important objects in the theory of finite fields and in finite geometry since they correspond to F q -linear transformations of the n-dimensional F q ...
arXiv:1909.00802v2
fatcat:ljw7cmfwv5dnnfwsvbdcgf2ufa
Computational learning theory
1992
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
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Abe [1] proves that the class of semilinear
sets of di-
mensions 1 and 2 with unary coding is PAC-learnable
by means of an Occam algorithm. ...
It is logical that cryptography (which tries to make unpredictable things ever easier to compute) and computational learning theory (which tries to make more powerful classes of concepts predictable) should ...
doi:10.1145/129712.129746
dblp:conf/stoc/Angluin92
fatcat:7aw3cnd745bellyhu7phywpul4
Incorporation of Deep Neural Network Reinforcement Learning with Domain Knowledge
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2107.14613v1 fatcat:eczsveq7zrddbaljvvbu5twc24
This paper inspects expansive ways to affect encode such information as sensible and mathematical limitations and portrays methods and results that came to a couple of subcategories under all of those ...
Integrating space data is uniquely important to the development of Knowledge understanding model, as well as other fields that aid in understanding information by utilizing the human-machine interface ...
Theorem theories are often extremely related to coaching of FFNN, as [16] broadly discuss. ...
arXiv:2107.14613v2
fatcat:cddkguo3gvcgxn6s67ca26ucii
Tight sets and m-ovoids of generalised quadrangles
2009
Combinatorica
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Geometric Codes and Hyperovals Anton Betten I will outline the theory of geometric codes and their relationship to the construction of hyperovals in Desarguesian projective planes of even order. ...
In the distance 5 case these codes and their duals have been studied a great deal, as they appear in many places and disguisesfor instance, cryptography, multiuser communications, orthogonal geometry over ...
doi:10.1007/s00493-009-2179-x
fatcat:3lv4kl6qafbfdemivsj73n6miq
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