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Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography [article]

Wenshuo Guo, Fang-Wei Fu
2022 arXiv   pre-print
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]

Nicolas Sendrier, Dimitris E. Simos
2013 Lecture Notes in Computer Science  
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]

Denis S. Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)
2019 arXiv   pre-print
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]

Jean-François Biasse, Giacomo Micheli, Edoardo Persichetti, Paolo Santini
2020 Lecture Notes in Computer Science  
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

Susanne C. Brenner, Shagi-Di Shih, Chi-Wang Shu, Lawrence F. Shampine, Harald Niederreiter, Jan Kok, David Elliott, Ren{e} Schoof, S. S. Wagstaff Jr.
1996 Mathematics of Computation  
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

H. P. Williams
1986 The American mathematical monthly  
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  
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  
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

Eimear Byrne, Marcus Greferath, Thomas Honold
2008 Designs, Codes and Cryptography  
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]

Alessandro Neri
2020 arXiv   pre-print
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

F. Ghanim, M. Darus
2012 ISRN Applied Mathematics  
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]

Olga Polverino, Ferdinando Zullo
2020 arXiv   pre-print
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

Dana Angluin
1992 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92  
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]

Aryan Karn, Ashutosh Acharya
2021 arXiv   pre-print
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

John Bamberg, Maska Law, Tim Penttila
2009 Combinatorica  
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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