CACTC
About ACA
Talks
Talk 1: An overview on algebraic invariants and the main parameters of some parametrized codes (M.G. Sarabia, C. Rentería Márquez, E. Sarmiento Rosales)
Abstract: The main goal of this work is to describe the parameters of some evaluation codes known as parameterized codes by using the relationships with the algebraic invariants of a quotient ring. We use some tools of algebraic geometry and commutative algebra to do this description. Some results in the case of codes parametrized by the edges of a graph or a clutter are given.
Talk 2: HIMMO: A collusion-resistant identity-based scheme for symmetric key generation ( Oscar García-Morchón, Ronald Rietman, Ludo Tolhuizen, Domingo Gómez, Jaime Gutiérrez )
Abstract: We describe HIMMO, a new scheme for identity-based symmetric key generation. Like the scheme of Blundo et al, HIMMO employs symmetric polynomials, which lead to very efficient implementations, but it is much less vulnerable against collusion attacks. HIMMO employs mixing modular operations over different rings and hiding part of the result of polynomial evaluation by only considering its least significant bits. We discuss the collusion resistance properties of HIMMO based on lattice-based cryptanalysis and provide figures on speed and memory usage of an implementation for various system parameters.
Talk 3: A Johnson-Type Bound for Group Codes and Lattices (Malihe Aliasgari, Mohammad-Reza Sadeghi)
Abstract: In this work we give and analyze a Johnson-type bound for group codes considering the G -norm. Johnson bounds have been given for binary and q-ary codes with respect to the Hamming distance. We borrow the idea of the G-norm from and define a new distance for codewords: the G-semidistance. We extend the Johnson-type bounds for binary and q-ary codes to the G-semidistance and give a relation between these bounds and our G-semidistance. By means of this, we present an upper bound on the number of codewords inside a G-ball and an ball, within a certain given radius, for both group codes and lattices.
Talk 4: Binomial Ideal Associated to a Lattice and Its Label Code (Malihe Aliasgari, Daniel Panario, Mohammad-Reza Sadeghi )
Abstract: In coding theory the study of the binomial ideal derived from an arbitrary code is currently of great interest. This is mainly because of a known relation between binomial ideals and lattices or codes. Also, studying the relation between binomial ideals associated to a lattice and its label code helps to solve the closest vector problem in lattices as well as decoding binary and non-binary codes and finding a label code of a lattice, as we do in this work.
Talk 5: On the Eficiency of Shortened Cyclic Multiple-Burst-Correcting Codes (Ana Lucila Sandoval Orozco, Luis Javier García Villalba, Mario Blaum )
Abstract: On channels with memory, the noise is not independent from transmission to transmission. As a consequence, transmission errors occur in clusters or bursts, and channels with memory are called burst-error channels. Examples of burst-error channels are mobile telephony channels, where the error bursts are caused by signal fading owing to multipath transmission; cable transmission, which is affected by impulsive switching noise and crosstalk; and magnetic recording, which is subject to dropouts caused by surface defects and dust particles.
Talk 6: The degree compatible Gröbner Fan for Linear Codes ( Natalia Dück, I. Márquez-Corbella, Edgar Martínez-Moro )
Abstract: In this talk, it will be shown how methods from the software system TiGERS can be modified in order to compute all reduced Gröbner bases with respect to a degree compatible ordering for code ideals even though these binomial ideals are not toric. To this end, the correspondence of linear codes and binomial ideals will be briefy described as well as their resemblance to toric ideals. Finally, we will hint at applications of the degree compatible Gröbner fan to the code equivalence problem.
Talk 7: Extending Construction X for Quantum Error-Correcting Codes (Akshay Degwekar, Kenza Guenda, T. Aaron Gulliver )
Abstract: In this talk, we extend the work of Lisonek and Singh on construction X for quantum error- correcting codes to finite fields of order p^2 where p is prime. The results obtained are applied to the dual of Hermitian cyclic codes to generate new quantum error-correcting codes.
Talk 8: McEliece Cryptosystem Based on Punctured Convolutional Codes and the Pseudo-Random Generators (Hamza Moufek, Kenza Guenda)
Abstract: The purpose of this paper is to present a new version of the McEliece cryptosystem based on punctured convolutional codes and the pseudo-random generators. We use the modified self-shrinking generator to fill the punctured pattern. More precisely we propose to fill out the pattern punctured by the bits generated using a pseudo random generator LFSR.
Talk 9: Some applications of idempotent semirings in Public Key Cryptography (Mariana Durcheva)
Abstract: We give a generalization of the Diffie-Hellman key exchange protocol, to the context of semigroup actions.
Talk 10: Evaluation Codes and Weierstrass Semigroups (Emma Previato)
Abstract: We report on a construction of modified evaluation codes by Dias and Neves. Evaluation codes are a type of Reed-Muller code, where the code is the image of a space of polynomial functions under the evaluation map on a given set of points in afine space. In their work, Dias and Neves assign weights to the coordinates, namely a finite sequence of natural numbers. The goal is to compute the parameters of the code, especially aiming at the Minimum-Distance- Separable property.
Talk 11: Edge-weighted Cayley graphs and p-ary bent functions (David Joyner)
Abstract: Let f:GF(p)^n->GF(p). When p=2, Bernasconi et al have shown that there is a correspondence between certain properties of f (eg, if it is bent) and properties of its associated Cayley graph. Analogously, but much earlier, Dillon showed that f is bent if and only of the "level curves" of f had certain combinatorial properties (again, only when p=2). The attempt is to investigate an analogous theory when p>2. More precisely, we try to investigate which graph-theoretical properties of Gamma_f can be characterized in terms of function-theoretic properties of f, and which function-theoretic properties of f correspond to combinatorial properties of the set of "level curves" f^{-1}(a) (a in GF(p)). It turns out that natural generalizations of the Bernasconi correspondence and Dillon correspondence are false.
Talk 12: A notion of multivariate BCH bounds and codes (José Joaquín Bernal Buitrago, Diana Haidive Bueno Carreño, Juan Jacobo Simón Pinero. )
Abstract: In this talk we use the techniques of computation of the minimum apparent distance of a hypermatrix in order to develop a notion of BCH bound and BCH code in the multivariate case. Then we extend the most classical results in BCH codes to the multivariate case and we show how to construct abelian codes with maximum dimension with respect to prefixed bounds for their minimum distance.
Talk 13: Error correcting pair: a new approach to Code-based Cryptography (I. Marquez-Corbella, Ruud Pellikaan)
Abstract: McEliece cryptosystem is the first public-key cryptosystem based on linear error-correcting codes. Although a code with an efficient bounded distance decoding algorithm is chosen as the secret key in this cryptosystem, not knowing the secret code and its decoding algorithm faced the attacker with the problem of decoding a random-looking linear code. Moreover, it is well known that the known efficient bounded distance decoding algorithm of the families of codes proposed for code-based cryptography (like Reed-Solomon codes, Goppa codes, alternant codes or algebraic geometry codes) can be described using error correcting pairs (ECP). That means that, the McEliece cryptosystem is not based on the intractability of bounded distance decoding but on the problem of retrieving an error-correcting pair from a random linear code. The aim of this article is to propose the class of codes with a t-ECP whose error-correcting pair is not easily reconstructed from the single knowledge of a generator matrix.
Talk 14: The extended and generalized rank weight enumerator of a code (Relinde Jurrius, Ruud Pellikaan )
Abstract: This paper investigates the rank weight enumerator of a code over L, where L is a finite extension of a field K. This is a generalization of the case where K = Fq and L = Fq^m of Gabidulin codes to arbitrary characteristic. We use the notion of counting polynomials, to define the (extended) rank weight enumerator, since in this generality the set of codewords of a given rank weight is no longer finite. Also the extended and generalized rank weight enumerator are studied in analogy with previous work on codes with respect to the Hamming metric.
Talk 15: Plaintext Recovery for One-Time Pads Used Twice (Gregory V. Bard, Theodore McDonough)
Abstract: The authors propose a method, based on matrix computations mod n, which efficiently solves the “two-time pad problem” for plaintexts chosen from the English language, and working with n = 29. The method should be effective for other modern spoken languages and similar sized n.
Talk 16: Some new almost difference sets via finite fields (Bo Phillips, Jace Robinson)
Abstract: Several construction techniques based on finite fields and cyclotomy are obtained during the last decade providing infinite classes of ADS. We obtain some new examples of such objects using a finite field of order 31, thereby obtaining an almost perfect sequence of length 62 whose existence status was previously open.
Talk 17: Some results on finite fields (James Hufford)
Abstract: In the study of perfect sequences, use of trace functions in finite fields has been a common technique, dating back to Singer’s classical examples of m- sequences. Many variations of Singer’s theme have been the topic of research by many mathematicians during the last few decades. In all these investigations, expressing the underlying function as a polynomial whose coefficients are from the prime subfield has been a main problem. Explicit answers require the use of Stickelberger’s congruence of Gauss sums. Using elementary methods, we provide a simple result along these lines.
Talk 18: On a class of difference set pairs (Ankita Bakshi, Deeksha )
Abstract: We provide a new construction technique for DSPs using group rings.
Talk 19: Difference Set Pairs : A Recursive Approach via group rings (K.T.Arasu, Anika Goyal , Abhishek Puri)
Abstract: Binary array pairs with optimal/ideal correlation values and their algebraic counterparts "difference set pairs" (DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian dfference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs). Discrete signals arising from DSPs find applications in cryptography, radar and wireless communications and CDMA systems. Our methods would employ group rings.