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  • Speeding up regular elliptic curve scalar multiplication without precomputation
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-07-02
    Kwang Ho Kim; Junyop Choe; Song Yun Kim; Namsu Kim; Sekung Hong

    This paper presents a series of Montgomery scalar multiplication algorithms on general short Weierstrass curves over fields with characteristic greater than 3, which need only 12 field multiplications per scalar bit using 8 $ \sim $ 9 field registers, thus outperform the binary NAF method on average. Over binary fields, the Montgomery scalar multiplication algorithm which was presented at the first

    更新日期:2020-07-02
  • Some group-theoretical results on Feistel Networks in a long-key scenario
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-07-02
    Riccardo Aragona; Marco Calderini; Roberto Civino

    The study of the trapdoors that can be hidden in a block cipher is and has always been a high-interest topic in symmetric cryptography. In this paper we focus on Feistel-network-like ciphers in a classical long-key scenario and we investigate some conditions which make such a construction immune to the partition-based attack introduced recently by Bannier et al.

    更新日期:2020-07-02
  • QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Farzane Amirzade; Mohammad-Reza Sadeghi; Daniel Panario

    Trapping sets significantly influence the performance of low-density parity-check codes. An $ (a, b) $ elementary trapping set (ETS) causes high decoding failure rate and exert a strong influence on the error floor of the code, where $ a $ and $ b $ denote the size and the number of unsatisfied check-nodes in the ETS, respectively. The smallest size of an ETS in $ (3, n) $-regular LDPC codes with girth

    更新日期:2020-01-08
  • A generalized quantum relative entropy
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Luiza H. F. Andrade; Rui F. Vigelis; Charles C. Cavalcante

    We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices $ \mathcal{P} $. This geodesic is defined from a deformed exponential function $ \varphi $ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss

    更新日期:2020-01-08
  • On the non-Abelian group code capacity of memoryless channels
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Jorge P. Arpasi

    In this work is provided a definition of group encoding capacity $ C_G $ of non-Abelian group codes transmitted through symmetric channels. It is shown that this $ C_G $ is an upper bound of the set of rates of these non-Abelian group codes that allow reliable transmission. Also, is inferred that the $ C_G $ is a lower bound of the channel capacity. After that, is computed the $ C_G $ of the group

    更新日期:2020-01-08
  • A shape-gain approach for vector quantization based on flat tori
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Fabiano Boaventura de Miranda; Cristiano Torezzan

    In this paper we present a vector quantization framework for Gaussian sources which combines a spherical code on layers of flat tori and the shape and gain technique. The basic concepts of spherical codes in tori layers are reviewed and two constructions are presented for the shape by exploiting the $ k/2 $-dimensional lattices $ D_{k/2} $ and $ A^{*}_{k/2} $ as its pre-image. A scalar quantizer is

    更新日期:2020-01-08
  • On perfect poset codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Luciano Panek; Jerry Anderson Pinheiro; Marcelo Muniz Alves; Marcelo Firer

    We consider on $ \mathbb{F}_{q}^{n} $ metrics determined by posets and classify the parameters of $ 1 $-perfect poset codes in such metrics. We show that a code with same parameters of a $ 1 $-perfect poset code is not necessarily perfect, however, we give necessary and sufficient conditions for this to be true. Furthermore, we characterize the unique way up to a labeling on the poset, considering

    更新日期:2020-01-08
  • Challenge codes for physically unclonable functions with Gaussian delays: A maximum entropy problem
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Alexander Schaub; Olivier Rioul; Jean-Luc Danger; Sylvain Guilley; Joseph Boutros

    Motivated by a security application on physically unclonable functions, we evaluate the probability distributions and Rényi entropies of signs of scalar products of i.i.d. Gaussian random variables against binary codewords in $ \{\pm1\}^n $. The exact distributions are determined for small values of $ n $ and upper bounds are provided by linking this problem to the study of Boolean threshold functions

    更新日期:2020-01-08
  • The weight distribution of families of reducible cyclic codes through the weight distribution of some irreducible cyclic codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2020-01-08
    Gerardo Vega; Jesús E. Cuén-Ramos

    The calculation of the weight distribution for some reducible cyclic codes can be reduced down to the corresponding one of a particular kind of irreducible cyclic codes. This reduction is achieved by means of a known identity (see [3,Theorem 1.1]). In fact, as will be shown here, the weight distribution of some families of reducible cyclic codes, recently reported in several works ([2,5,7,11,12]),

    更新日期:2020-01-08
  • New classes of strictly optimal low hit zone frequency hopping sequence sets
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Hongyu Han; Sheng Zhang

    Low hit zone frequency hopping sequences (LHZ FHSs) with favorable partial Hamming correlation properties are desirable in quasi-synchronous frequency hopping multiple-access systems. An LHZ FHS set is considered to be strictly optimal when it has optimal partial Hamming correlation for all correlation windows. In this study, an interleaved construction of new sets of strictly optimal LHZ FHSs is proposed

    更新日期:2019-11-20
  • Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Dean Crnković; Ronan Egan; Andrea Švob

    In this paper we introduce the notion of orbit matrices of integer matrices such as Seidel and Laplacian matrices of some strongly regular graphs with respect to their permutation automorphism groups. We further show that under certain conditions these orbit matrices yield self-orthogonal codes over finite fields $ \mathbb{F}_q $, where $ q $ is a prime power and over finite rings $ \mathbb{Z}_m $

    更新日期:2019-11-20
  • Designs from maximal subgroups and conjugacy classes of Ree groups
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Jamshid Moori; Bernardo G. Rodrigues; Amin Saeidi; Seiran Zandi

    In this paper, using a method of construction of $ 1 $-designs which are not necessarily symmetric, introduced by Key and Moori in [5], we determine a number of $ 1 $-designs with interesting parameters from the maximal subgroups and the conjugacy classes of the small Ree groups $ ^2G_2(q) $. The designs we obtain are invariant under the action of the groups $ ^2G_2(q) $.

    更新日期:2019-11-20
  • New and updated semidefinite programming bounds for subspace codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Daniel Heinlein; Ferdinand Ihringer

    We show that $A_2(7, 4) \leq 388$ and, more generally, $A_q(7, 4) \leq (q^2-q+1) [7] + q^4 - 2q^3 + 3q^2 - 4q + 4$ by semidefinite programming for $q \leq 101$. Furthermore, we extend results by Bachoc et al. on SDP bounds for $A_2(n, d)$, where $d$ is odd and $n$ is small, to $A_q(n, d)$ for small $q$ and small $n$.

    更新日期:2019-11-20
  • Abelian non-cyclic orbit codes and multishot subspace codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Gustavo Terra Bastos; Reginaldo Palazzo Júnior; Marinês Guerreiro

    In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, Abelian orbit codes are defined and a construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As

    更新日期:2019-11-20
  • Three parameters of Boolean functions related to their constancy on affine spaces
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Claude Carlet; Serge Feukoua

    The $ k $-normality of Boolean functions is an important notion initially introduced by Dobbertin and studied in several papers. The parameter related to this notion is the maximal dimension of those affine spaces contained in the support $ supp(f) $ of the function or in its co-support $ cosupp(f) $. We denote it by $ norm\,(f) $ and call it the norm of $ f $.The norm concerns only the affine spaces

    更新日期:2019-11-20
  • Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Steven T. Dougherty; Joe Gildea; Adrian Korban; Abidin Kaya

    We describe eight composite constructions from group rings where the orders of the groups are 4 and 8, which are then applied to find self-dual codes of length 16 over $ \mathbb{F}_4 $. These codes have binary images with parameters $ [32,16,8] $ or $ [32,16,6] $. These are lifted to codes over $ \mathbb{F}_4+u\mathbb{F}_4 $, to obtain codes with Gray images of extremal self-dual binary codes of length

    更新日期:2019-11-20
  • A construction of $ \mathbb{F}_2 $-linear cyclic, MDS codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    Sara D. Cardell; Joan-Josep Climent; Daniel Panario; Brett Stevens

    In this paper we construct $ \mathbb{F}_2 $-linear codes over $ \mathbb{F}_{2}^{b} $ with length $ n $ and dimension $ n-r $ where $ n = rb $. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime $ p $, let $ n = p-1 $ and utilize a partition of $ \mathbb{Z}_n $. Then we apply

    更新日期:2019-11-20
  • Isogeny formulas for Jacobi intersection and twisted hessian curves
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-11-20
    João Paulo da Silva; Julio López; Ricardo Dahab

    The security of public-key systems is based on the difficulty of solving certain mathematical problems. With the possible emergence of large-scale quantum computers several of these problems, such as factoring and computing discrete logarithms, would be efficiently solved. Research on quantum-resistant public-key cryptography, also called post-quantum cryptography (PQC), has been productive in recent

    更新日期:2019-11-20
  • Giophantus distinguishing attack is a low dimensional learning with errors problem
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-09-11
    Jintai Ding; Joshua Deaton; Kurt Schmidt

    In this paper, we attack the recent NIST submission Giophantus, a public key encryption scheme. We find that the complicated structure of Giophantus's ciphertexts leaks information via a correspondence from a low dimensional lattice. This allows us to distinguish encrypted data from random data by the LLL algorithm. This is a more efficient attack than previous proposed attacks.

    更新日期:2019-09-11
  • Group signature from lattices preserving forward security in dynamic setting
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-09-04
    Meenakshi Kansal; Ratna Dutta; Sourav Mukhopadhyay

    We propose the first lattice-based dynamic group signature scheme achieving forward security. Our scheme is proven to be secure against framing attack, misidentification attack and preserves anonymity under the learning with errors (${\mathsf{LWE}}$) and short integer solution (${\mathsf{SIS}}$) assumptions in the random oracle model. More interestingly, our setting allows the group manager to generate

    更新日期:2019-09-04
  • Some results on \begin{document}$ \mathbb{Z}_p\mathbb{Z}_p[v] $\end{document}-additive cyclic codes
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-09-04
    Lingyu Diao; Jian Gao; Jiyong Lu

    $ \mathbb{Z}_p\mathbb{Z}_p[v] $-Additive cyclic codes of length $ (\alpha,\beta) $ can be viewed as $ R[x] $-submodules of $ \mathbb{Z}_p[x]/(x^\alpha-1)\times R[x]/(x^\beta-1) $, where $ R = \mathbb{Z}_p+v\mathbb{Z}_p $ with $ v^2 = v $. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as $ R[x] $-submodules of $ \mathbb{Z}_p[x]/(x^\alpha-1)\times

    更新日期:2019-09-04
  • On polycyclic codes over a finite chain ring
    Adv. Math. Commun. (IF 0.734) Pub Date : 2019-09-04
    Alexandre Fotue-Tabue; Edgar Martínez-Moro; J. Thomas Blackford

    Galois images of polycyclic codes over a finite chain ring $ S $ and their annihilator dual are investigated. The case when a polycyclic code is Galois-disjoint over the ring $ S, $ is characterized and, the trace codes and restrictions of free polycyclic codes over $ S $ are also determined giving an analogue of Delsarte's theorem relating the trace code and the annihilator dual code.

    更新日期:2019-09-04
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