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 Cryptography and Communications   [SJR: 0.55]   [H-I: 8]   [12 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447    Published by Springer-Verlag  [2351 journals]
• Enumeration formulae for self-dual, self-orthogonal and complementary-dual
quasi-cyclic codes over finite fields
• Authors: Anuradha Sharma; Taranjot Kaur
Pages: 401 - 435
Abstract: Let $$\mathbb {F}_{q}$$ denote the finite field of order q, and let ℓ,m be positive integers with $$\gcd (m,q)=1.$$ In this paper, we enumerate all self-orthogonal, self-dual and complementary-dual ℓ-quasi-cyclic codes of length m ℓ over $$\mathbb {F}_{q}$$ by placing the Euclidean inner product on $$\mathbb {F}_{q}^{m\ell }.$$
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0228-7
Issue No: Vol. 10, No. 3 (2018)

• Two classes of near-optimal frequency-hopping sequence sets with
prime-power period
• Authors: Shanding Xu; Xiwang Cao; Guangkui Xu; Gaojun Luo
Pages: 437 - 454
Abstract: In this paper, a kind of generalized cyclotomy with respect to a prime power is introduced and properties of the corresponding generalized cyclotomic numbers are investigated. Based on the generalized cyclotomy, two classes of frequency-hopping sequence (FHS) sets with prime-power period are presented. Meanwhile, we derive the Hamming correlation distribution of the new FHS sets. The results show that the proposed FHSs and FHS sets have (near-) optimal maximum Hamming correlation (MHC). These classes of near-optimal FHS sets have new parameters which are not covered in the literature.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0229-6
Issue No: Vol. 10, No. 3 (2018)

• On lattice-based algebraic feedback shift registers synthesis for
multisequences
• Authors: Li-Ping Wang; Daqing Wan
Pages: 455 - 465
Abstract: In this paper we show that algebraic feedback shift registers synthesis problems over residue class rings, some ramified extensions and some quadratic integer rings for multisequences are reduced to the successive minima problem in lattice theory. Therefore they can be solved by polynomial-time algorithms since the number of multiple sequences is fixed.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0230-0
Issue No: Vol. 10, No. 3 (2018)

• The exact autocorrelation distribution and 2-adic complexity of a class of
binary sequences with almost optimal autocorrelation
• Authors: Yuhua Sun; Qiang Wang; Tongjiang Yan
Pages: 467 - 477
Abstract: Pseudo-random sequences with good statistical properties, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of binary sequences with three-level autocorrelation and analyze the 2-adic complexity of this class of sequences. Our results show that the 2-adic complexity of such a binary sequence with period N is at least (N + 1) − log2 (N + 1). We further show that it is maximal for infinitely many cases. This indicates that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0233-x
Issue No: Vol. 10, No. 3 (2018)

• Revisiting RC4 key collision: Faster search algorithm and new 22-byte
colliding key pairs
• Authors: Amit Jana; Goutam Paul
Pages: 479 - 508
Abstract: If two different secret keys of stream cipher RC4 yield the same internal state after the key scheduling algorithm (KSA) and hence generate the same sequence of keystream bits, they are called a colliding key pair. The number of possible internal states of RC4 stream cipher is very large (approximately 21700), which makes finding key collision hard for practical key lengths (i.e., less than 30 bytes). Matsui (2009) for the first time reported a 24-byte colliding key pair and one 20-byte near-colliding key pair (i.e., for which the state arrays after the KSA differ in at most two positions) for RC4. Subsequently, Chen and Miyaji (2011) designed a more efficient search algorithm using Matsui’s collision pattern and reported a 22-byte colliding key pair which remains the only shortest known colliding key pair so far. In this paper, we show some limitations of both the above approaches and propose a faster collision search algorithm that overcomes these limitations. Using our algorithm, we are able to find three additional 22-byte colliding key pairs that are different from the one reported by Chen and Miyaji. We additionally give 12 new 20-byte near-colliding key pairs. These results are significant, considering the argument by Biham and Dunkelman (2007), that for shorter keys there might be no instances of collision at all.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0231-z
Issue No: Vol. 10, No. 3 (2018)

• Generalized nonbinary sequences with perfect autocorrelation, flexible
alphabets and new periods
• Authors: Serdar Boztaş; Ferruh Özbudak; Eda Tekin
Pages: 509 - 517
Abstract: We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztaş and Udaya 10) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel alternatives for wireless communications and radar system designers for applications in ranging and synchronisation as well as channel identification.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0237-6
Issue No: Vol. 10, No. 3 (2018)

• Cyclic codes over a non-commutative finite chain ring
• Authors: R. Sobhani
Pages: 519 - 530
Abstract: In this study, we consider the finite (not necessary commutative) chain ring $$\mathcal {R}:=\mathbb {F}_{p^{m}}[u,\theta ]/{\left < u^{2} \right >}$$ , where θ is an automorphism of $$\mathbb {F}_{p^{m}}$$ , and completely explore the structure of left and right cyclic codes of any length N over $$\mathcal {R}$$ , that is, left and right ideals of the ring $$\mathcal {S}:=\mathcal {R}[x]/{\left < x^{N}-1 \right >}$$ . For a left (right) cyclic code, we determine the structure of its right (left) dual. Using the fact that self-dual codes are bimodules, we discuss on self-dual cyclic codes over $$\mathcal {R}$$ . Finally, we study Gray images of cyclic codes over $$\mathcal {R}$$ and as some examples, three linear codes over $$\mathbb {F}_{4}$$ with the parameters of the best known ones, but with different weight distributions, are obtained as the Gray images of cyclic codes over $$\mathcal {R}$$ .
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0238-5
Issue No: Vol. 10, No. 3 (2018)

• Permutation polynomials of the form cx + Tr q l / q ( x a ) $cx+\text {Tr}_{q^{l}/ q}(x^{a})$ and permutation trinomials over finite fields with
even characteristic
• Authors: Kangquan Li; Longjiang Qu; Xi Chen; Chao Li
Pages: 531 - 554
Abstract: Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. Particularly, permutation polynomials with few terms are more popular for their simple algebraic form and additional extraordinary properties. Very recently, G. Kyureghyan and M.E. Zieve (2016) studied permutation polynomials over $$\mathbb {F}_{q^{n}}$$ of the form $$x+\gamma \text {Tr}_{q^{n}/q}(x^{k})$$ , where q is odd, and nine classes of permutation polynomials were constructed. In this paper, we present fifteen new classes of permutation polynomials of the form $$cx+\text {Tr}_{q^{l}/ q}(x^{a})$$ over finite fields with even characteristic, which explain most of the examples with q = 2 k , k > 1, k l < 14 and $$c\in \mathbb {F}_{q^{l}}^{*}$$ . Furthermore, we also construct four classes of permutation trinomials.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0236-7
Issue No: Vol. 10, No. 3 (2018)

• Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable
codes with length 3
• Authors: Xuli Zhang; Jing Jiang; Minquan Cheng
Pages: 555 - 565
Abstract: Separable code (SC, Cheng and Miao IEEE Trans. Inf. Theory 57, 4843–4851, 2011), frameproof code (FPC, Boneh and Shaw IEEE Trans. Inf. Theory 44, 1897–1905, 1998) and strongly separable code (SSC, Jiang et al. Des. Codes Cryptogr. 79:303–318, 2016) are used to construct anti-collusion codes. SSC is better than FPC and SC in the applications for multimedia fingerprinting since SSC has lower identifying complexity than that of SC (the same complexity as FPC) and weaker structure than that of FPC. In this paper, we first derive several upper bounds on the number of codewords of a $$\overline {t}$$ -SSC. Then we focus on $$\overline {3}$$ -SSCs with codeword length 3 and obtain the following two main results: (1) An equivalence between an SSC and an SC is derived; (2) An improved lower bound Ω(q 5/3 + q 4/3 − q) on the size of a q-ary SSC when $$q={q_{1}^{6}}$$ for any prime power q 1 ≡ 1 (mod 6), which is better than the previously known bound $$\lfloor \sqrt {q}\rfloor ^{3}$$ , is obtained by means of a difference matrix and a known result on the subsets of $$\mathbb {F}^{n}_{q}$$ containing no three points on a line.
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0235-8
Issue No: Vol. 10, No. 3 (2018)

• New results on permutation polynomials of the form ( x p m − x + δ ) s
+ x p m + x over ð”½ p 2m
• Authors: Zhengbang Zha; Lei Hu; Zhizheng Zhang
Pages: 567 - 578
Abstract: Permutation polynomials over finite fields have significant applications in coding theory, cryptography, combinatorial designs and many other areas of mathematics and engineering. In this paper, we study the permutation behavior of polynomials with the form $$(x^{p^{m}}-x+\delta )^{s}+x^{p^{m}}+x$$ over the finite field $$\mathbb {F}_{p^{2m}}$$ . By using the Akbary-Ghioca-Wang (AGW) criterion, we present several new classes of permutations over $$\mathbb {F}_{p^{2m}}$$ based on some bijections over the set $$\{t\in \mathbb {F}_{p^{2m}} t^{p^{m}}+t=0\}$$ or the subfield $$\mathbb {F}_{p^{m}}$$ .
PubDate: 2018-05-01
DOI: 10.1007/s12095-017-0234-9
Issue No: Vol. 10, No. 3 (2018)

• Modified planar functions and their components
• Authors: Nurdagül Anbar; Wilfried Meidl
Pages: 235 - 249
Abstract: Zhou (J. Combin. Des. 21(12), 563–584, 2013) introduced modified planar functions in order to describe (2 n , 2 n , 2 n , 1) relative difference sets R as a graph of a function on the finite field $$\mathbb {F}_{2^{n}}$$ , and pointed out that projections of R are difference sets that can be described by negabent or bent4 functions, which are Boolean functions given in multivariate form. One of the objectives of this paper is to contribute to the understanding of these component functions of modified planar functions. We identify the versions of the Walsh transforms that apply to modified planar functions on $$\mathbb {F}_{2^{n}}$$ and their components, obtain a description of modified planar functions by their components which is similar to that of the classical planar functions in odd characteristic as a vectorial bent function, and point out some further properties of these components. Finally we introduce vectorial bent4 functions (over finite fields), which correspond to relative difference sets in certain groups. We give conditions under which Maiorana-McFarland functions are such functions, hence give rise to relative difference sets in $$\mathbb {Z}_{2}^{n/2}\times \mathbb {Z}_{4}^{n/2}$$ .
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0218-9
Issue No: Vol. 10, No. 2 (2018)

• Construction of de Bruijn sequences from product of two irreducible
polynomials
• Authors: Zuling Chang; Martianus Frederic Ezerman; San Ling; Huaxiong Wang
Pages: 251 - 275
Abstract: We study a class of Linear Feedback Shift Registers (LFSRs) with characteristic polynomial f(x) = p(x)q(x) where p(x) and q(x) are distinct irreducible polynomials in ð”½2[x]. Important properties of the LFSRs, such as the cycle structure and the adjacency graph, are derived. A method to determine a state belonging to each cycle and a generic algorithm to find all conjugate pairs shared by any pair of cycles are given. The process explicitly determines the edges and their labels in the adjacency graph. The results are then combined with the cycle joining method to efficiently construct a new class of de Bruijn sequences. An estimate of the number of resulting sequences is given. In some cases, using cyclotomic numbers, we can determine the number exactly.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0219-8
Issue No: Vol. 10, No. 2 (2018)

• Classification and Construction of quaternary self-dual bent functions
• Authors: Lin Sok; MinJia Shi; Patrick Solé
Pages: 277 - 289
Abstract: Quaternary self-dual bent functions are studied from the viewpoints of existence, construction, and symmetry. A search algorithm is described to classify their orbits under the orthogonal group in low dimensions. A connection with self-dual bent Boolean functions shows that they do not exist in odd number of variables.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0216-y
Issue No: Vol. 10, No. 2 (2018)

• The weight distribution of a class of two-weight linear codes derived from
Kloosterman sums
• Authors: Pan Tan; Zhengchun Zhou; Deng Tang; Tor Helleseth
Pages: 291 - 299
Abstract: Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, a class of p-ary two-weight linear codes is constructed using a generic construction developed by Ding et al. recently, where p is a prime. Their length and weight distribution are closed-form expressions of Kloosterman sums over prime finite fields, and are completely determined when p = 2 and p = 3. The dual of this class of linear codes is also studied and is shown to be optimal or almost optimal in the binary case.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0221-1
Issue No: Vol. 10, No. 2 (2018)

• Binary linear codes with two or three weights from niho exponents
• Authors: Gaojun Luo; Xiwang Cao; Shanding Xu; Jiafu Mi
Pages: 301 - 318
Abstract: Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, date storage systems, strongly regular graphs and some other fields. In this paper, we present several classes of binary linear codes with two or three weights and study their weight distributions. Two classes of strongly regular graphs are constructed from binary linear codes with two weights. Numerical results show that some of the obtained codes are either optimal or near optimal with respect to certain bounds on linear codes.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0220-2
Issue No: Vol. 10, No. 2 (2018)

• A sequence construction of cyclic codes over finite fields
• Authors: Cunsheng Ding
Pages: 319 - 341
Abstract: Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer electronics, and data storage systems. There are several approaches to constructing all cyclic codes over finite fields, including the generator matrix approach, the generator polynomial approach, and the generating idempotent approach. Another one is a sequence approach, which has been intensively investigated in the past decade. The objective of this paper is to survey the progress in this direction in the past decade. Many open problems are also presented in this paper.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0222-0
Issue No: Vol. 10, No. 2 (2018)

• Quadratic residue codes over the ring ð”½ p [ u ] / 〈 u m − u
〉 $\mathbb {F}_{p}[u]/\langle u^{m}-u\rangle$ and their Gray images
• Authors: Mokshi Goyal; Madhu Raka
Pages: 343 - 355
Abstract: Let m ≥ 2 be any natural number and let $$\mathcal {R}=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^{2}\mathbb {F}_{p}+\cdots +u^{m-1}\mathbb {F}_{p}$$ be a finite non-chain ring, where u m = u and p is a prime congruent to 1 modulo (m − 1). In this paper we study quadratic residue codes over the ring $$\mathcal {R}$$ and their extensions. A Gray map from $$\mathcal {R}^{n}$$ to $$(\mathbb {F}_{p}^{m})^{n}$$ is defined which preserves self duality of linear codes. As a consequence, we construct self-dual, formally self-dual and self-orthogonal codes over $$\mathbb {F}_{p}$$ . To illustrate this, several examples of self-dual, self-orthogonal and formally self-dual codes are given. Among others a [9,3,6] linear code over $$\mathbb {F}_{7}$$ is constructed which is self-orthogonal as well as nearly MDS. The best known linear code with these parameters (ref. Magma) is not self-orthogonal.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0223-z
Issue No: Vol. 10, No. 2 (2018)

• Perfect sequences over the quaternions and (4 n , 2, 4 n , 2 n )-relative
difference sets in C n × Q 8
• Authors: Santiago Barrera Acevedo; Heiko Dietrich
Pages: 357 - 368
Abstract: Perfect sequences over general quaternions were introduced in 2009 by Kuznetsov. The existence of perfect sequences of increasing lengths over the basic quaternions Q 8 = {±1, ±i, ±j, ±k} was established in 2012 by Barrera Acevedo and Hall. The aim of this paper is to prove a 1–1 correspondence between perfect sequences of length n over Q 8 ∪ q Q 8 with q = (1 + i + j + k)/2, and (4n, 2, 4n, 2n)-relative difference sets in C n × Q 8 with forbidden subgroup C 2; here C m is a cyclic group of order m. We show that if n = p a + 1 for a prime p and integer a ≥ 0 with n ≡ 2 mod 4, then there exists a (4n, 2, 4n, 2n)-relative different set in C n × Q 8 with forbidden subgroup C 2. Lastly, we show that every perfect sequence of length n over Q 8 ∪ q Q 8 yields a Hadamard matrix of order 4n (and a quaternionic Hadamard matrix of order n over Q 8 ∪ q Q 8).
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0224-y
Issue No: Vol. 10, No. 2 (2018)

• Matrix parametrized shift registers
• Authors: Andrew Klapper
Pages: 369 - 382
Abstract: High speed pseudorandom sequence generators have played roles in an array of applications in communications, cryptography, and computing. At the heart of many of these generators are shift registers of various types. Researchers have studied linear feedback shift registers (LFSRs), feedback with carry shift registers (FCSRs), and various generalizations such as ring FCSRS and algebraic feedback shift registers. The analysis of these sequence generators typically proceeds by defining an algebraic structure on the set of infinite output sequences, based on a choice of uniformizing parameter (e.g., power series for LFSRs, N-adic numbers for FCSRs). In this paper we introduce a new generalization of FCSRs in which the uniformizing parameter $$N\in \mathbb {Z}$$ is replaced by a square matrix, T, resulting in what we call T-generators. We describe an algebraic structure, the T-adic numbers, and use it to study the periodicity of T-generators.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0226-9
Issue No: Vol. 10, No. 2 (2018)

• Message Authentication Based on Cryptographically Secure CRC without
Polynomial Irreducibility Test
• Authors: Elena Dubrova; Mats Näslund; Göran Selander; Fredrik Lindqvist
Pages: 383 - 399
Abstract: In this paper, we present a message authentication scheme based on cryptographically secure cyclic redundancy check (CRC). Similarly to previously proposed cryptographically secure CRCs, the presented one detects both random and malicious errors without increasing bandwidth. The main difference from previous approaches is that we use random instead of irreducible generator polynomials. This eliminates the need for irreducibility tests. We provide a detailed quantitative analysis of the achieved security as a function of message and CRC sizes. The results show that the presented scheme is particularly suitable for the authentication of short messages.
PubDate: 2018-03-01
DOI: 10.1007/s12095-017-0227-8
Issue No: Vol. 10, No. 2 (2018)

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