Authors:Xianfang Wang; Jian Gao; Fang-Wei Fu Pages: 545 - 562 Abstract: In this paper, we give the complete weight enumerators of two classes of linear codes over the finite field \(\mathbb {F}_{p}\) , where p is a prime. These linear codes are the torsion codes of MacDonald codes over the finite non-chain ring \(\mathbb {F}_{p}+v\mathbb {F}_{p}\) , where v 2 = v. We also employ these linear codes to construct systematic authentication codes with new parameters. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0198-1 Issue No:Vol. 9, No. 5 (2017)

Authors:Shuai Xue; Wen-Feng Qi; Xiao-Yuan Yang Pages: 563 - 580 Abstract: In this paper, the best linear approximations of addition modulo 2 n are studied. Let x = (x n−1, x n−2,…,x 0) and y = (y n−1, y n−2,…,y 0) be any two n-bit integers, and let z = x + y (mod 2 n ). Firstly, all the correlations of a single bit z i approximated by x j ’s and y j ’s (0 ≤ i, j ≤ n − 1) are characterized, and similar results are obtained for the linear approximation of the xoring of the neighboring bits of z i ’s. Then the maximum correlations and the best linear approximations are presented when these z j ’s (0 ≤ j ≤ n − 1) are xored in any given means. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0203-8 Issue No:Vol. 9, No. 5 (2017)

Authors:Thalia M. Laing; Keith M. Martin; Maura B. Paterson; Douglas R. Stinson Pages: 581 - 597 Abstract: A localised multisecret sharing scheme is a multisecret sharing scheme for an ordered set of players in which players in the smallest sets who are authorised to access secrets are close together in the underlying ordering. We define threshold versions of localised multisecret sharing schemes, we provide lower bounds on the share size of perfect localised multisecret sharing schemes in an information theoretic setting, and we give explicit constructions of schemes to show that these bounds are tight. We then analyse a range of approaches to relaxing the model that provide trade-offs between the share size and the level of security guarantees provided by the scheme, in order to permit the construction of schemes with smaller shares. We show how these techniques can be used in the context of an application to key distribution for RFID-based supply-chain management motivated by the proposal of Juels, Pappu and Parno from USENIX 2008. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0202-9 Issue No:Vol. 9, No. 5 (2017)

Authors:Yuan Cao; Qingguo Li Pages: 599 - 624 Abstract: Let \(R=\mathbb{Z}_{4}[u]/ \langle u^k \rangle=\mathbb{Z}_{4}+u \mathbb{Z}_{4}+\ldots+u^{k-1}\mathbb{Z}_{4}\) ( \(u^{k}=0\) ), where k ≥ 2 is an positive integer. For any odd positive integer n, it is known that cyclic codes of length n over R are identified with ideals of the ring \(R[x]/\langle x^{n}-1\rangle\) . In this paper, an explicit representation for each cyclic code over R of length n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes of length n over R is obtained. Precisely, the dual code of each cyclic code and self-dual cyclic codes of length n over R are investigated. As an application, some good quasi-cyclic codes of length 7k and index k over ℤ4 are obtained from cyclic codes over R = ℤ4 [u] / 〈u k 〉 when k = 2, 3, 4. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0204-7 Issue No:Vol. 9, No. 5 (2017)

Authors:Xianfang Wang; Can Xiang; Fang-Wei Fu Pages: 625 - 635 Abstract: In this paper, we devise ideal and probabilistic secret sharing schemes for two kinds of compartmented access structures. The first one is a compartmented access structures with hierarchical compartments. The second one is the compartmented access structures with strictly lower bounds. We propose ideal and probabilistic schemes for these two compartmented access structures by using the idea of bivariate interpolation. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0205-6 Issue No:Vol. 9, No. 5 (2017)

Authors:Minjia Shi; Rongsheng Wu; Yan Liu; Patrick Solé Pages: 637 - 646 Abstract: We construct an infinite family of three-Lee-weight codes of dimension 2m, where m is singly-even, over the ring \(\mathbb {F}_{p}+u\mathbb {F}_{p}\) with u 2=0. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain an infinite family of abelian p-ary three-weight codes. When m is odd, and p≡3 (mod 4), we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. An application to secret sharing schemes is given. PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0206-5 Issue No:Vol. 9, No. 5 (2017)

Authors:Chunming Tang; Yanfeng Qi Pages: 647 - 664 Abstract: This paper is devoted to the characterization of hyper-bent functions. Several classes of hyper-bent functions have been studied, such as Charpin and Gong’s family \(\sum \limits _{r\in R}\text {Tr}_{1}^{n} (a_{r}x^{r(2^{m}-1)})\) and Mesnager’s family \(\sum \limits _{r\in R}\text {Tr}_{1}^{n}(a_{r}x^{r(2^{m}-1)}) +\text {Tr}_{1}^{2}(bx^{\frac {2^{n}-1}{3}})\) . In this paper, we generalize these results by considering the following class of Boolean functions over \(\mathbb {F}_{2^{n}}\) : $$\sum\limits_{r\in R}\sum\limits_{i=0}^{2}T{r^{n}_{1}}(a_{r,i} x^{r(2^{m}-1)+\frac{2^{n}-1}{3}i}) +T{r^{2}_{1}}(bx^{\frac{2^{n}-1}{3}}), $$ where \(n=2m\) , m is odd, \(b\in \mathbb {F}_{4}\) , and \(a_{r,i}\in \mathbb {F}_{2^{n}}\) . With the restriction of \(a_{r,i}\in \mathbb {F}_{2^{m}}\) , we present a characterization of hyper-bentness of these functions in terms of crucial exponential sums. For some special cases, we provide explicit characterizations for some hyper-bent functions in terms of Kloosterman sums and cubic sums. Finally, we explain how our results on binomial, trinomial and quadrinomial hyper-bent functions can be generalized to the general case where the coefficients \(a_{r,i}\) belong to the whole field \(\mathbb {F}_{2^{n}}\) . PubDate: 2017-09-01 DOI: 10.1007/s12095-016-0207-4 Issue No:Vol. 9, No. 5 (2017)

Authors:Zhiqiang Lin; Dongdai Lin; Dingyi Pei Pages: 431 - 443 Abstract: Linear Feedback Shift Registers (LFSRs) and Feedback with Carry Shift Registers (FCSRs) are two pseudo-random generators which are widely used in many cryptographic applications. The Ring representation of them has been proposed using a matrix approach. In this paper, we show how to construct Ring LFSRs and Ring FCSRs with low diffusion delay (close to the expected value \(\sqrt {n}\) ) when considering other hardware cryptographic criteria. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0183-8 Issue No:Vol. 9, No. 4 (2017)

Authors:Zhixiong Chen Pages: 445 - 458 Abstract: We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0185-6 Issue No:Vol. 9, No. 4 (2017)

Authors:Madhu Raka; Leetika Kathuria; Mokshi Goyal Pages: 459 - 473 Abstract: Let \(\mathcal {R}=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^{2}\mathbb {F}_{p}+u^{3}\mathbb {F}_{p}\) with u 4 = u be a finite non-chain ring, where p is a prime congruent to 1 modulo 3. In this paper we study (1−2u 3)-constacyclic codes over the ring \(\mathcal {R}\) , their equivalence to cyclic codes and find their Gray images. To illustrate this, examples of (1−2u 3)-constacyclic codes of lengths 2 m for p = 7 and of lengths 3 m for p = 19 are given. We also discuss quadratic residue codes over the ring \(\mathcal {R}\) and their extensions. A Gray map from \(\mathcal {R}\) to \(\mathbb {F}_{p}^{4}\) is defined which preserves self duality and gives self-dual and formally self-dual codes over \(\mathbb {F}_{p}\) from extended quadratic residue codes. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0184-7 Issue No:Vol. 9, No. 4 (2017)

Authors:Pramod Kumar Kewat; Priti Kumari Pages: 475 - 499 Abstract: Let \(n_{1}=df+1\) and \(n_{2}=df^{\prime }+1\) be two distinct odd primes with positive integers \(d,\ f,\ f^{\prime }\) and \(\gcd (f,f^{\prime })=1\) . In this paper, we compute the linear complexity and the minimal polynomial of the two-prime Whiteman’s generalized cyclotomic sequence of order \(d=6\) over \(\text {GF}(q)\) , where \(q=p^{m}\) and p is an odd prime and m is an integer. We employ this sequence of order 6 to construct several classes of cyclic codes over \(\text {GF}(q)\) with length \(n_{1}n_{2}\) . We also obtain lower bounds on the minimum distance of these cyclic codes. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0191-8 Issue No:Vol. 9, No. 4 (2017)

Authors:László Mérai; Harald Niederreiter; Arne Winterhof Pages: 501 - 509 Abstract: The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo p. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0189-2 Issue No:Vol. 9, No. 4 (2017)

Authors:Hongyu Han; Daiyuan Peng; Udaya Parampalli Pages: 511 - 522 Abstract: In quasi-synchronous frequency-hopping multiple-access systems where relative delays are restricted within a certain correlation zone, low-hit-zone frequency-hopping sequences (LHZ-FHSs) are commonly employed to minimize multiple-access interferences. In this paper, we present two classes of optimal LHZ-FHS sets with respect to the Peng-Fan-Lee bound, which are obtained from an m-sequence and its decimated sequence, respectively. The parameters of these LHZ-FHS sets are new and flexible. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0192-7 Issue No:Vol. 9, No. 4 (2017)

Authors:Santanu Sarkar; Prakash Dey; Avishek Adhikari; Subhamoy Maitra Pages: 523 - 543 Abstract: Differential Fault Attack (DFA) considers injection of faults and the most general set-up should take care of faults at random location and random time. Then one should be able to identify the exact location as well as the exact timing of the fault (including the multi bit ones) with the help of fault signatures. In this paper we solve the problem of DFA under a general frame-work, introducing the idea of probabilistic signatures. The method considers the Maximum Likelihood approach related to probability distributions. Our techniques subsume all the existing DFAs against the Grain family, MICKEY 2.0 and Trivium. In the process we provide improved fault attacks for all the versions of Grain family and also for MICKEY 2.0. Our generalized method successfully takes care of the cases where certain parts of the keystream bits are missing (this situation may arise for authentication purpose). In particular, we show that the unsolved problem of identifying the faults in random time for Grain 128a can be solved in this manner. Moreover, for MICKEY 2.0, our method not only provides improvement in fault identification probability but also reduces the required faults by 60 %, compared to the best known result. PubDate: 2017-07-01 DOI: 10.1007/s12095-016-0197-2 Issue No:Vol. 9, No. 4 (2017)

Authors:Amit Jana; Goutam Paul 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: 2017-06-09 DOI: 10.1007/s12095-017-0231-z

Authors:Yuhua Sun; Qiang Wang; Tongjiang Yan 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: 2017-06-08 DOI: 10.1007/s12095-017-0233-x

Authors:Geong Sen Poh; Moesfa Soeheila Mohamad; Ji-Jian Chin Abstract: Searchable Symmetric Encryption (SSE) allows a user to store encrypted documents on server(s) and later efficiently searches these documents in a private manner. So far most existing works have focused on a single storage server. Therefore in this paper we consider the natural extension of SSE to multiple servers. We believe it is of practical interest, given that a user may choose to distribute documents to various cloud storage that are now readily available. The main benefit compared to a single server scheme is that a server can be set to hold only subset of encrypted documents/blocks. A server learns only content of documents/blocks that it stores in the event of successful leakage attack or ciphertext cryptanalysis, provided servers do not collude. We define formally an extension of single server SSE to multiserver and instantiate provably secure schemes that provide the above feature. Our main scheme hides total number of documents and document size even after retrieval, achieving less leakages compared to prior work, while maintaining sublinear search time for each server. We further study leakages under the new setting of non-colluding and colluding servers. PubDate: 2017-06-07 DOI: 10.1007/s12095-017-0232-y

Authors:Li-Ping Wang; Daqing Wan 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: 2017-05-29 DOI: 10.1007/s12095-017-0230-0

Authors:Shanding Xu; Xiwang Cao; Guangkui Xu; Gaojun Luo 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: 2017-05-22 DOI: 10.1007/s12095-017-0229-6

Authors:Anuradha Sharma; Taranjot Kaur 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: 2017-05-17 DOI: 10.1007/s12095-017-0228-7