FOX is a family of block ciphers published in 2004 and is famous for its provable security to cryptanalysis. In this paper, we present multiple 4-round impossible differentials and several new results of impossible differential attacks on 5,6,7-round FOX64 and 5-round FOX128 with the multiple differentials and the new early abort technique which shall reduce the data complexity and the time complexity respectively. In terms of the data complexity and the time complexity, our results are better than any of the previously known attacks.

Let v=p1m1p2m2…ptmt be the canonical prime factorization of v. In this paper, we give a construction of optimal ((s+1)×v,s+1,1) two-dimensional optical orthogonal codes with both at most one-pulse per wavelength and at most one-pulse per time slot, where s | gcd(p1-1,p2-1,...,pt-1). The method is much simpler than that in [1]. Optimal (m×v,k,1) two-dimensional optical orthogonal codes are also constructed based on the Steiner system S[2,k,m].

In this paper, we construct ideal and probabilistic secret sharing schemes for some multipartite access structures, including the General Hierarchical Access Structure and Compartmented Access Structures. We devise an ideal scheme which implements the general hierarchical access structure. For the compartmented access structures, we consider three special access structures. We propose ideal and probabilistic schemes for these three compartmented access structures by bivariate interpolation.

Jacobi sequences have good cryptography properties. Li et al. [X. Li et al., Linear Complexity of a New Generalized Cyclotomic Sequence of Order Two of Length pq*, IEICE Trans. Fundamentals, vol.E96-A, no.5, pp.1001-1005, 2013] defined a new modified Jacobi sequence of order two and got its linear complexity. In this corresponding, we determine the linear complexity and minimal polynomials of the new modified Jacobi sequence of order d. Our results show that the sequence is good from the viewpoint of linear complexity.

Recent research has shown that the class of rotation symmetric Boolean functions is beneficial to cryptographics. In this paper, for an odd prime p, two sufficient conditions for p-variable rotation symmetric Boolean functions to be 1-resilient are obtained, and then several concrete constructions satisfying the conditions are presented. This is the first time that resilient rotation symmetric Boolean functions have been systematically constructed. In particular, we construct a class of 2-resilient rotation symmetric Boolean functions when p=2m+1 for m ≥ 4. Moreover, several classes of 1-order correlation immune rotation symmetric Boolean functions are also got.

Recently the word-based stream ciphers have been the subject of a considerable amount of research. The theory of such stream ciphers requires the study of the complexity of a multisequence. Let S1, S2, . . . , Sm be m N-ary sequences of period T, i.e., a multisequence. The relationship between the joint N-adic complexity and the number of the nonzero columns of the generalized Fourier transform for the N-ary multisequence is determined which generalizes the well-known result about the joint linear complexity and the generalized Fourier transform for a multisequence to the case of the joint N-adic complexity.

In this paper, we consider the Reed-Solomon codes over Fqm with evaluations in a subfield Fq. By the “virtual extension”, we can embed these codes into homogeneous interleaved Reed-Solomon codes. Based on this property and the collaborative decoding algorithm, a new probabilistic decoding algorithm that can correct errors up to $rac{m}{m+1}(n-k)$ for these codes is proposed. We show that whether the new decoding algorithm fails or not is only dependent on the error. We also give an upper bound on the failure probability of the new decoding algorithm for the case s=2. The new decoding algorithm has some advantages over some known decoding algorithms.

Linear codes with locality r and availability t have a wide application in distribution storage because they permit local repair and parallel accesses of hot data. In this letter, the locality and availability of some linear codes based on finite geometry are given. According to these results, we give some linear codes that have higher rate than known codes with the same locality and availability.

In distributed storage systems, codes with lower repair locality are much more desirable due to their superiority in reducing the disk I/O complexity of each repair process. Motivated partially by both codes with information (r,δ1)c locality and codes with cooperative (r,l) locality, we propose the concept of codes with information (r,l,δ) locality in this paper. For a linear code C with information (r,l,δ) locality, values at arbitrary l information coordinates of an information set I can be recovered by connecting any of δ existing pairwise disjoint local repair sets with size no more than r, where a local repair set of l coordinates is defined as the set of some other coordinates by which one can recover the values at these l coordinates. We derive a lower bound on the codeword length n for [n,k,d] linear codes with information (r,l,δ) locality. Furthermore, we indicate its tightness for some special cases. Particularly, some existing results can be deduced from our bound by restriction on parameters.

In network coding, for the case that the network topology is unknown completely, random linear network coding has been proposed as an acceptable coding technique. In this paper, we define average failure probability of random linear network coding in order to characterize the performance of random network coding, and then analyze this failure probability for different known topological information of network. We obtain several upper bounds on the failure probabilities, and further show that, for some networks, these upper bounds are tight or asymptotically tight. Moreover, if the more topological information of the network is utilized, the better upper bounds are acquired.

In this paper, the linear complexity and minimal polynomials of Legendre sequences over Fq have been calculated, where q = pm and p is a prime number. Our results show that Legendre sequences have high linear complexity over Fq for a large part of prime power number q so that they can resist the linear attack method.

In the paradigm of network coding, when the network topology information cannot be utilized completely, random linear network coding (RLNC) is proposed as a feasible coding scheme. But since RLNC neither considers the global network topology nor coordinates codings between different nodes, it may not achieve the best possible performance of network coding. Hence, the performance analysis of RLNC is very important for both theoretical research and practical applications. Motivated by a fact that different network topology information can be available for different network communication problems, we study and obtain several upper and lower bounds on the failure probability at sink nodes depending on different network topology information in this paper, which is also the kernel to discuss some other types of network failure probabilities. In addition, we show that the obtained upper bounds are tight, the obtained lower bound is asymptotically tight, and we give the worst cases for different scenarios.

In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.