Construction of resilient Boolean functions in odd variables having strictly almost optimal (SAO) nonlinearity appears to be a rather difficult task in stream cipher and coding theory. In this paper, based on the modified High-Meets-Low technique, a general construction to obtain odd-variable SAO resilient Boolean functions without directly using PW functions or KY functions is presented. It is shown that the new class of functions possess higher resiliency order than the known functions while keeping higher SAO nonlinearity, and in addition the resiliency order increases rapidly with the variable number n.

Linear complexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-error linear complexity of p-ary sequences with period pn. For p-ary sequences of period pn with linear complexity pn-p+1, n≥1, we present all possible values of the p-error linear complexity, and derive the exact formulas to count the number of the sequences with any given p-error linear complexity.

Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.

The differential fault analysis of SOSEMNAUK was presented in Africacrypt in 2011. In this paper, we improve previous work with algebraic techniques which can result in a considerable reduction not only in the number of fault injections but also in time complexity. First, we propose an enhanced method to determine the fault position with a success rate up to 99% based on the single-word fault model. Then, instead of following the design of SOSEMANUK at word levels, we view SOSEMANUK at bit levels during the fault analysis and calculate most components of SOSEMANUK as bit-oriented. We show how to build algebraic equations for SOSEMANUK and how to represent the injected faults in bit-level. Finally, an SAT solver is exploited to solve the combined equations to recover the secret inner state. The results of simulations on a PC show that the full 384 bits initial inner state of SOSEMANUK can be recovered with only 15 fault injections in 3.97h.

In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.

Recently nonlinear feedback shift registers (NFSRs) have frequently been used as basic building blocks for stream ciphers. A major problem concerning NFSRs is to construct NFSRs which generate de Bruijn sequences, namely maximum period sequences. In this paper, we present a new necessary condition for NFSRs to generate de Bruijn sequences. The new condition can not be deduced from the previously proposed necessary conditions. It is shown that the number of NFSRs whose feedback functions satisfy all the previous necessary conditions but not the new one is very large.

In this letter, we first introduce a new generalized cyclotomic sequence of order two of length pq, then we calculate its linear complexity and minimal polynomial. Our results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for use in stream cipher cryptosystems.

Based on Tu-Deng's conjecture and the Tu-Deng function, in 2010, X. Tang et al. proposed a class of Boolean functions in even variables with optimal algebraic degree, very high nonlinearity and optimal algebraic immunity. In this corresponding, we consider the concatenation of Tang's function and another Boolean function, and study its cryptographic properties. With this idea, we propose a class of 1-resilient Boolean functions in odd variables with optimal algebraic degree, good nonlinearity and suboptimal algebraic immunity based on Tu-Deng's conjecture.

Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums. A lower bound on the linear complexity profile is also presented in terms of the correlation measure.

This paper contributes to a new generalized cyclotomic sequences of order two with respect to p1e1p2e2… ptet. The emphasis is on the linear complexity and autocorrelation of new prime-square sequences and two-prime sequences, two special cases of these generalized cyclotomic sequences. Our method is based on their characteristic polynomials. Results show that these sequences possess good linear complexity. Under certain conditions, the autocorrelation functions of new prime-square sequences and two-prime sequences may be three-valued.

The linear complexity and its stability of periodic sequences are of fundamental importance as measure indexes on the security of stream ciphers and the k-error linear complexity reveals the stability of the linear complexity properly. The k-error linear complexity of periodic sequences is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. For 2pn-periodic binary sequences, where p is an odd prime and 2 is a primitive root modulo p2, we present and prove the unique expression of the linear complexity. Moreover we show a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.

In their paper, G. Gong and S.Q. Jiang construct a new pseudo-random sequence generator by using two ternary linear feedback shift registers (LFSR). The new generator is called an editing generator which a combined model of the clock-controlled generator and the shrinking generator. For a special case (Both the base sequence and the control sequence are mm-sequence of degree n), the period, linear complexity, symbol distribution and security analysis are discussed in the same article. In this paper, we expand the randomness results of the edited sequence for general cases, we do not restrict the base sequence and the control sequence has the same length. For four special cases of this generator, the randomness of the edited sequence is discussed in detail. It is shown that for all four cases the editing generator has good properties, such as large periods, high linear complexities, large ratio of linear complexity per symbol, and small un-bias of occurrences of symbol. All these properties make it necessary to resist to the attack from the application of Berlekamp-Massey algorithm.