Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any $m$, one can construct infinitely many $n$-variable ($n$ even), $m$-resilient functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.Comment: 14 pages, 2 table

Construction of Highly Nonlinear Resilient Boolean Functions Satisfying Strict Avalanche Criterion

A method is proposed to construct resilient Boolean functions on $n$ variables ($n$ even) satisfying strict avalanche criterion (SAC) with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of cryptographic Boolean functions which were not known earlier are obtained

On the Randomness of the Editing Generator

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 a suitable crypto-generator for stream cipher applications

Forgery Attacks on Chang et al.\u27s signature scheme with message recovery

It is found that Chang et al.\u27s signature scheme with message recovery is not as secure as they claimed, in fact. In this letter, two forgery attacks is proposed to show that the signature can be forged on any uncontrolled messages. To overcome these attacks, the one-way hash functions and the message redundancy schemes may be still used

Divisible difference sets, relative difference sets and sequences with ideal autocorrelation

In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets. This paper proves that, for a p-ary sequence with d-form property, the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p - 1 relative difference sets. Moreover, a new way to construct cyclic divisible difference sets is presented. (C) 2013 Elsevier Inc. All rights reserved.In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets. This paper proves that, for a p-ary sequence with d-form property, the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p - 1 relative difference sets. Moreover, a new way to construct cyclic divisible difference sets is presented. (C) 2013 Elsevier Inc. All rights reserved