A Simple Computational Model for Acceptance/Rejection of Binary Sequence Generators

A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic operations. The proposed model can serve as a deterministic alternative to existing probabilistic methods for checking balancedness in binary sequence generators. The procedure here described can be devised as a first selective criterium for acceptance/rejection of this type of generators.Comment: 16 pages, 0 figure

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time

Nonlinearity and propagation characteristics of balanced boolean functions

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable by any previously known construction method. We also present methods for constructing balanced Boolean functions that are highly nonlinear and satisfy the strict avalanche criterion (SAC). Furthermore we present methods for constructing highly nonlinear balanced Boolean functions satisfying the propagation criterion with respect to all but one or three vectors. A technique is developed to transform the vectors where the propagation criterion is not satisfied in such a way that the functions constructed satisfy the propagation criterion of high degree while preserving the balancedness and nonlinearity of the functions. The algebraic degrees of functions constructed are also discussed, together with examples illustrating the various constructions

Rotation symmetric Boolean functions---count and cryptographic properties

The article of record as published may be located at http://dx.doi.org/10.1.1.137.6388Rotation symmetric (RotS) Boolean functions have been used as components of different cryptosystems. This class of Boolean functions are invariant under circular translation of indices. Using Burnsideﾒs lemma it can be seen that the number of n-variable rotation symmetric Boolean functions is 2gn, where gn = 1 nPt|n (t) 2n t , and (.) is the Euler phi-function. In this paper, we find the number of short and long cycles of elements in Fn2 having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier

Strengthening Crypto-1 Cipher Against Algebraic Attacks

In the last few years, several studies addressed the problem of data security in Mifare Classic. One of its weaknesses is the low random number quality. This causes SAT solver attacks to have lower complexity. In order to strengthen Crypto-1 against SAT solver attacks, a modification of the feedback function with better cryptographic properties is proposed. It applies a primitive polynomial companion matrix. SAT solvers cannot directly attack the feedback shift register that uses the modified Boolean feedback function, the register has to be split into smaller groups. Experimental testing showed that the amount of memory and CPU time needed were highest when attacking the modified Crypto-1 using the modified feedback function and the original filter function. In addition, another modified Crypto-1, using the modified feedback function and a modified filter function, had the lowest percentage of revealed variables. It can be concluded that the security strength and performance of the modified Crypto-1 using the modified feedback function and the modified filter function are better than those of the original Crypto-1

Four Neighbourhood Cellular Automata as Better Cryptographic Primitives

Three-neighbourhood Cellular Automata (CA) are widely studied and accepted as suitable cryptographic primitive. Rule 30, a 3-neighbourhood CA rule, was proposed as an ideal candidate for cryptographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack. The cryptographic properties like diffusion and randomness increase with increase in neighbourhood radius and thus opens the avenue of exploring the cryptographic properties of 4-neighbourhood CA. This work explores whether four-neighbourhood CA can be a better cryptographic primitive. We construct a class of cryptographically suitable 4-neighbourhood nonlinear CA rules that resembles rule 30. One 4-neighbourhood nonlinear CA from this selected class is shown to be resistant against Meier-Staffelbach attack on rule 30, justifying the applicability of 4-neighbourhood CA as better cryptographic primitives