Heuristic search of (semi-)bent functions based on cellular automata

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter

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

Algorithm 959: VBF: A Library of C plus plus Classes for Vector Boolean Functions in Cryptography

VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This implementation uses the NTL library from Victor Shoup, adding new modules that call NTL functions and complement the existing ones, making it better suited to cryptography. The class representing a vector Boolean function can be initialized by several alternative types of data structures such as Truth Table, Trace Representation, and Algebraic Normal Form (ANF), among others. The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity, linearity distance, algebraic degree, linear structures, and frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions are presented. Finally, three real applications of the library are described: the first one analyzes the KASUMI block cipher, the second one analyzes the Mini-AES cipher, and the third one finds Boolean functions with very high nonlinearity, a key property for robustness against linear attacks