A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions

Cryptographic algorithms and functions should possess some of the important functional requirements such as: non-linearity, resiliency, propagation and immunity. Several previous studies were executed to analyze these characteristics of the cryptographic functions specifically for Boolean and symmetric functions. Randomness is a requirement in present cryptographic algorithms and therefore, Symmetric Random Function Generator (SRFG) has been developed. In this paper, we have analysed SRFG based on propagation feature and immunity. Moreover, NIST recommended statistical suite has been tested on SRFG outputs. The test values show that SRFG possess some of the useful randomness properties for cryptographic applications such as individual frequency in a sequence and block-based frequency, long run of sequences, oscillations from 0 to 1 or vice-versa, patterns of bits, gap bits between two patterns, and overlapping block bits. We also analyze the comparison of SRFG and some existing random number generators. We observe that SRFG is efficient for cryptographic operations in terms of propagation and immunity features

Equivalence classes of Boolean functions for first-order correlation

International audienceThis paper presents a complete characterization of the first order correlation immune Boolean functions that includes the functions that are 1-resilient. The approach consists in defining an equivalence relation on the full set of Boolean functions with a fixed number of variables. An equivalence class in this relation, called a first-order correlation class, provides a measure of the distance between the Boolean functions it contains and the correlation-immune Boolean functions. The key idea consists on manipulating only the equivalence classes instead of the set of Boolean functions. To achieve this goal, a class operator is introduced to construct a class with n variables from two classes of n - 1 variables. In particular, the class of 1-resilient functions on n variables is considered. An original and efficient method to enumerate all the Boolean functions in this class is proposed by performing a recursive decomposition of classes with less variables. A bottom up algorithm provides the exact number of 1-resilient Boolean functions with seven variables which is 23478015754788854439497622689296. A tight estimation of the number of 1-resilient functions with eight variables is obtained by performing a partial enumeration. It is conjectured that the exact complete enumeration for general n is intractabl