A Resilient Functions For Stream Cipher Applications: Modified Tarrannikov’s Construction And Analysis Of Their Algebraic Immunity

Boolean functions with good cryptographic properties (high algebraic degree, balancedness, high order of correlation immunity and high nonlinearity) have an important significance in stream cipher (combiner model or filter model) since these functions allow to construct stream cipher resistant to various attacks. In this work the modified Tarannikov’s construction method is considered. This construction permits to obtain functions achieving all necessary criteria for being used in the pseudorandom generators in stream ciphers. Thus, this allows constructing recursively the resilient function achieving Siegenthaler’s bound and Sarkar, et al.’s bound using a resilient function in a smaller number of variables. Finally, we used the modified Tarannikov’s construction for designing keystream generators for digital images encryption.