Abstract:
In conventional cryptography, Boolean functions play a major role in the construction of symmetric key primitives such as block ciphers and stream ciphers. Various criteria, including balancedness, nonlinearity, autocorrelation, algebraic degree and algebraic immunity are used for measuring the cryptographic strength of Boolean function. Block and stream ciphers are made from Boolean functions that usually require a compromise between several conflicting cryptographic criteria. This dissertation work focuses on study of various properties of Boolean functions and construction of Boolean function by. heuristic approach with 'a compromise between several conflicting cryptographic criteria (nonlinearity, autocorrelation, algebraic immunity).
A Boolean function, when used in cryptosystems, should be designed properly to resist algebraic attacks. Algebraic Immunity is a measure of the capability of a Boolean function to withstand algebraic attacks. So far, the Boolean functions were designed keeping in mind the other cryptographic criteria, and then it has been checked whether it can provide good algebraic immunity too. In this dissertation, algebraic immunity has chosen as one of the criterion along with nonlinearity and autocorrelation for search and
Boolean functions with highest possible algebraic immunity of [n2] have been constructed.
Results with optimum tradeoff among properties like nonlinearity, algebraic, degree, algebraic immunity and autocorrelation have been obtained, that remained as an open problem. For the first time, Boolean function of 5' variables with nonlinearity of 12, autocorrelation value 8, algebraic immunity 3 and algebraic degree 3 has been constructed.
