Efficient zero — Knowledge identification based on one way Boolean transformations

An innovative method for formulating non-linear, one-way Boolean transformations is presented. These transformations are used at the core of an efficient implementation of the theoretically strict concept of zero knowledge identification of users. This implementation uses one-way non-linear Boolean transformations instead of operations on large numbers as a means of reducing the computational overheads related to user authentication for legitimate users and computational systems, without compromising system security. The principles, related to user identification and authentication using Boolean functions, are first presented. The necessary properties of the Boolean functions required are hence determined. A procedure for formulating non-linear one-way Boolean transformations, suitable for use in the context of user identification and authentication is presented. The procedure is iterative and scalable. The steps comprising the procedure are analytically presented. A numerical example of the calculations involved is also given. The computational effort required for formulating one such function of average complexity that is suitable for a large variety of applications, is approximated analytically. The results of statistical experiments verifying the validity of the approximation are also presented. These calculations demonstrate that the proposed method can be feasibly applied, even the only available computational capability is derived from an ordinary personal computer.