6 research outputs found
A Carlitz type result for linearized polynomials
For an arbitrary -polynomial over we study the
problem of finding those -polynomials over for which
the image sets of and coincide. For we provide
sufficient and necessary conditions and then apply our result to study maximum
scattered linear sets of
A Carlitz type result for linearized polynomials
For an arbitrary q-polynomial f over GF(q^n) we study the problem of finding those q-polynomials g over GF(q^n) for which the image sets of f(x)/x and g(x)/x coincide. For n < 6 we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of PG(1,q^5)
Mathematical aspects of the design and security of block ciphers
Block ciphers constitute a major part of modern symmetric cryptography. A mathematical analysis is necessary to ensure the security of the cipher. In this thesis, I develop several new contributions for the analysis of block ciphers. I determine cryptographic properties of several special cryptographically interesting mappings like almost perfect nonlinear functions. I also give some new results both on the resistance of functions against differential-linear attacks as well as on the efficiency of implementation of certain block ciphers