29 research outputs found
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
On values of the Bessel function for generic representations of finite general linear groups
We find a recursive expression for the Bessel function of S. I. Gelfand for
irreducible generic representations of
. We show that special values of
the Bessel function can be realized as the coefficients of -functions
associated with exotic Kloosterman sums, and as traces of exterior powers of
Katz's exotic Kloosterman sheaves. As an application, we show that certain
polynomials, having special values of the Bessel function as their
coefficients, have all of their roots lying on the unit circle. As another
application, we show that special values of the Bessel function of the Shintani
base change of an irreducible generic representation are related to special
values of the Bessel function of the representation through Dickson
polynomials.Comment: 36 pages. Comments are welcom