Год выпуска: 2010 Автор: Andreas Helde Издательство: LAP Lambert Academic Publishing Страниц: 68 ISBN: 9783838329970
Описание
We present the noncommutative version of the Polly Cracker cryptosystem, which is more promising than the commutative version. This is partly because many of the ideals in a free (noncommutative) algebra have an infinite Grobner basis, which can be used as the public key in the cryptosystem. We start with a short brief of the commutative case, which are stated to not provide sufficient security. Further, we see that it is hard to prove that noncommutative ideals have an infinite reduced Grobner basis for all admissible orders. Nevertheless, in chapter 4 we consider some ideals for which it seems infeasible to realize a finite Grobner basis. These are considered further in a cryptographic setting, and there will be shown that one class of ideals seems more promising than the others with respect to encountering attacks on the cryptosystem. In fact, at the end of this thesis we are proposing a way of constructing a cryptosystem based on this class of ideals, such that any linear algebra...
