Quasigroup transformations and their cryptographic potentials

Ass. Prof. Danilo Gligoroski


Abstract
In the present era of global communications, any serious modern battery of cryptographic modules, that will enable secure communication, among other algorithms, must include a block cipher, preferably a stream cipher, collision free hash function and cryptographically strong nonlinear pseudo random number generator. The state of the art algorithms for above mentioned cryptographic computations, usually (or almost exclusively) use bitwise operations and shifting registers, as a fastest approach, and differ between each other significantly. Usually, when computing security level have to be raised on higher level, then complete redesign of the algorithms is needed.

In this talk I will speak about a quasigroup transformations on strings and their potentials to be used in cryptography. The talk is a summary of our research that I have done for several years in Institute of Informatics at Faculty of Natural Sc. in Skopje together with two other researchers: Prof. S. Markovski and Ass. Prof. V. Bakeva. We think that some of the problems in design and redesign of cryptographic algorithms can be overcome by quasigroup transformations.

To show that, we have developed several cryptographic algorithms: a block cipher, a stream cipher, a hash function with variable length of output that is strongly collision free and a nonlinear pseudo random number generator. All those algorithms are developed using only several programming primitives based on quasigroup string transformations, the algorithms are reconfigurable from the point of view of used quasigroups, they are flexible on the length of blocks that are encoded and on the length of the password, and they can be successfully implemented both in embedded systems as well as in big security programming modules. All algorithms that I will describe in my talk can be efficiently parallelized and that can make them competitive with other algorithms in their category. The algoritms for quasigroup transformations that we propose, have another interesting property. Namely, examining the randomness of different PRNGs, we noticed that those PRNGs that fell on some tests of randomness, can be simply and effectively improved, and then pass the tests, just by transforming the output of the PRNG by a quasigroup transformation. So, the quasigroup transformations can be used as PRNGs improvers, but also they can be used as randomness improvers of so called "pour sources of randomness". Finally, in this talk I will discuss the possibilities for building the hierarchies of trusted and secure levels ofcommunications by using embedded quasigroups.

Web link for more details: http://www.pmf.ukim.edu.mk/~danilo/ResearchPapers/Crypto/