Galois rings and algebraic cryptography
Generating quasigroups for cryptographic applications
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...
GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application...