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A first Catalgorithm?

Geneste J.-F.

International Journal of Electronics and Telecommunications

2018

Vol. 64, No. 2

185--188

We propose building a new PKC in a ring structure, the classification of rings being an open problem. The difficulty of the scheme is based on retrieving the eigenvalues of endomorphism on a finite type module over a non-commutative ring. It is resistant to a chosen cipher text attack. Working in the fraction ring of a non-commutative ring makes our scheme a zero-knowledge proof of knowledge, result indistinguishable, in the Naor-Yung model. Finally, a dramatic improvement in security is obtained through the drawing with uniform probability of the working ring at high frequency.

Semihereditary rings and related topics

Gubareni N.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

33--38

A ring A is called right (left) semihereditary if all finitely generated right (left) ideals of A are projective. In this paper we consider non-commutative semihereditary rings and show their connection with non-commutative valuation rings. We also present some criterion for a module to be flat.