KTH/SU Mathematics Colloquium
05-11-23
Joachim Rosenthal, University of Zürich
Building Public Key Crypto-Systems from Semi-Rings
Cryptography has a long history and its main objective is the
transmission of data between two parties in a way which
guarantees the privacy of the information. There are other
interesting applications such as digital signatures, the problem
of authentication and the concept of digital cash to name a few.
The proliferation of computer networks resulted in a large demand
for cryptography from the private sector.
A basic building block in public key cryptography are the one-way
trapdoor functions. These are one-one functions which can be
efficiently computed. The inverse function can however only be
computed if some additional trapdoor is known. The best known
one-way trapdoor function is the RSA function whose difficulty of
inverting is related to the difficulty of factoring. Other
one-way trapdoor functions use the arithmetic of elliptic curves
and more general abelian varieties,
In this talk we will first provide a survey for the
non-specialists. We then explain some new ideas on how to bulid
one-way trapdoor functions from actions of finite simple
semi-rings on finite semi-modules. The presented results
constitute joint work with Elisa Gorla, Gerard Maze and Chris
Monico and Jens Zumbrägel.