Martin Juras | Searcharxiv

arXiv2016

Public-key cryptosystem based on invariants of diagonalizable groups

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on Euclidean algorithm).

cs.CR↗

arXiv2015

Eisenstein-Dumas criterion and the action of $2\times 2$ nonsingular triangular matrices on polynomials in one variable

Let $K$ be a valued field (in general $K$ is not heselian) with valuation $v$ and $A(x)\in K[x]$ be a polynomial of degree $n$. We find necessary and sufficient conditions for the existence of the elements $s,t,u\in K$, $s\neq 0\neq u$, such that at least one of the polynomials $u^nA(\frac{sx+t}{u})$, $(tx+u)^nA(\frac{sx}{tx+u})$, $(ux)^nA(\frac{tx+s}{ux})$ or $(ux+t)^nA(\frac{s}{ux+t})$ is an Eisenstein-Dumas polynomial at $v$, provided that the characteristic of the residue field of $v$ does not divide $n$. Furthermore, we show that if the orbit $A(x)GL(2,K)$ contains an Eisenstein-Dumas polynomial at $v$, then an Eisenstein-Dumas polynomial at $v$ can be found in a certain one-parameter subset of this orbit.

math.NT↗