Some public-key cryptosystems based on the tropical semiring have been proposed in
recent years because of their increased efficiency, since the multiplication is actually an …

In this paper, we introduce two general schemes of algebraic cryptography. We show that
many of the systems and protocols considered in literature that use two-sided multiplications …

In this dissertation, we consider an extension of the discrete logarithm problem to the case of
a semigroup acting on a finite set: the Semigroup Action Problem (SAP). New protocols and …

Because there is no multiplication of numbers in tropical algebra and the problem of solving
the systems of polynomial equations in tropical algebra is NP‐hard, in recent years some …

When we replace addition and multiplication of real numbers by the operations of taking the
maximum of two numbers and of adding two numbers respectively, we obtain the so-called …

Recently, public-key cryptography based on tropical semi-rings have been proposed.
However, the majority of them are damaged. The main reason is that they use a public …

In recent years, the tropical polynomial factorization problem, the tropical matrix
decomposition problem, and the tropical multivariate quadratic equation solving problem …

The discrete-logarithm problem and related problems are important in public-key
cryptography; however, these problems can be reduced to the hidden-subgroup problem …

The idempotent semirings Rmax and Rmin play a crucial role in several areas of
mathematics and their applications such as discrete mathematics, algebraic geometry …

We propose a new class of key establishment schemes which are based on geometric
generalizations of the classical Diffie-Hellman. The simplest of our schemes–based on the …