Fractal Magmas and Public-Key Cryptography

Abstract

In this paper, we deal with magmas the simplest algebras with a single binary operation. The main result of our research is algorithms for generating chain of finite magmas based on the self-similarity principle of its Cayley tables. In this way the cardinality of a magmas domain is twice as large as the previous one for each magma in the chain, and its Cayley table has a block-like structure. As an example, we consider a cyclic semigroup of binary operations generated by a finite magmas operation with a low-cardinality domain, and a modify the Diffie-Hellman-Merkle key exchange protocol for this case.

Malliavin–Stein method: a survey of some recent developments

“…Although Stein's method is already successfully used for quantifying functional limit theorems of the Donsker type (see [11,12], as well as [34,35,45,91] for a discussion of recent developments), the general problem of assessing the discrepancy between probability distributions on infinite-dimensional spaces (like, e.g., on classes of smooth functions or on the Skorohod space) is essentially open.…”