Cryptography Based on Square-Free Prefixes in Monoids

In this paper we introduce a new class of cryptographic primitives based on square-free prefixes in commutative and noncommutative monoids. The security of the proposed constructions relies on the difficulty of recovering a square-free prefix from a 1s-type factorization, which leads to a new computational problem, called the Square-Free Prefix Recovery Problem (SFPRP). We formalize SFPRP, present encryption and signature schemes based on this problem, and discuss complexity issues and open questions related to its commutative and noncommutative variants. These results constitute a first step towards cryptography based on structural properties of monoids.