Algebraic (trapdoor) one-way functions: Constructions and applications

Algebraic (Trapdoor) One-Way Functions and Their Applications

In this paper we introduce the notion of Algebraic (Trapdoor) One Way Functions, which, roughly speaking, captures and formalizes many of the properties of number-theoretic one-way functions. Informally, a (trapdoor) one way function F : X → Y is said to be algebraic if X and Y are (finite) abelian cyclic groups, the function is homomorphic i.e. F (x) · F (y) = F (x · y), and is ringhomomorphic...

Algebraic Methods for Constructing One-way Trapdoor Functions

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 one-way trapdoor functions based on the difficulty of such problems are proposed. Several instances are studied both from a conceptual and cryptographic point of view. We discuss the application of existing gene...

One-Time Trapdoor One-Way Functions

Trapdoors are widely used in cryptography, in particular for digital signatures and public key encryption. In these classical applications, it is highly desirable that trapdoors remain secret even after their use. In this paper, we consider positive applications of trapdoors that do not remain secret when they are used. We introduce and formally define one-time trapdoor one-way functions (OTTOW...

Trapdoor one-way permutations and multivariate polynominals

Adaptive One-Way Functions and Applications

We introduce new and general complexity theoretic hardness assumptions. These assumptions abstract out concrete properties of a random oracle and are significantly stronger than traditional cryptographic hardness assumptions; however, assuming their validity we can resolve a number of long-standing open problems in cryptography.