We show how to construct length-preserving 1-1 one-way
functions based on popular intractability assumptions (e.g., RSA, DLP).
Such 1-1 functions should not
be confused with (infinite) families of (finite) one-way permutations.
What we want and obtain is a single (infinite) 1-1 one-way function.
In this paper we compare hardness of two well known problems: the Diffie-Hellman problem and the root finding problem. We prove that in any cyclic group computing Diffie-Hellman is not weaker than root finding if certain circumstances are met. As will be discussed in the paper this theorem can affect ... more >>>
