Uniform complexity and digital signatures

Abstract

A concept of uniform complexity is defined and a class of functions is shown to have uniform complexity. A special case of these results is used to develop a new digital signature method, which makes forging signatures as hard as factoring a large number and which allows to sign all messages directly. The signature production involves only one exponentiation modulo a large number and the signature checking the comparison of a fourth and a second power modulo a large number. Therefore this new method is faster than known methods with the same degree of safety.