On Universal Primitive Functions

On Universal Functions

Extended Primitive Recursive Functions

— In this paper we extend the notion of primitive recursive function to the case in which the domain is N* and the range is a subset oj N*. We give a rigorvus characterization oj tins class oj functions and show différences icith the classical primitive recursive functions. Résumé. — Dans cette note nous étendons la notion de f onction primitive recursive à tous les cas dans lesquels le domaine...

Primitive Recursive Functions

1. Definition of recursive functions. In this paper, we shall consider certain reductions in the recursion scheme for defining primitive recursive functions. Hereafter, we shall refer to such functions simply as recursive functions. In §1, we define what is meant by a recursive function, and also define some recursive functions which will be used. The statement of the principal results of the p...

Unary Primitive Recursive Functions

In this article, we will study certain reductions in the schemes that conform unary primitive recursive functions (i.e. primitive recursive functions of one argument) and we will extend some results previously researched by R. M. Robinson in [15]. Furthermore, we will introduce formal notation for unary primitive recursive functions. §

A Primitive for Proving the Security of Every Bit andAbout Universal Hash Functions & Hard CorePredicates ?

In 1999, J. H astad and M. NN aslund 13] could prove that every bit is a hard core of the RSA function. From this work we extract an abstract theorem about the hidden number problem which can be used to prove that every bit is a hard core of many speciic cryptographic functions. Applications are RSA, ElGamal, Rabin, a modiied Diie-Hellman function, Pailler's cryptosystem, the Diie-Hellman funct...