The validation of cryptographic algorithms

Abstract

Since the appearance of public-key cryptography in the seminal Diffie-Hellman paper, many new schemes have been proposed and many have been broken. Thus, the simple fact that a cryptographic algorithm has withstood cryptanalytic attacks for several years is, by itself, a kind of validation procedure. A completely different paradigm is provided by the concept of provable security. Stated in a more accurate way, this approach proposes computational reductions to well established problems such as factoring or the discrete logarithm problem. Recently, the scope of this method has been considerably widened by using a model where concrete cryptographic tools are replaced by ideal objects: in this model, DES is viewed as a random permutation and SHA as a random function with the appropriate range. Basically, this is another technique for spotting error designs and validating cryptographic algorithms. When cryptanalysis and security proofs combine with each other so that there is virtually no gap between them, the resulting picture becomes quite convincing. The present paper gives several examples of such a situation taken from various areas of cryptography such as signature schemes, public-key identification or even symmetric-key techniques.