Statistical analysis of the Diffie-Hellman key exchange protocol in a finite group

Abstract

This paper presents a novel methodology to test the security of the Diffie-Hellman public key exchange protocol. The security of many cryptographic schemes rely on the hardness of this problem. We are presenting a purely statistical test to compare this problem in different groups. We are using groups included in the Zp group with p prime as a major example, however the methods presented are not restricted to these groups. The presentation of the results is primarily intended to introduce novel applications of statistical methodologies to the area of mathematical cryptography. As such we will emphasize the cryptographical aspects of the work more than the statistical notions.