On relationship of computational diffie-hellman problem and computational square-root exponent problem

Abstract

The Computational Square-Root Exponent Problem (CSREP), which is a problem to compute a value whose discrete logarithm is a square root of the discrete logarithm of a given value, was proposed in the literature to show the reduction between the discrete logarithm problem and the factoring problem. The CSREP was also used to construct certain cryptography systems. In this paper, we analyze the complexity of the CSREP, and show that under proper conditions the CSREP is polynomial-time equivalent to the Computational Diffie-Hellman Problem (CDHP). We also demonstrate that in group G with certain prime order p, the DLP, CDHP and CSREP may be polynomial time equivalent with respect to the computational reduction for the first time in the literature. © 2011 Springer-Verlag Berlin Heidelberg.