Potential Vulnerability of Encrypted Messages: Decomposability of Discrete Logarithm Problems

This paper provides a framework that reduces the computational complexity of the discrete logarithm problem. The paper describes how to decompose the initial DLP onto several DLPs of smaller dimensions. De-composability of the DLP is an indicator of potential vulnerability of encrypted messages transmitted via open channels of the Internet or within corporate networks. Several numerical examples illustrate the framework and show its computational efficiency.