A Survey of the Discrete Logarithm Problem

The Discrete Logarithm Problem (DLP) plays an important role in the field of cryptography, and it has been a subject of in-depth research among cryptographers and mathematicians in recent times because of its computational difficulty. This work provides a short survey of the DLP and the Baby-step Giant-step (BSGS) method for solving this problem. In this paper, the BSGS method was implemented to verify and analyse its computational complexity using the C programming language and General Multiple Precision Arithmetic Library (GNU MP). Furthermore, the computation time was calculated for instances of up to 45-bit size.