new variations of discrete logarithm problem

The security of public key cryptography relies on the complexity of certain mathematical hard problems. it is vital to comprehend the intricacy of these problems to develop secure cryptographic schemes and security protocols. this paper provides an overview of some widely recognized hard problems associated with the discrete logarithm problem, including the reductions among them. furthermore, we introduce a novel hard problem that is equivalent to the discrete logarithm problem, which also has a decisional version. additionally, a set of new problems is presented, which can be instrumental in the design of secure encryption schemes. this paper is intended to provide crucial insights into the realm of hard problems in cryptography, facilitating a better understanding of security measures.