Iranian Society of Cryptology The ISC International Journal of Information Security 2008-2045 15 3 2023 10 01 New Variations of Discrete Logarithm Problem 91 100 184477 10.22042/isecure.2023.184477 EN Mahdi Mahdavi Oliaee Electrical Engineering Department, Shahid Beheshti University, Tehran, Iran Sahar Khaleghifard Electrical Engineering Department, Shahid Beheshti University, Tehran, Iran Zahra Ahmadian Electrical Engineering Department, Shahid Beheshti University, Tehran, Iran Journal Article 2023 12 04 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. https://www.isecure-journal.com/article_184477_c2c03cef45133db287c4d1f1e580f743.pdf