Variations of Diffie-Hellman problem

• Main Authors: BAO, Feng, DENG, Robert H., ZHU, Huafei
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: Diffie-Hellman problem; square Diffie-Hellman problem; inverse Diffie-Hellman problem; divisible Diffie-Hellman problem; Information Security
• Online Access: https://ink.library.smu.edu.sg/sis_research/1083; https://ink.library.smu.edu.sg/context/sis_research/article/2082/viewcontent/Bao2003_VariationsOfDiffie_HellmanProblem_pv.pdf
• Institution: Singapore Management University

This paper studies various computational and decisional Diffie-Hellman problems by providing reductions among them in the high granularity setting. We show that all three variations of computational Diffie-Hellman problem: square Diffie-Hellman problem, inverse Diffie-Hellman problem and divisible Diffie-Hellman problem, are equivalent with optimal reduction. Also, we are considering variations of the decisional Diffie-Hellman problem in single sample and polynomial samples settings, and we are able to show that all variations are equivalent except for the argument DDH ⇐ SDDH. We are not able to prove or disprove this statement, thus leave an interesting open problem. Keywords: Diffie-Hellman problem, Square Diffie-Hellman problem, Inverse Diffie-Hellman problem, Divisible Diffie-Hellman problem