Abstract
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 \(\Leftarrow\) SDDH. We are not able to prove or disprove this statement, thus leave an interesting open problem.
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Bao, F., Deng, R.H., Zhu, H. (2003). Variations of Diffie-Hellman Problem. In: Qing, S., Gollmann, D., Zhou, J. (eds) Information and Communications Security. ICICS 2003. Lecture Notes in Computer Science, vol 2836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39927-8_28
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DOI: https://doi.org/10.1007/978-3-540-39927-8_28
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