Abstract
There are many variants of the computational Diffie–Hellman problem that are necessary to provide security of many cryptographic schemes. Two of them are the square Diffie–Hellman problem and the square root Diffie–Hellman problem. Recently, the first and third authors proved that these two problems are polynomial-time equivalent under a certain condition (Roh and Hahn in Des Codes Cryptogr 62(2):179–187, 2011). In this paper, we generalize this result. We introduce the l-th power Diffie–Hellman problem and the l-th root Diffie–Hellman problem and show that these two problems are polynomial-time equivalent for \(l = O (\log p)\) under a condition similar to that of Roh and Hahn (2011), where p is the order of the underlying group.
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Roh, D., Kim, IY. & Hahn, S.G. The l-th power Diffie–Hellman problem and the l-th root Diffie–Hellman problem. AAECC 29, 41–57 (2018). https://doi.org/10.1007/s00200-017-0321-3
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DOI: https://doi.org/10.1007/s00200-017-0321-3
Keywords
- Discrete logarithm problem
- Computational Diffie–Hellman problem
- Square Diffie–Hellman problem
- Square root Diffie–Hellman problem
- l-th power Diffie–Hellman problem
- l-th root Diffie–Hellman problem