Variations of Diffie-Hellman problem
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 D...
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| Main Authors: | , , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2003
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| Subjects: | |
| 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 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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 |
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