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Does breaking CDH also break DLP?

de flag

Does breaking the computational Diffie-Hellman problem in a group also always break discrete logarithms in that group?

fgrieu avatar
ng flag
The present question is a less precise version of [these](https://crypto.stackexchange.com/q/13034/555) [two](https://crypto.stackexchange.com/q/62944/555).
LinusK avatar
de flag
Not sure I understand. I read this paper http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.4432&rep=rep1&type=pdf but they do not claim that breaking CDH always breaks DLP (only under certain circumstances). However, I believe it is generally true.
fgrieu avatar
ng flag
AFAIK there is no known group where we can break CDH but not solve the DLP. According to [this](https://doi.org/10.1007/0-387-34799-2_38) there are classes of groups where the two are proven equivalent. That would mean that we don't know an answer to your question except in some classes of groups, where it is yes. I don't know more.
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