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So, I am currently trying to understand the differences between DH and ECDH. I understand the basics between how the two algorithms work, however, I do not clearly understand how to compare the security of one to another, meaning the size of the DH key used vs the EC curve size used.

The question thus is, what DH key sizes correspond to which EC curve sizes?, and how can we effectively compare these two sizes?

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    This doesn't have and easy answer, see: https://www.keylength.com/en/compare/ – kelalaka Apr 24 '21 at 22:15
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    ... where DH is sometimes mentioned as the "Discrete Logarithm Problem" or "DLP"... – Maarten Bodewes Apr 25 '21 at 00:11
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    Although you could look at https://crypto.stackexchange.com/questions/62013/ https://crypto.stackexchange.com/questions/25577/ https://crypto.stackexchange.com/questions/1975/ https://crypto.stackexchange.com/questions/8687/ and next door https://security.stackexchange.com/questions/101044/ https://security.stackexchange.com/questions/59190/ https://security.stackexchange.com/questions/42558/ https://security.stackexchange.com/questions/5487/ https://security.stackexchange.com/questions/48300/ – dave_thompson_085 Apr 25 '21 at 02:37

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