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I'm using TLS with a Diffie-Hellman key exchange to negotiate the symmetric keys. How long should the exponents be?

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marked as duplicate by CodesInChaos, Paŭlo Ebermann Jun 26 '13 at 19:43

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Which key-exchange are you talking about? DHE? – CodesInChaos Jun 26 '13 at 6:42
    
Yes, Diffie Hellman. – Clay Freeman Jun 26 '13 at 15:42

Diffie-Hellman exponents need at a size at least twice the security level.

So for elliptic curve DH you need the same size as the underlying field. For example 256 bits for P-256.

For finite-field DH you still need twice the security level as exponent, but significantly larger fields. For example for an 80 bit level you need 160 bit exponents and a ~1024 bit field.

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