How small are we talking about when defining the small public/private key exponent

Question

I've been wondering about the 'small' part of the attacks on RSA, like the small public key exponent and the small private key exponent and what's not really clear is how small are we talking about? Like is it how small with respect to the large prime numbers or what exactly?

“RSA with small exponents?”, “low-exponent RSA”, and “What security authorities and standards reject e=3 in RSA, when, and with what rationale?” might be interesting to checking on… — e-sushi, May 30 '14 at 07:58

score 1 · Accepted Answer · edited Apr 13 '17 at 12:48

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Exponentiation by squaring takes time approximately proportional to the number of bits in the exponent. 3 has been used but allows attacks on some weak padding schemes. 65537 ($=2^{16}+1$) is the one used widely in practice.

Cf. Impacts of not using RSA exponent of 65537

edited Apr 13 '17 at 12:48

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answered May 30 '14 at 07:44

otus

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How small are we talking about when defining the small public/private key exponent

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