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?
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$\begingroup$ “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… $\endgroup$– e-sushiCommented May 30, 2014 at 7:58
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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.
