In another interesting post, one of the developers/security researchers behind Phuctor suggests that using different exponents with RSA keys will "[increase] the costs of attacking your setup astronomically."
While the author does state that "it is not said nor implied here that there's any sort of theoretical vulnerability related to using 65537 as an exponent for RSA," this suggestion gets me thinking.
I have a few interrelated questions:
- Is it possible to generate (PGP|SSH|SSL) RSA keys that use a different exponent?
- Does a different, larger exponent increase the work effort required for an attacker? Does it increase the work effort required for legitimate uses?
- If I generate keys with a different exponent, do I lose compatibility with certain systems? ie: if a system supports 2048bit RSA, will it likely also support 2048bit RSA with a different exponent?
Using a different exponent seems interesting to me, but people often have been compromised when they made a choice they didn't fully understand: even when they think they're adding security, they may be, in fact, diminishing it.