[Cryptography] Lower bound for the size of an RSA key's private exponent

[Jon Callas]

> On Feb 19, 2017, at 4:46 PM, Bertrand Mollinier Toublet <crypto-metzdowd at bmt-online.org> wrote:
> 
> All,
> 
> So, I guess my question becomes: what are the upper and lower bounds of the Carmichael totient value of a modulus of size n bits? Upper value is slightly smaller than the modulus, but potentially still n bits. Lower bound, though, I'm not sure. 
> 
> Thoughts?

It's 3.

Here's my Gordian Knot construction:

Create an RSA key with a public exponent of 3. Make sure it's actually secure. Swap the public and private keys, publishing the formerly private key as the public key and keeping the formerly public key as the private one. 

The private exponent is now 3.

	Jon