RSA: Encrypting message using multiple keys

Question

Is it possible to get additional security by encrypting a message using 2 or more RSA keys?

EDIT: A few clarifications:

The context I am most interested in doing this for is encrypting a randomly generated symmetric key.

I don't want to limit the question to encrypting twice in a row; the purpose is to avoid the high computational cost of large RSA keys. Using less straightforward tactics such as breaking the message into parts and encrypting them separately should be considered as an option.

It should be assumed that getting only part of the message is acceptable.

If you know of any publications where this is discussed specifically by an expert, or algorithms that use multiple RSA keys, then please contribute.

Answer 1

No.

It is not safe to do thought experiments regarding cryptography. You are advised to keep narrowly to the path trodden by the experts.

And when the experts want to protect something better, they use a bigger key-size (at least 2048 bits is required, smaller certificates are insufficient for any peace of mind) or use elliptic curve certificates in preference to RSA.

Incidentally, you're remember that your message body is typically encrypted with a symmetric cipher and a random key, and that just this random key is encrypted with the public key of the recipient. Double-encrypting this secret key won't make this secret key longer, and won't impact an attacker's ability to brute-force that.

Quantum cryptography - I mention it only as an exciting aside, you need not factor this into your choice - promises interesting things for the keysizes: the RSA keys will be wiped out by Shor's algorithm, but the symmetric keys (Grover's) will be only half-lengthed (128-bits will be equiv to 64-bits, so will be crackable). There is of course debate about whether such quantum machines can be implemented etc etc :)

Answer 2

No.

If Key A is compromised than encrypted with A+B will protect against the compromise, but outside that special case, you get no additional benefit.