# RSA signature signing

For assymetric encryption such as RSA, I understand that Alice can sign a document with her secret key and send it to Bob, which he can then verify.

Sign: $\sigma=m^d \bmod N$

Verify: $v=\sigma^e \bmod N$

This may be a silly question, but what if it was the other way around, Bob wants to send a document to Alice. How would he sign it to say it was from him. Can he do it without introducing "Bob's secret key" and just use the scheme provided, or does he have to do that? or is there better way?

• Beware that above is plaintext RSA. You would need a padding scheme to make this secure. I'm personally more in favor of "private key" instead of "secret key" (making it a "public / private key pair" for asymmetric crypto and a (shared) "secret key" for symmetric crypto. – Maarten Bodewes Dec 10 '16 at 23:42