Most of the time people forgot that the real aim of the adversary against encryption is accessing the message. For example, in the RSA case, we talk about the factoring of the modulus to reach the private key to reveal the encrypted messages. If proper encryption is not used then instead of factoring one can try the possible message space or the cube-root attack.
In the RSA case, if ever a real size is built for the Shor's period finding algorithm the attacker can factor the modulus and then can reveal the messages by using the private key in polynomial time or better in BQP.
- Is it possible with a modified Shor's algorithm ( or another ) that doesn't factor the modulus but reveals the message encrypted under textbook RSA or properly padded RSA?
- Is there a published work similar to this?
This is only meaningful in the case that revealing the messages without factoring may require less QBit than the Original Shor's algorithm.