No I don't think it was specific. I believe he was just guesstimating the exponential power required to do anything more interesting than basic math. We were all rather young students at the time so I don't think he had a specific application in mind. It was all rather new back then anyways, hard to imagine all the applications.

He is probably referencing the 128 bit security threshold most crypto systems seek to achieve. However this doesn’t really line up with the number of qubits needed to break said crypto, which is typically much larger (thousands of qubits, plus error correction to survive millions of operations).

Edit: less than a doubling. Eg from 128 to 192 or from 256 to 384. I meant to say a doubling is sufficient.