Does anyone have any ideas on the best forum to elaborate on the following
idea? I'm obviously presenting it here in shortened form (so someone might
actually read the message), but would like to provide more details.
For a fairly long amount of time, conventional computers will be able to
prepare keys long enough to defeat decryption by quantum computers. But
public key encryption can survive regardless of how advanced quantum
computers get. The basic idea is to use the quantum computer itself to
prepare a key that is too big to fit into quantum memory. This can be
accomplished by generating primes which are, say, 5/6 the size of a key that
the quantum computer can break. The two primes can then be multiplied (and
used) on a conventional machine. A user such as a bank could change keys
daily if quantum memory capacity increases, thereby requiring astronomical
growth of quantum memory if decryption ability keeps up with encryption ability.
These primes, by assumption, could be generated by factoring a random number
and using the largest factor, if it was big enough. Sounds far fetched, but
in the strange new world of quantum computing, we can easily factor any
number that will fit into the quantum machine. The only thing left to be
determined is the distribution of the largest prime factor of a random
number. D.W. Knuth [1981, pp. 367-369] discusses this in The Art of
Computer Programming, Vol. II. The bottom line is that one could generate
large primes fast enough for the idea to be feasible.
Although some quantum computers have been slow, any quantum computer big
enough to serve as a factoring engine will have to be fast as blue blazes to
prevent decoherence problems, so speed shouldn't be an issue.
I'd appreciated any suggestions by readers on where to explore this in depth.
--Terry Cooper
