Public-Key Crypto-systems Using Symmetric-Key Crypto-algorithms

The prospect of quantum computing makes it timely to consider the future of public-key crypto-systems. Both factorization and discrete logarithm correspond to a single quantum measurement, upon a superposition of candidate keys transformed into the fourier domain. Accordingly, both these problems can be solved by a quantum computer in a time essentially proportional to the bit-length of the modulus, a speed-up of exponential order.