Progress in quantum computational cryptography

Shor's algorithms for the integer factorization and the discrete logarithm problems can be regarded as a negative effect of the quantum mechanism on public-key cryptography. From the computational point of view, his algorithms illustrate that quantum computation could be more powerful. It is natural to consider that the power of quantum computation could be exploited to withstand even quantum adversaries. Over the last decade, quantum cryptography has been discussed and developed even from the computational complexity-theoretic point of view. In this paper, we will survey what has been studied in quantum computational cryptography.