Quantum Public-Key Cryptosystems

This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f , plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f . This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.