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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum-message-oriented public-key encryption scheme beyond computational hypothesis

Min Liang, Li Yang

Published Apr 21, 2012• 1 citation
Publisher

Abstract

We propose two definitions of quantum one-way transformation and quantum trapdoor one-way transformation beyond computational hypothesis, and give four examples. Then, we present a general way to construct a quantum public-key encryption scheme from a quantum one-way transformation and a quantum trapdoor oneway transformation, and give a concrete example which is quantum-message-oriented. The security of this kind of encryption schemes is based on the one-way property of quantum one-way transformation and quantum trapdoor one-way transformation, and this kind of schemes is information-theoretically secure.

DOI
10.1117/12.922500

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We propose two definitions of quantum one-way transformation and quantum trapdoor one-way transformation beyond computational hypothesis, and give four examples. Then, we present a general way to construct a quantum public-key encryption scheme from a quantum one-way transformation and a quantum trapdoor oneway transformation, and give a concrete example which is quantum-message-oriented. The security of this kind of encryption schemes is based on the one-way property of quantum one-way transformation and quantum trapdoor one-way transformation, and this kind of schemes is information-theoretically secure.
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Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.
We formalize and study the notion of a quantum trapdoor function. This is an efficiently computable unitary that takes as input a "public" quantum state and a classical string xxx, and outputs a quantum state. This map is such that (i) it is hard to invert, in the sense that it is hard to recover xxx given the output state (and many copies of the public state), and (ii) there is a classical trapdoor that allows efficient inversion. We show that a quantum trapdoor function can be constructed from any quantum-secure one-way function. A direct consequence of this result is that, assuming just the existence of quantum-secure one-way functions, there exists a public-key encryption scheme with a (pure) quantum public key.