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arXiv:0801.2840 · Physical Review A

Applications of single-qubit rotations in quantum public-key cryptography

Georgios M. Nikolopoulos

Published Mar 28, 2008• 102 citations
arXivHTMLPDF

Abstract

We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevo's theorem.

DOI
10.1103/physreva.77.032348

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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.
Abstract Asymmetric encryption has some important applications in the field of communication. In classical computers, most public key encryption schemes are designed based on computational assumption. In other words, they can ensure computational security. When the computing power is large enough, it will pose a threat to these encryption schemes. We propose a quantum public key encryption scheme which based on properties of quantum physics. Our scheme realizes encryption and decryption with few resources and does not rely on any computational assumption. The key in our scheme consists of classical bits and qubits. Where the private key are classical bit and public key are qubits. The public key are generated through private key. We analyze the performance and security of the scheme. Our scheme ensures the information-theoretic secure and can be implemented easily.
The major threat in data communication in present day is security. To reduce the threat caused in the communication channel quantum cryptography is emerging as a replacement to its classical counterpart. This paper focuses on a quantum key distribution protocol for the knapsack cryptosystem using a one-way trapdoor function by qubit rotation. The protocol exploits a qubit in superposition state for a single bit message communication. The security of the protocol is owing to the fact that any random quantum state cannot be replicated.
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