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

Quantum unicity distance

Chong Xiang, Li Yang

Published Apr 10, 2012• 1 citation
Publisher

Abstract

We attempt to develop Shannon's concept of the unicity distance into the quantum context. Based on the definition of information-theoretic security for quantum cryptography, we present a quantum probabilistic encryption algorithm with bounded information-theoretic security, and then work out its quantum unicity distances. The result shows that quantum unicity distance is much bigger than the unicity distance of classical cryptography.

DOI
10.1117/12.922555

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We attempt to develop Shannon's concept of the unicity distance into the quantum context. Based on the definition of information-theoretic security for quantum cryptography, we present a quantum probabilistic encryption algorithm with bounded information-theoretic security, and then work out its quantum unicity distances. The result shows that quantum unicity distance is much bigger than the unicity distance of classical cryptography.
Abstract In this paper, we consider the relationship between C Shannon’s unicity distance, which is determined by the number of symbols of the encrypted message required to uniquely find the encryption key of the cryptosystem in information-theoretical sense, ε -secrecy criterion in quantum cryptography and Holevo information. A lower bound for the unicity distance for ε -secret keys in quantum cryptography is obtained. The relationship between unicity distance, ε -secrecy criterion in quantum cryptography and Holevo information is demonstrated.
We present a quantum probabilistic encryption algorithm of private-key encryption scheme based on conjugate coding of qubit-string. Usually, probabilistic encryption algorithm is adopted in public-key encryption protocols. Here we consider its function of increasing the unicity distance of both classical and quantum private-key encryption scheme. The security of quantum probabilistic private-key encryption against two kinds of attacks is analyzed. Based on no-signalling postulate we show that the scheme can resist the attack to the key. The protocol's security against plaintext attack is also investigated under the concept of information-theoretic indistinguishability of encryption. Finally, we give a conjecture related with the Breidbart's attack.
We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext attack is also investigated by considering the information-theoretic indistinguishability of the encryption scheme. Finally, we make a conjecture regarding Breidbart's attack.
The existing quantum cryptography is a classical cryptography in nature and basically insecure because of its classical (conventional) bits, classical encryption algorithm and classical (public) channel. A novel topic about successful communication between the legitimate users, Alice and Bob, is discussed with probability of solution uniqueness of Bob’s decryption equation. We find, by probabilistic analysis, that success of communication between Alice and Bob is probabilistic with a probability bigger than 1/2. It is also novel to define insecurity of the quantum cryptography by probability of solution uniqueness of the search equation of Eve, the eavesdropper. The probability of Eve’s success to find the plain-text of Alice (and Bob) is greater than 1/2, and so the quantum cryptography is seriously insecure.