Research On Some Issues Of Quantum Cryptography

Quantum cryptography is a cryptolographical resource based on quantum mechanics rather than classical mechanics, and significant to information security. The paper is built on the mathematical frame of quantum mechanics, and focuses on the unconditional security of quantum key distributions and quantum ciphers. The major results of my research are following.1. The essence of quantum key distribution protocols is the function of detecting non-orthogonal quantum states, and thus it is crucial how to detect the error syndromes occurring on the quantum states. Now, most quantum key distribution protocols employ the alternative | 0? ,|1? and | +? ,|?? bases to detect all possible errors on the qubits exchanged. This paper analyzes Bell-state measurement {|Φ+ ? ,|Φ? ? ,|Ψ+ ? ,|Ψ??} basis show its capacity of error detecting. This paper proposed a new quantum key distribution on 4-dimensional Hilbert space on Bell- state measurements, which saves a great amount of classical and quantum communication.2. 2. Based on the reasonability of Bell-state measurement, this paper also shows the equivalence of two quantum key distribution protocols with random chosen EPR pairs, and points out the two protocols have a defect on the way of determining the error number, and modify the defect to complete the proof of unconditional security.3. 3. To make error-detecting strategy capable, a condition must be satisfied, i.e., there have to be some methods to estimate the error number correctly. It's widely known that random sampling tests can present an upper bound of error number caused by illegal eavesdroppers successfully with probability exponentially close to 1, which means that it can judge whether quantum error-correcting codes or classical information reconciliation and privacy amplification work. This paper improves random sampling tests from a single-sample method to the multiple-sample one. This cause quantum key distribution protocols with random sampling tests more efficient.4. Quantum mechanics contributes not only on public-key systems, but also on the private-key ones. For the ciphers using non-orthogonal quantum states to encrypt classical or quantum information, there are still some remarkable features which are not found in the classical cryptographic world. Specially, the quantum cipher-texts are with error-detecting property and the key entropies are different against different quantum plaintext–known attacks. To show such things in formulas, quantum secure channel is defined, and presents some results of the key entropies and its corresponding bounds of BB84 quantum coding against the collective and coherent plaintext-known attacks.5. Some classical cryptographic theories can serve quantum cryptography too. This paper employs the classical Hash functions to replace random sampling tests to determine the upper bound of error numbers, which avoids the frequent requests for authentic classical communication. By combining quantum ciphers and classical Hash functions, two quantum cryptographic algorithms are presented in the paper, and are more practical for usual applications.