| Summary: | 碩士 === 國立成功大學 === 資訊工程學系碩博士班 === 98 === Today, information security techniques such as DES, AES, RSA, and ElGamal are based on the cryptography theory. These cryptosystems are computationally secure. The purpose of these cryptosystems is to prevent attackers from breaking them in a certain period of time. Therefore, such cryptosystems are not perfectly secure. The development of the quantum computer has called into question the security of cryptosystems that are based on the fact that an attacker is unable to solve mathematical problems such as RSA (based on the factoring problem), because such problems have been found to be solvable in polynomial time. Therefore, a number of classical mathematical problems in cryptography may render them insecure in the future because of quantum computation. Fortunately, the quantum computer can be used not only to break traditional cryptosystems but also to develop quantum cryptography based on quantum mechanics.
Quantum cryptography is an important research area wherein quantum phenomena such as the Heisenberg uncertainty principle and the no-cloning theorem are used to ensure secure communication over quantum channels.
Quantum cryptography has two basic characteristics: unconditional security and eavesdropping detectability. Unconditional security means an attacker cannot break the cryptosystem, even using infinite resources. Eavesdropping detectability means the communicators can use the measurement uncertainty to check for the presence of eavesdropping.
The quantum key distribution protocol (QKDP) is one of the most important research topics in quantum cryptography. In this protocol, two communicators use the quantum state and quantum channel to share a common secret key. Then, they use this common secret key to communicate. In order to check for the presence of eavesdropping in quantum transmission, the two communicators use a public discussion channel to detect this attack on the basis of the principles of quantum mechanics.
The quantum secret sharing (QSS) protocol is another important research topic. In this protocol, secret information is split into several shadows. A single shadow alone cannot be used to recover the secret, but a sufficient number of shadows can be used to do so. For example, in three-party QSS, an employer splits a secret into two shadows and then sends one to each of her two agents. Neither agent alone can recover the employer’s secret information. Only when they collaborate, the employer’s secret can be recovered. Therefore, a dishonest agent cannot recover the employer’s secret information on his/her own. In 2006, Deng et al. used the GHZ states to propose a quantum secret sharing protocol. In 2009, Gao proposed a quantum secret sharing protocol based on three-dimensional Bell states. In our thesis, we will use the techniques of decoy photons, block-transmission, etc., to increase the qubit efficiency and reduce the number of unnecessary operations and quantum devices. Moreover, we will propose another quantum secret sharing protocol, an unbalanced-trust quantum secret sharing protocol, for applications in which one agent has more power (trust) than the other. In this protocol, an agent with more power (trust) also acquires more information. As a result, there is a high probability that this agent will be able to guess the secret holder’s information. Moreover, the agent with more power (trust) can recover half of the secret holder’s information alone, but must cooperate with the other agent to recover the other half.
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