摘要
秘密分享是一种将秘密分割保存的密码技术,具有广泛的应用场景.本文通过 G-like 三体纠缠态和一个单粒子量子态制备了一个新的四体量子纠缠态,利用该纠缠态中四个不同粒子在 Z 基下的测量结果的相关性,设计了一个可验证的半量子秘密分享协议.该协议的安全性依赖于量子力学原理,而非传统密码学中的数学困难问题.协议涉及一个具备完全量子能力的秘密分享者 Trent(具备完全量子能力意味着 Trent 可以执行任何不违背量子力学原理的操作)和三个只具备受限量子能力的秘密恢复者 Alice、Bob 和 Charlie(这些参与者只能执行某些特定的量子操作).Trent 将用于恢复秘密信息的密钥编码在四体纠缠态的不同粒子的量子测量结果中,并将其中的三个粒子分别分发给三个秘密恢复者,以完成密钥的分割.只有当三个秘密恢复者合作并提供正确的测量结果,方可恢复 Trent 要分享的秘密信息,任意少于三方的秘密恢复者将得不到秘密信息.为了确保用于恢复秘密信息的测量结果的保密性,本文利用贝尔纠缠态的特性进行窃听检测.此外,为了使协议能够抵抗恶意的秘密恢复者因提供错误测量结果而导致诚实的秘密恢复者得到错误的秘密信息这类攻击,协议额外增加了用于验证和解密秘密信息的密钥,在确保所有的秘密恢复者均提供了正确的测量结果后再将其分发给秘密恢复者.安全性分析表明,本文提出协议可抵抗常见的外部攻击和内部恶意参与者的欺骗攻击.此外,本文也分析了比特翻转、相位翻转、去极化、振幅阻尼等量子噪声对协议的影响.
Abstract
Secret sharing is a cryptographic technique for keeping secrets divided and it has a wide range of application scenarios.In this study,a new four-body quantum entangled state is prepared by a G-like three-body entangled state and a single-particle quantum state.A verifiable semi-quantum secret-sharing protocol is designed based on the measurements'correlation with the Z basis of the four different particles in the entangled state.The protocol's security relies on quantum mechanical principles rather than the mathematically difficult problems in conventional cryptography.The pro-tocol involves one secret holder,Trent,who has full quantum capabilities,i.e.,Trent can perform any operation that does not violate the principles of quantum mechanics,and three secret reconstructors,Alice,Bob,and Charlie,who have only restricted quantum capabilities,i.e.,these participants can only perform certain specific quantum operations.Trent splits the key used to recover the secret into quantum measurement results of the four-body entangled state.The secret information Trent wants to share can only be recovered if the three recovers cooperate and provide the correct measurement results,and any less than three secret recovers will not get the secret information.To ensure the confidentiality of the measurements used to recover the secret information,this study exploits the properties of Bell entangled states for eavesdropping detection.In addition,in order to make the pro-tocol resistant to an attack that a malicious secret reconstructor provides wrong measurement results and the honest secret reconstructor gets wrong secret information,the protocol additionally adds a key for verifying and decrypting the secret information,which is distributed to the secret reconstructors after ensuring that all secret reconstructors have provided correct measurement results.The security analysis shows that the proposed protocol can resist common external attacks and internal attacks by malicious participants.In addition,the effect of quantum noise is also analyzed such as bit flipping,phase flipping,depolarization,and amplitude damping on the proposed protocol.
国家科技期刊平台
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