AI 中文总结
本文研究带噪声量子公钥加密的密文变换可延展性，通过适配温和测量引理推广无噪声场景的可忽略函数，关联不可区分性与安全阈值，为量子密钥分发的永久安全性提供新研究方向。
AI 中文摘要
我们刻画了Malavolta和Walter近期提出的量子公钥加密协议的带噪声变体，该协议证明了在Alice与Bob两轮交互后，可严格构建量子密钥分发的永久安全性概念。为研究向量子密钥分发相关密码协议注入噪声的方向，我们论证了通过密文变换的可延展性假设进一步探究永久安全性的必要性。可延展性假设由Maurer和Tackmann提出，用于比较“先认证后加密”与“先加密后认证”协议在转发错误、删除错误及重构概率等多种表达式下的表现，这类概率可进一步用于建立目标密码协议的不可区分性与安全阈值间的关联。为深化该关联，我们通过适配量子信息论中的温和测量引理，证明迹距离的上界可用于推广Malavolta和Walter在无噪声场景中得到的可忽略函数。除带噪声场景下的可忽略函数与更高安全阈值相关外，仍需探究本文中用于界定迹距离的计算是否可与更侧重博弈论方法的其他场景建立关联。
英文摘要
We characterize a noisy variant of a Quantum public encryption protocol recently introduced by Malavolta and Walter which demonstrated that the notion of everlasting security can be rigorously formulated for Quantum key distribution after two rounds of interaction between Alice and Bob. To address one possible direction of research that is related to injecting noise in the cryptographic protocol related to Quantum key distribution we formulate arguments for further examining the notion of everlasting security through malleability assumptions on transformations of the ciphertext. Assumptions surrounding malleability were introduced by Maurer and Tackmann for the purposes of comparing how authenticate then encrypt, and encrypt then authenticate, protocols behave through a variety of expressions for the forwarding error, deleting error, and reconstruction probabilities. Such probabilities are put to further use for obtaining connections between the indistinguishability and security threshold for a cryptographic protocol of interests. To further build upon such associations we demonstrate, through an adaptation of the Gentle Measurement Lemma from Quantum information theory, how upper bounds on the trace distance can be used to generalize the negligibility function obtained by Malavolta and Walter in the noiseless setting. Besides the fact that the negligibility function in the noisy setting is related to a higher security threshold it continues to remain of interest to determine whether computations provided in this work for upper bounding the trace distance can be related to other settings that are centered more on game-theoretic approaches.
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