Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. Roughly speaking, a non-malleable code for a family of tampering functions guarantees that no adversary can tamper (using functions from this family) the encoding of a given message into the encoding of a related distinct message. Non-malleable secret sharing schemes are a strengthening of non-malleable codes which satisfy additional privacy and reconstruction properties. We first focus on the $2$-split-state tampering model, one of the strongest and most well-studied adversarial tampering models. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until the recent work by Aggarwal, Boddu, and Jain (arXiv 2022), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. We also present explicit constructions of such schemes that achieve low-error non-malleability.

翻译：非可塑编码是密码学与编码理论交叉领域的基础性对象。这类编码即使在无法进行纠错和检错的环境下仍能提供安全保证，并已应用于若干其他密码学任务。简而言之，针对某一篡改函数族F的非可塑编码保证：任何敌手都无法（通过该族中的函数）将给定消息的编码篡改为另一相关不同消息的编码。非可塑秘密共享方案是非可塑编码的强化版本，其额外满足隐私性与重构性质。我们首先聚焦于2-分割态篡改模型——这是最强且研究最深入的敌手篡改模型之一。在该模型中，码字被分割为两部分并存储于物理隔离的服务器中，敌手可对各部分独立使用任意函数进行篡改。该模型可通过令敌手独立篡改每个份额自然地扩展到多方秘密共享场景。以往关于分割态篡改模型下非可塑编码与秘密共享的研究仅考虑经典消息的编码。此外，在Aggarwal、Boddu与Jain（arXiv 2022）的近期工作之前，具备量子能力与共享纠缠的敌手尚未被纳入考量，且先验地无法判定先前的方案在此模型下是否安全。本研究首次提出面向共享纠缠量子敌手且适用于量子消息的分割态非可塑编码与秘密共享方案概念，并给出此类方案的具体构造以实现低误差非可塑性。