Rate 1/5 非可延展码对抗纠缠分裂态篡改
Rate 1/5 Non-Malleable Codes against Entangled Split-State Tampering
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对纠缠双分裂态篡改，构造速率至少1/5-ξ的经典消息非可延展码，实现最坏情况安全，基于置换构造并改进为规定消息加均匀填充。
AI中文摘要：
我们构造了针对经典消息的高效信息论非可延展码，该码能够抵御两个不通信的、具有任意预共享纠缠的局部量子篡改操作。对于每个足够小的固定 $\xi>0$ 和所有足够大的第一份额长度 $n$，该码的速率至少为 $1/5-\xi$，具有完美正确性和错误概率 $2^{-n^{\Omega(1)}}$。安全性对每条消息均成立，且每次攻击都有一个与消息无关的模拟器。这解决了纠缠双分裂态模型中最坏情况经典消息的常数速率问题。我们的构造基于 Batra、Boddu 和 Jain 的基于置换的双分裂构造，该构造对均匀随机消息实现了接近 $1/5$ 的速率。我们保留了他们的架构，但将置换的均匀消息输入替换为规定的消息与新鲜均匀填充的拼接。我们的主要贡献是针对此修改的最坏情况安全性归约。
英文摘要：
We construct efficient information-theoretic non-malleable codes for classical messages that are secure against two noncommunicating local quantum tampering operations with arbitrary pre-shared entanglement. For every sufficiently small fixed $ξ>0$ and all sufficiently large first-share lengths $n$, the codes have rate at least $1/5-ξ$, perfect correctness, and error $2^{-n^{Ω(1)}}$. Security holds for every message, with a single message-independent simulator for each attack. This resolves the constant-rate question for worst-case classical messages in the entangled two-split-state model. Our construction builds on the permutation-based two-split construction of Batra, Boddu, and Jain, which achieves rate approaching $1/5$ for uniformly random messages. We retain their architecture but replace the uniform message input to the permutation with a prescribed message concatenated with fresh uniform padding. Our main contribution is a worst-case security reduction for this modification.
