基于网络编码的后量子密码学
Network Coding-Based Post-Quantum Cryptography
摘要：
为了在高通信速率下实现安全的后量子密码学，提出了一种新的混合通用网络编码密码系统（HUNCC）。我们提供的安全网络编码方案是混合的，它结合了信息理论安全与公钥密码学。此外，该方案具有通用性，可应用于任何通信网络和任何公钥密码体制。我们的混合方案是基于信息理论的个人保密的概念，传统上依赖于假设，窃听者只能观察一个子集的通信链路之间的信任方-一个假设，往往是具有挑战性的强制执行。对于这种设置，已经开发了几种代码结构，其中消息在每个路径上传输之前以保证仅观察子集的对手对每个单独的消息具有足够的不确定性的方式线性混合。相反，在本文中，我们采取计算的观点，并构造一个编码方案，其中任意安全的密码系统是利用一个子集的链接，而预处理类似于在个人安全。在此方案下，我们证明了1）一个计算安全保证的对手观察到的整个链接2）一个信息理论的安全保证的对手观察到的一个子集的链接，和3）信息速率接近网络的容量，大大提高了目前的解决方案。我们方案的一个可能令人惊讶的结果是，为了保证计算安全级别b，使用计算后量子方案加密单个链路就足够了。此外，随着通信链路数目的增加，信息速率接近1。
英文摘要：
We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it combines information-theory security with public-key cryptography. In addition, the scheme is general and can be applied to any communication network, and to any public-key cryptosystem. Our hybrid scheme is based on the information theoretic notion of individual secrecy, which traditionally relies on the assumption that an eavesdropper can only observe a subset of the communication links between the trusted parties - an assumption that is often challenging to enforce. For this setting, several code constructions have been developed, where the messages are linearly mixed before transmission over each of the paths in a way that guarantees that an adversary which observes only a subset has sufficient uncertainty about each individual message. Instead, in this paper, we take a computational viewpoint, and construct a coding scheme in which an arbitrary secure cryptosystem is utilized on a subset of the links, while a pre-processing similar to the one in individual security is utilized. Under this scheme, we demonstrate 1) a computational security guarantee for an adversary which observes the entirety of the links 2) an information theoretic security guarantee for an adversary which observes a subset of the links, and 3) information rates which approach the capacity of the network and greatly improve upon the current solutions. A perhaps surprising consequence of our scheme is that, to guarantee a computational security level b, it is sufficient to encrypt a single link using a computational post-quantum scheme. In addition, the information rate approaches 1 as the number of communication links increases.
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