Network Coding-Based Post-Quantum Cryptography

Abstract

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. That is, using HUNCC, we can ensure post-quantum security in networks where it is not possible to use publickey encryption over all the links in the network. In addition, the information rate approaches 1 as the number of communication links increases. As a concrete example, in a multipath network with three links, using a 128-bit computationally secure McEliece cryptosystem only over one link, we obtain a 128-bit computational security level over all paths with a total information rate of 0.91 in the network.

Quantum computing: A taxonomy, systematic review and future directions

“…Authors have focused on implementing this approach and suggested improving the performance in implementation, applying standard model or quantum random oracle model to get better experiences. The hardness of distinguishing a code from pseudorandom code : Rank metrics play important role in various applications associated with code‐based cryptography. Few applications include space–time coding, network coding, and asymmetric key‐based cryptosystems 227–229 . Hardness is a theoretical property of a code.…”

“…The cryptosystems based on these schemes are well protected from various attacks with different coding schemes. However, the hardness of the rank metric is required to ensure security in various applications like post‐quantum cryptography security with network coding 227 . Bardet et al 222 discussed the algebraic attack on the rank metric in a code‐based cryptosystem.…”

Post-Quantum Security for Ultra-Reliable Low-Latency Heterogeneous Networks

“…In order to improve the throughput, [5] introduced individual computational security. This notion is to computational security as individual security is to strong security.…”

“…A secure scheme, which obtains a trade-off between a postquantum security guarantee (for a strong Eve) and throughput, was presented in [5]. The scheme is called a hybrid universal network-coding cryptosystem (HUNCC).…”

“…The first stage is a pre-processing stage in which we code for security and in the second stage we code for reliability. For security, we consider the linear mixing performed by HUNCC [5], where a post-quantum McEliece encryption [7] is applied to the trusted communication links. For reliability, we consider three options: SP SR-ARQ [8], SP AC-RLNC [2] and MP AC-RLNC [3].…”