Secure Network Coding Based on Lattice Signature

Huifang Yu, Ning Wang

Fenghe Wang, Shaoquan Shi, Chunxiao Wang

Shang Tao, Pei Hengli, Liu Jianwei

To provide a high-security guarantee to network coding and lower the computing complexity induced by signature scheme, we take full advantage of homomorphic property to build lattice signature schemes and secure network coding algorithms. Firstly, by means of the distance between the message and its signature in a lattice, we propose a Distance-based Secure Network Coding (DSNC) algorithm and stipulate its security to a new hard problem Fixed Length Vector Problem (FLVP), which is harder than Shortest Vector Problem (SVP) on lattices. Secondly, considering the boundary on the distance between the message and its signature, we further propose an efficient Boundary-based Secure Network Coding (BSNC) algorithm to reduce the computing complexity induced by square calculation in DSNC. Simulation results and security analysis show that the proposed signature schemes have stronger unforgeability due to the natural property of lattices than traditional Rivest-Shamir-Adleman (RSA)-based signature scheme. DSNC algorithm is more secure and BSNC algorithm greatly reduces the time cost on computation.

Chuck Easttom

Daniele Micciancio, Oded Regev

Dong Xie, Haipeng Peng, Lixiang Li +1 more

In contrast to traditional "store-and-forward" routing mechanisms, network coding offers an elegant solution for achieving maximum network throughput.The core idea is that intermediate network nodes linearly combine received data packets so that the destination nodes can decode original files from some authenticated packets.Although network coding has many advantages, especially in wireless sensor network and peer-to-peer network, the encoding mechanism of intermediate nodes also results in some additional security issues.For a powerful adversary who can control arbitrary number of malicious network nodes and can eavesdrop on the entire network, cryptographic signature schemes provide undeniable authentication mechanisms for network nodes.However, with the development of quantum technologies, some existing network coding signature schemes based on some traditional number-theoretic primitives vulnerable to quantum cryptanalysis.In this paper we first present an efficient network coding signature scheme in the standard model using lattice theory, which can be viewed as the most promising tool for designing post-quantum cryptographic protocols.In the security proof, we propose a new method for generating a random lattice and the corresponding trapdoor, which may be used in other cryptographic protocols.Our scheme has many advantages, such as supporting multi-source networks, low computational complexity and low communication overhead.