Abstract
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.
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