An Efficient Homomorphic MAC with Small Key Size for Authentication in Network Coding

Abstract

Recently, homomorphic message authentication code (MAC) schemes have been proposed to resist against pollution attacks in network coding. However, existing methods face a common challenge: the generated MAC t belongs to a small finite field F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , which means that an adversary could attack by randomly guessing the value of t, and succeed with probability 1/q. Since q is a predetermined system parameter which is typically set as 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> , the resulted security 1/256 could be unsatisfactory in practice. In this paper, we propose an efficient homomorphic MAC for authentication in network coding. The proposed method achieves a reliable security parameter 1/q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> using only one key, where l could be chosen according to different security requirements. Compared with previous approaches that using multiple tags, the proposed homomorphic MAC has both low computation and communication overheads.