A Novel Homomorphic MAC Scheme for Authentication in Network Coding

Abstract

Recently, homomorphic message authentication code (MAC) schemes have been proposed to thwart pollution attacks in network coding. However, existing schemes adopt the inner product operation to construct the MAC, which could be broken with probability Pr=1/q, where the predetermined system parameter q 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> . Usually, the homomorphic MAC with a security parameter Pr=1/2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> may not be sufficient in practice. In this letter, we propose a novel scheme and its key idea is to employ the trace function over a finite field to construct the homomorphic MAC. The proposed method could achieve a reliable security Pr=1/q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> without increasing the field size or employing multiple keys, where l is a positive integer greater than or equal to 1.