Connecting the Complexity of MQ- and Code-Based Cryptosystems

We study the connection between the MQ problem and the de­coding problem, through the intermediate MRHS representation. The main goal of this study is to explicitly bound the complexity of solving MQ systems with decoding tools. The main observation is that although the MQ problem over GF(2) can be efficiently transformed to syndrome decoding, the existing general decoding methods are not suitable to solve the system as efficiently as expected from the MQ representation.