Oil and Vinegar

This chapter deals with multivariate signature schemes following the concept of Oil and Vinegar. After introducing the basic (balanced) Oil and Vinegar (OV) signature scheme, we describe its cryptanalysis by the incvariant subspace attack of Kipnis and Shamir and how this attack is prevented in the unbalanced Oil and Vinegar scheme (UOV). We then introduce the signature scheme Rainbow, which can be seen as multi-layer version of UOV and discuss its security and efficiency. Finally, we present techniques to reduce the public key size of UOV and Rainbow.