MQ Signatures for PKI

It is well known that multivariate quadratic (MQ) digital signature schemes have small signatures but huge public keys. However, in some settings, such as public key infrastructure (PKI), both variables are important. This paper explains how to transform any MQ signature scheme into one with a much smaller public key at the cost of a larger signature. The transformation aims to reduce the combined size of the public key and signature and this metric is improved significantly. The security of our transformation reduces to that of the underlying MQ signature scheme in the random oracle model. It is possible to decrease signature sizes even further but then its security is related to the conjectured hardness of a new problem, the Approximate MQ Problem (AMQ).