On the hardness of the sum of k mins problem

The sum of k mins protocol was proposed by Hopper and Blum as a protocol for secure human identification. The goal of the protocol is to let an unaided human securely authenticate to a remote server. The main ingredient of the protocol is the sum of k mins problem. The difficulty of solving this problem determines the security of the protocol. In this paper, we show that the sum of k mins problem is NP-Complete and W[1]-Hard. This latter notion relates to fixed parameter intractability. We also discuss the use of the sum of k mins protocol in resource-constrained devices.