Chained Threshold Proxy Signature without and with Supervision

Threshold proxy signature (TPS) scheme facilitates a manager to delegate his signing capability to a group of n subordinates without revealing his own private key, such that a subgroup of at least t les n subordinates is required to generate a proxy signature. In reality, the situation can be more complicated. First of all, the subgroup may further delegate proxy signing capabilities to another subgroup of subordinates (in the form of a chain). This is a group-to-group delegation problem. In addition, a supervising agent (SA) may be introduced to supervise the subordinates, such that proxy signing can only be successfully executed with SApsilas agreement. This is a delegation with supervision problem. These two extensions of delegation problems are not solved yet. This paper designs two provably secure cryptographic schemes chained threshold proxy signature (CTPS) scheme and chained threshold proxy signature with supervision (CTPSwS) scheme to solve these two delegation problems.