Threshold Proxy Signature (TPS) scheme facilitates a manager to delegate his signing capability to a group of n2 sub-ordinates without revealing his own private key, such that a subgroup of at least t2 ≤ n2 subordinates is required to generate a proxy signature. In reality, the situation can be more complicated. First of all, the subgroup may further delegate their proxy signing capabilities to another group of n3 subordinates such that at least another subgroup of at least t3 ≤ n3 subordinates are of the proxy signing capabilities (in the form of a chain). t2 can be unequal to t3 depending on the concrete requirement. This is a group-to-group delegation problem. In addition, a supervising agent (SA) may be introduced in the above chain to supervise the subordinates, such that proxy signing can only be successfully executed with SA’s agreement. This is a delegation with supervision problem in the threshold delegation chain described above. 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.
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