ID-based multi-proxy signature, proxy multi-signature and multi-proxy multi-signature schemes from bilinear pairings

In electronic world, proxy signature is a solution of delegation of signing capabilities. Proxy signatures can combine other special signatures to obtain some new types of proxy signatures. Due to the various applications of the bilinear pairings in cryptography, many identity based signature schemes have been proposed. In this paper, we propose an identity based multi-proxy signature scheme and an identity based proxy multi-signature scheme from bilinear pairings. Both of them can be regarded as a special case of corresponding variants of identity based threshold signature scheme. Based on these two schemes, we propose an identity based multi-proxy multi-signature scheme.