Multi-proxy signature and 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 pairing-based signature schemes have been proposed. In this paper, we propose a multi-proxy signature scheme and a proxy multi-signature scheme from bilinear pairings. We also show that both of them satisfy all the security properties required by proxy signatures.