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Org/2005/116 22. : Short signatures without random oracles. L. ) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004) 23. : Eﬃcient selective-ID secure identity based encryption without random oracles. L. ) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. au Abstract. A proxy signature scheme allows an entity to delegate its signing capability to another entity (proxy) in such a way that the proxy can sign messages on behalf of the delegator. Proxy signatures have found numerous practical applications such as distributed systems, mobile agent applications, etc.

Springer, Heidelberg (2004) 17. : Proxy Signature: Delegation Of the Power to Sign Messages. IEICE Trans. Fundamentals E79-A(9), 1338–1353 (1996) 18. : A Proposal of Short Proxy Signature Using Pairing. In: International Conference on Information Technology (ITCC 2005), pp. 631–635. IEEE Computer Society Press, Los Alamitos (2005) 19. : Extended Proxy Signatures for Smart Cards. , Mambo, M. ) ISW 1999. LNCS, vol. 1729, pp. 247–258. Springer, Heidelberg (1999) Identity-Based Proxy Signature from Pairings 31 20.

24 W. Wu et al. 1 Bilinear Pairing Let G1 be a cyclic additive group of prime order q, P is the generator of G1 , GT denotes a multiplicative group of the same order. Let e : G1 × G1 → GT be a bilinear pairing with the following properties: – e is bilinear: e(aP, bP ) = e(P, P )ab , for all a, b ∈ ZZ q . – e is non-degenerate: e(P, P ) = 1GT . – e is eﬃciently computable. We say G1 is a bilinear group if there exists a group GT , and a bilinear pairing e : G1 × G1 → GT as above, and e, and the group action in G1 and GT can be computed eﬃciently.