1. Server-Aided Verification : Theory and Practice Source: ASIACRYPT 2005, LNCS 3788, pp. 605-623 Author: Marc Girault and David Lefranc Presenter: Chun-Yen Lee

2. First SAV Protocols for Pairing-Based Schemes Zhang, Safavi-Naini and Susilo – ZSNS signature scheme Boneh-Boyen signature schemes

3. First SAV Protocols for Pairing-Based Schemes Verifier checks if f is a public function I : public parameters including the public key (r, sigma): signature

4. First SAV Protocols for Pairing-Based Schemes Verifier

5. Proof Auxiliary completeness. Auxiliary soundness. Computational gain. Auxiliary non-repudiation.

6. Application to the ZSNS Signature Scheme Auxiliary completeness – Auxiliary non-repudiation – SAV construction allow the misbehaving prover to send any value. – Then, during the computation of, transmit the right value to – I is finally.

7. Application to the ZSNS Signature Scheme Signer – public parameters – public key U – private key x – signature Verifier

8. Application to the ZSNS Signature Scheme π : ZSNS signature scheme π* : generic protocol : verification of the equation

9. Lemma 2. – Assuming – if communicating with q H : hash oracle; q S : signing oracle – I be with a probability – q-BCAA problem (q ≥ q H + q S − 1 ) Application to the ZSNS Signature Scheme

10. S1 – A – l H S2 – makes a hash query – A answers w i and adds the couple (m i,w i ) in l H Application to the ZSNS Signature Scheme

11. S3 – A S H – makes a signing query m i if has been queried to the hash oracle – there exists a unique couple (m i,w i ) in l H ; – if,then A fails, otherwise A answers if has not been queried to the hash oracle – A answers – (m i,h i ) in l H ; h i in S H Application to the ZSNS Signature Scheme

12. S4 After making all the queries to the oracles – outputs a couple ( ). If & ( )is such that A sends to the value Otherwise, A fails and then stops S5 Finally, answers a value – If – A the couple ( ) Application to the ZSNS Signature Scheme

13. A end if : 1. S3, the messages queried to the signing oracle are all different from which occurs with a probability equal to 2.S4, If & ( )is such that – 3.S5, answers a value – Application to the ZSNS Signature Scheme

14. Conclusion 1.We have formalized the concept of a server- aided verification protocol. 2.We have analyzed in new model. 3.We have presented a generic SAV protocol for pairing-based schemes.