1. A New Multi-Proxy Multi- Signature Scheme Source: National Computer Symposium, vol. F, Taiwan, pp. 19-26, 2001 Author: Shin-Jia Hwang and Chiu-Chin Chen Presenter: Li-Tzu Chang

2. Outline Introduction A new multi-Proxy multi-signature scheme  The proxy certificate generation phase  The multi-proxy multi-signature generation phase  The multi-proxy multi-signature verification phaes Conclusions

3. Introduction Original group of signers can authorize a group of proxy signers under the agreement of all signers both in the original group and proxy group. Then only the cooperation of all singers in proxy could generate multi-proxy multi-signatures. 代理簽章具有下列特點  Distinguishability  Unforgeability  Identifiability  Undeniability

4. Introduction 代理簽章之授權型態  完全授權  部分授權  授權憑證  結合授權憑證之部分授權

5. Outline Introduction A new multi-Proxy multi-signature scheme  The proxy certificate generation phase  The multi-proxy multi-signature generation phase  The multi-proxy multi-signature verification phaes Conclusions

6. A new multi-Proxy multi-signature scheme U i : original signer. i=1,…,n x ui : private key of U i y ui : public key of U i,such that y ui = g x ui mod p Pj: proxy signer, j=1,…,m x pj : private key of P j y pj : public key of P j,such that y pj = g x pj mod p w: proxy warrant M:

7. A new multi-Proxy multi-signature scheme The proxy certificate generation phase Step 1: Each original signer U i select a random integer, compute Each proxy signer P j select a random integer, compute Step 2: Each signer compute Step 3: Each signer compute

8. A new multi-Proxy multi-signature scheme The proxy certificate generation phase Step 4: Each signer verifies the correctness of v t. Step 5: If v t equations hold, each member of the proxy group P j compute

9. A new multi-Proxy multi-signature scheme The multi-proxy multi-signature generation phase

10. A new multi-Proxy multi-signature scheme The multi-proxy multi-signature generation phase

11. A new multi-Proxy multi-signature scheme The multi-proxy multi-signature verification phaes

12. Outline Introduction A new multi-Proxy multi-signature scheme  The proxy certificate generation phase  The multi-proxy multi-signature generation phase  The multi-proxy multi-signature verification phaes Conclusions

13. Does not need secure channels. Provides the distinguishability and identifiability functions. Against the insider attack.