1. Certificateless Threshold Ring Signature Source: Information Sciences 179(2009) 3685-3696 Author: Shuang Chang, Duncan S. Wong, Yi Mu, Zhenfeng Zhang Presenter: Chun-Yen Lee

2. Outline  Introduction  Definition  Proposed scheme  Conclusion

3. Introduction  2001 Rivest et al. Ring signature  2002 Bresson et al. extended the notion of ring signature to threshold setting  2003 Al-Riyami and Paterson certificateless public key cryptography

4.  Ring signature spontaneity anonymity  Threshold setting key escrow  certificateless public key cryptography

5. Outline  Introduction  Definition  Proposed scheme  Conclusion

6. Definition  SetUp  MasterKeyGen  PartialKeyGen  UserKeyGen  Sign  Verify

7. Outline  Introduction  Definition  Proposed scheme  Conclusion

8. An efficient 1-out-of-n certificateless ring signature A t-out-of-n certificateless Threshold Ring Signature (CL-TRS)

9. An efficient 1-out-of-n certificateless ring signature  SetUp Input: Output: param  MasterKeyGen Input: param Randomly pick a master secret key Master public key

10. An efficient 1-out-of-n certificateless ring signature  PartialKeyGen Input (param, msk, ID)  UserKeyGen Input (param, mpk, ID) Randomly pick a user secret key user public key

11. An efficient 1-out-of-n certificateless ring signature  Sign Input (param, mpk, R, S, m)   Randomly pick  Compute

12. An efficient 1-out-of-n certificateless ring signature  Compute  Compute  The signature is

13. An efficient 1-out-of-n certificateless ring signature  Verify Input (param, mpk, R, 1, S, m, σ) if

14. An efficient 1-out-of-n certificateless ring signature A t-out-of-n certificateless Threshold Ring Signature (CL-TRS)

15. CL-TRS  Sign Input (param, mpk, R, S, m) 1.

16. CL-TRS 2. 3. Compute  construct a polynomial f of degree n-t f(0)=c, f(i)=c i

17. CL-TRS 4. Compute 5.Compute The signature is

18. CL-TRS  Verify Input param, mpk, R, t, m, the degree of polynomial f is n-t

19. Outline  Introduction  Definition  Proposed scheme  Conclusion

20. Conclusion  The author proposed one efficient 1-out-of-n CL-TRS and another t-out-of-n CL-TRS.  Both of them are more efficient than previous ones in both computational complexity and signature size.