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

3. Ring signature Introduction

4. Ring signature Introduction Public Key Secret Key

5. Ring signature Introduction Public Key Secret Key

6. Ring signature Introduction Public Key Secret Key

7. 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

8. Outline  Introduction  Definition  Proposed scheme

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

10. Definition  SetUp System parameters (param)  MaterKeyGen master public key (mpk) master secret key (msk)

11. Definition  PartialKeyGen  UserKeyGen Master Public Key Master Secret Key params ID params ID user partial key (psk) user secret key (usk) user public key (upk)

12. Definition Public Key Secret Key Sign verify

13. Sign Definition Public Key Secret Key verify

14. Outline  Introduction  Definition  Proposed scheme

15. 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

16. 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

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

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

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