1. Identity Base Threshold Proxy Signature Jing Xu, Zhenfeng Zhang, and Dengguo Feng Form eprint Presented by 魏聲尊

2. Outline Introduction Definition (t,n) threshold proxy Signature Scheme Conclusion

3. Introduction Proxy signature allow original signature to delegate his singing capability to another user ID Base :public key can derive via a public algorithm

4. Introduction (t,n) threshold proxy signature scheme: Applications: e-cash, mobile agent, mobile communication etc. Original user Proxy group of n member >=t

5. Definition Security Requirement of ID-Base Threshold Proxy Signature –Distinguishability –Secrecy –Proxy Protected –Unforgeability –Nonrepudiation

6. The bilinear pairing: G be a cyclic additive group generated by P, order = q (prime), V be a multiplicative group of same order. Let be a pairing which satisfies the following condition: 1.Bilinearity:,That is,. 2.Non-degeneracy:,such that 3.Computability:,there is an efficient algorithm to compute Definition

7. Param-generation Key-generation Secret-share-generation Proxy-share-generation Proxy-signature-generation Proxy-signature-verification Proposed (t,n) threshold proxy Signature Scheme

8. Param-generation –Pick a random master key and set –Choose hash functions –original signer be the proxy group of n proxy signer Key-generation: –Compute and associated private key for original signer and proxy signers

9. Proposed (t,n) threshold proxy Signature Scheme Secret-share-generation –Each randomly chooses a (t-1)-degree polynomial with random coefficients and publish – sends to, can validate it by checking the equality – compute his secret share and publish

10. Proposed (t,n) threshold proxy Signature Scheme Proxy-share-generation: Let be the warrant. in PS gets their own proxy singing key share as follow: –1. first randomly choose and computes Let.Then he compute The signature on is. Finally, sends and to each –2. verify the signature by if is accept, compute as his own proxy secret

11. Proposed (t,n) threshold proxy Signature Scheme Proxy-share-generation: –3. randomly chooses a (t-1)-degree polynomial with random coefficients and publishes can be got by each proxy signer as Furthermore, sends to –4. can validate it by. compute his proxy singing key share and publish

12. Proposed (t,n) threshold proxy Signature Scheme Proxy-signature-generation: Let be the actual proxy signature 1. Lagrange interpolation formula to compute,Let 2. Each compute his own proxy signature share by compute and 3.designated clerk validate by if it accept, computes The proxy signature of m is Proxy-signature-verification verify proxy signature by

13. Proposed (t,n) threshold proxy Signature Scheme >=t Original signer n proxy signer Designer clerk

14. Conclusion Security –Distinguishability: warrant and the public keys of the original signer and the proxy signer must in occur in the verification equation of threshold proxy scheme –Secrecy: because of the ID-Base signature scheme, any party private key must be kept secret. –Proxy Protected: the original signer does know private key –Unforgeability: without the private key, no one can forge the proxy – singer to create and pass the verification –Nonrepudiation: the valid proxy signature contain the warrant The first ID-Base threshold proxy signature scheme