Proxy Blind Signature Scheme

1. Proxy Blind Signature Scheme Author: Sunder Lai , Amit Kumar Awasthi Source: Journal of Information Science and Engineering Date: Dec/3/2003 Speaker: 陳東怡

2. Outline • Introduction • Proposed Scheme • Efficiency • Security Analysis • Conclusion

3. Introduction • Blind signature: • User C can obtain signature of A on any given message without revealing any information of the message • Proxy blind signature: • The original singer A delegates his signature authority to proxy singer B in such a way B can sign any message on behalf of the original A

4. Introduction • Proxy unprotected: • Proxy and original singer can both generate a valid proxy signature • Proxy protected: • Only proxy can generate a valid signature Original A Signature Authority Proxy blind signature Proxy B User C

5. Proposed Scheme • Notations:

6. Proposed Scheme (cont.) • Proxy phase 1. Proxy Generation • Choose and compute 2. Proxy Delivery • The original singer sends (s, r ) to a proxy B in a secure way and makes public

7. Proposed Scheme (cont.) 3. Proxy Verification • Verify if • if (s ,r) satisfies this congruence, B accepts it as a • valid proxy, otherwise rejects it. • Signing phase 1. B choose a random num computes and sends it to the receiver C

8. Proposed Scheme (cont.) 2. C choose randomly and computes and sends e to B 3. After receiving e, B computes and sends it to C 4. Now C computes The tuple (m, Sp, e’ ) is the proxy blind signature

9. Proposed Scheme (cont.) • Verification phase The verifier of the proxy blind signature computes Here e’’ = e’ if the tuple (m, Sp, e) is a valid proxy signature

10. Proposed Scheme (cont.) • Proxy protected case • Proxy phase • 1. Proxy Generation • Choose and compute • 2. Proxy Delivery • The original singer sends (s, r ) to a proxy B in a secure • way and makes public

11. Proposed Scheme (cont.) • 3. Proxy Verification and key alternation • After confirming the validity of the pair (σ ,r) B • alters the proxy key as The Signing phase and the Verification phase are same as in the proxy unprotected case

12. Efficiency Phase Total Proxy generation Signature generation Signature verification 4E+2M 3E+3M+2I 2E+M 9E+6M+2I where E denotes Exponential computation, M denotes Multiplication load , I denotes Inversion

13. Security Analysis • With different congruence, the original signature and the proxy signature can be distinguished. • It is impossible to create a valid proxy signature without knowing xB or s or both. • Original signer cannot deny his agreement because yp is computed from ya.

14. Conclusion • A proxy blind signature scheme with which a proxy user is able to make proxy blind signature and verifier may verify it very similar to proxy signature schemes.