臺灣博碩士論文加值系統

原始簽章者可以透過(t,l)門檻式代理簽章系統將自己的簽章權限分散授權給一個有l位簽章參與者者的代理群體。在獲得授權後，只有t個以上的簽章參與者合作可以產生合法的代理簽章。
在本論文中，提出第一個以GQ簽章協定為基礎的(t,l)門檻式代理簽章系統。這個系統符合代理簽章所需滿足的所有需求；並且在動態攻擊者的假設環境下，依舊符合門檻式簽章的所有安全需求。

A (t,l) threshold proxy signature is a signature scheme that is designed to delegate the original signer signing capability to a designated group of l proxy signers. Only any t or more proxy signers of the designated group can generate the proxy signature behalf of the original signer.
In this thesis, we propose the first (t,l) threshold proxy signature scheme based on GQ signature. The proposed scheme satisfies all requirements of a proxy signature and a threshold signature under adaptive adversary.

第一章 引言 1
第一節 研究動機 1
第二節 研究重點與成果 3
第三節 各章節簡介 4
第二章 相關研究 5
第一節 代理簽章系統 5
第二節 (t,l)門檻式簽章系統 9
第一小節 私密分享 9
第二小節 (t,l)門檻式簽章系統及相關研究 10
第三節 門檻式代理簽章系統 13
第三章 基本的技術與原理 15
第一節 相關定理與假設 15
第一小節 以數論為基礎的假設 15
第二小節 零知識互動式證明系統 16
第二節 隨機可驗證私密分享協定 17
第三節 分散式金鑰產生協定 21
第四節 GQ簽章系統 25
第五節 以GQ簽章為基礎的代理簽章系統 26
第四章 以GQ簽章為基礎的門檻式代理簽章系統 30
第一節 問題分析 30
第二節 以GQ簽章為基礎的門檻式代理簽章系統 32
第三節 門檻式簽章系統特性分析 36
第一小節 正確性分析 36
第二小節 安全性分析 37
第四節 代理簽章系統特性分析 41
第五章 結論與未來研究方向 44
參考文獻 45
附錄 48

[1] R. Canetti, R. Gennaro, S. Jarecki, H. Krawczyk and T. Rabin, “Adaptive security for threshold systems,” In Proceedings of Advances in Cryptology - Crypto’99, vol. 1666 of LNCS, pp. 98-115, Springer-Verlag, 1999.
[2] C.K. Chu, L.S. Liu and W.G. Tzeng, “A Threshold GQ Signature Scheme,” In Crptology ePrint Archive 2003-016 , http://eprint.iacr.org/2003/016.ps, 2003.
[3] M. Cerecedo, T. Matsumto, and J. Iami, “Efficient and secure multiparty generation of digital signatures based on discrete logarithms,” In Proceedings of IEICE Transaction on Fundamentals, E76-A(4):532-545, 1993.
[4] A. De Santis, Y. Desmedt, Y. Frankel and M.Yung, “Who to share a function securely,” In Proceeding of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 522-533, Montre’alMay, Que’bec, Canada, 23-25 May, 1992.
[5] Y. Desmedt and Y. Frankel, “Threshold cryptosystems,” In Proceedings of Advances in Cryptology - Crypto’89, vol. 435 of LNCS, pp. 307-315, Springer-Verlag, 1989.
[6] Y. Desmedt and Y. Frankel, “Shared generation of authentications and signatures,” In Proceedings of Advances in Cryptology - Crypto’91, vol. 576 of LNCS, pp. 457-469, Springer-Verlag, 1992.
[7] Y. Desmedt and Y. Frankel, “Parallel reliable threshold multisignature,” In Technical Report TR-92-04-02, April, Dept. of EE and CS, Univ. of Wisconsin Milwaukee, 1992.
[8] Y. Frankel, P. D. MacKenzie and M. Yung, “Adaptive-secure optimal- resilience proactive RSA,” In Proceedings of Advances in Cryptology - AsiaCrypt’99, vol. 1716 of LNCS, pp. 180-194, Springer-Verlag, 1999.
[9] R. Gennaro, S. Jarecki, H. Krawczyk and T. Rabin, “Robust Threshold DSS Signatures,” In Proceedings of Advances in Cryptology - EuroCrypt’96 , vol. 1070 of LNCS, pp. 354-371, Springer-Verlag, 1996.
[10] R. Gennaro, S. Jarecki, H. Krawczyk and T. Rabin, “Robust and Efficient Sharing of RSA Functions,” In Proceedings of Advances in Cryptology - Crypto’96, vol. 1109 of LNCS, pp. 157-172, Springer-Verlag, 1996.
[11] R. Gennaro, S. Jarecki, H. Krawczyk and T. Rabin, “Secure distributed key generation for discrete-log based cryptosystems,” In Proceedings of Advances in Cryptology - EuroCrypt’99, vol. 1592 of LNCS, pp. 295-310, Springer-Verlag, 1999.
[12] K.S. Huang, “Time Bounded Proxy Signature,” National Chiao Tung University ,Master Thesis, 2002.
[13] J. Herranz and G. Sa’ez, “Fully distributed proxy Signatures,” In Crptology ePrint Archive 2002-051 , http://eprint.iacr.org/2002/051.ps, 2002.
[14] S. Kim, S. Park and D. Won, “Proxy signatures, revisited,” In Proceedings of International Conference on Information and Communication Security, vol. 1334 of LNCS, pp. 223-232, Springer- Verlag, 1997.
[15] J. Lee, J. Cheon and S. Kim, “An Analysis of Proxy Signatures: Is a Secure Channel Necessary?,” In Proceedings of Advances in Cryptology - CT-RSA ‘03, vol. 2612 of LNCS, pp. 68-79, Springer-Verlag, 2003.
[16] B. Lee and K. Kim, “Strong Proxy Signatures,” IEICE Transactions on Fundamentals, vol. E82-A, No. 1, 1999.
[17] B. Lee, H. Kim and K. Kim, “Strong Proxy Signature and its Applications,” In Proceedings of Symposium on Cryptography and Information Security, vol. 2/2, pp. 603-608, 2001.
[18] M. Mambo, K. Usuda, and E. Okamoto, “Proxy signatures for delegating signing operation,” In Proceedings of the 3rd ACM Conference on Computer and Communications Security, pp. 48-57, 1996.
[19] M. Mambo, K. Usuda, and E. Okamoto, “Proxy Signatures: Delegation of the Power to Sign Messages,” IEICE Transactions on Fundamentals, vol. E79-A, no. 9, pp. 1338-1354, 1996.
[20] T.P Pedersen, “Non-interactive and information-theoretic secure verifiable secret sharing,” In Proceedings of Advances in Cryptology - Crypto’91, vol. 576 of LNCS, pp. 129-140, Springer-Verlag, 1991.
[21] R. Rivest, A. Shamir and L. Adleman. “A method for obtaining digital signature and public key cryptosystems,” Communication of ACM, vol. 21, no. 2, pp. 120-126, 1978.
[22] V. Shoup. “Practical threshold signature,” In Proceedings of Advances in Cryptology - EuroCrypt’00, vol. 1807 of LNCS, pp. 207-220, Springer-Verlag, 2000.
[23] A. Shamir. “How to share a secret,” Communications of the ACM, 22(11), pp. 612-613, Nov. 1979.
[24] D.R.Stinson and R. Strobl, “Provably Secure Distributed Schnorr Signatures and a (t, n) Threshold Scheme for Implicit Certificates,” In Sixth Australian Conference on Information Security and Privacy (ACISP 2001), vol. 2119 of LNCS, pp. 417-434, Springer-Verlag, 2001.
[25] K. Zhang, “Threshold proxy signature schemes,” In Proceedings of 1st International Information Security Workshop, vol. 1396 of LNCS, pp. 282-229 Springer-Verlag, 1998.