臺灣博碩士論文加值系統

繼Mambo等人提出代理簽章法後，因應實際的需求，許多群體導向式的代理簽章法陸續被提出。在本論文中，我們將提出一些群體導向式的代理簽章法。首先提出的是多人授權代理簽章法，多人授權代理簽章法首先由Yi等學者提出，然而他們的方法被Sun學者指出是不安全的，且Sun學者提出了新法。可惜的是，不管是Sun或是Yi等學者所提的方法，都有代理授權憑證大小隨簽章者人數成正比的問題，為解決這個問題，我們提出新的多人授權代理簽章法。為整合多人授權代理簽章法及授權予多人代理簽章法，再提出新的多人授權予多人的代理簽章概念，與兩個多人授權予多人的代理簽章法。另外也提出新的群體授權予群體的門檻式代理簽章法的概念及方法，在所提的方法中有門檻式代理授權及全體同意代理授權的兩種選擇，門檻式代理授權提供較有效率的選擇，而全體同意代理授權則較具彈性。除了符合代理簽章的基本要求外，我們所提出的方法有下列的優點：代理授權憑證的大小固定；不只原始簽章者，代理簽章者也同意代理授權憑證的產生；對原始簽章者及代理簽章者提供公平保護；可以區分代理授權憑證或代理簽章所造成的錯誤；可以防禦內部攻擊。最後，也提出了對一些已知群體導向式的代理簽章法的攻擊。

After Mambo et al. proposed the concept of proxy signatures, many group-oriented proxy signature schemes are proposed due to practical situations. Some new group-oriented proxy signature schemes are proposed. One is the proxy multi-signature scheme. The proxy multi-signature schemes are proposed by Yi et al.. Since Yi et al.’s scheme is insecure, Sun proposed his two proxy multi-signature schemes. However, in both Sun’s and Yi et al.’s schemes, the proxy certificate is proportional to the size of the signers. To overcome this shortage, our scheme is proposed. To integrate proxy multi-signature schemes and multi-proxy signature scheme, we proposed the new concept of multi-proxy multi-signatures. To realize this concept, two multi-proxy multi-signature schemes are proposed. Then another new concept of threshold-proxy threshold-signatures and a corresponding scheme are proposed. The new scheme provides the options for the generation of threshold-proxy certificates: threshold and total agreements. The threshold agreement is more efficient while the total agreement provides flexibility. Except satisfying the basic requirements of proxy signature schemes, our three schemes have many advantages. The size of the proxy certificate is constant. Not only the original group but also the proxy group reach the proxy authorization agreement. The fair protection is provided for the original and proxy signers. Mistakes due to illegal proxy certificates or proxy signatures can be distinguished. Our schemes are secure against the insider attack. Finally, some attacks are proposed on some group-orient proxy signature schemes.

Tables of Contents
Chapter 1 Introduction ………………………………………… P. 01
Chapter 2 Review of the Past Research Results…………… P. 07
2.1 Review of Hwang and Shi’s Scheme…………………… P. 07
2.2 Review of Sun’s Schemes ……………………………… P. 09
2.2.1 Proxy-unprotected Proxy Multi-signature Scheme… P. 09
2.2.2 Proxy-protected Proxy Multi-signature Scheme…… P. 10
Chapter 3 Our Proxy Multi-signature Scheme ……………… P. 12
3.1 Our Proxy Multi-signature Scheme …………………… P. 12
3.2 Security Analysis and Discussions …………………… P. 14
Chapter 4 Our Multi-proxy Multi-signature Schemes……… P. 17
4.1 Our Multi-proxy Multi-signature Scheme with Clerks P. 17
4.2 Our Multi-proxy Multi-signature Schemes without Clerks……………………………………………………………… P. 21
4.3 Security Analysis and Discussions…………………… P. 23
Chapter 5 Our Threshold-proxy Threshold-signature scheme……………………………………………………………… P. 30
5.1 Our Threshold-proxy Threshold-signature Scheme…… P. 31
5.2 Security Analysis and Discussions …………………… P. 38
Chapter 6 The Attacks on Group-orient Proxy Signature Schemes ……………………………………………………………………… P. 44
6.1 The Attacks on Threshold Proxy Signature Schemes… P. 44
6.1.1 Review of Hwang et al.’s Nonrepudiable
Threshold Proxy Signature Scheme with
Known Signers…………………………………………………… P. 44
6.1.2 An insider attack on Hwang et al.’s scheme…… P. 47
6.2 The Attacks on Yi et al.’s Proxy Multi-signature
Schemes………………………………………………… P. 49
Chapter 7 Conclusions ………………………………………… P. 53
References ……………………………………………………… P. 56

List of Tables
Table 1 The Definitions of Symbols ……………………… P. 28
Table 2 The Computation Cost of Multi-proxy
Multi-signature schemes……………………………………… P. 29
Table 3 The Communication Cost of Multi-proxy
Multi-signature Schemes…………………………… P. 29
Table 4 The Computation Cost of
Threshold-proxy Threshold-signature Schemes…………… P. 43
Table 5 The Communication Cost of
Threshold-proxy Threshold-signature Schemes… P. 43

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