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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/5936

Title: Paillier密碼系統之探討與同形加密的應用
A study on Paillier Cryptosystem and its application
Authors: Ching-Yi Chen
Contributors: NTOU:Department of Computer Science and Engineering
Keywords: Paillier密碼系統;同形加密;零知識證明;秘密分享
Paillier cryptosystem;homomorphic encryption;zero knowledge proof;secret sharing
Date: 2003
Issue Date: 2011-06-22T08:42:04Z
Abstract: 隨著網路技術的日趨成熟,伴隨而來的網路安全問題也日趨嚴重,為了保護個人私密資料免於外洩,相關密碼學技術及各種密碼系統的協定與應用紛紛傾囊而出。 在本篇論文中我們實作了Paillier[4]密碼系統,提出一個產生Paillier密碼系統鑰匙的演算法並符合其各項性質,補充了在Paillier[4]中所缺少的相關定理與證明,在論文中我們提出了兩個植基於Paillier密碼系統同形性質的應用,分別為安全的投票協定與安全的競標協定。在安全的投票協定方面,我們提出的協定適用於小型會議的選舉,不需要公布候選人的得票數就可以公證的決定當選者,我們使用了一個可信賴的第三者來分享密鑰,以零知識證明來確保投票過程的合法性,使用mix and match的子協定在不洩露候選人得票數的前提下來比較得票數多寡,整個投票過程都是可公開驗證的;在安全的競標協定方面,我們採用Paillier同形密文向量做為投標者的出價表示方法,每一個投標者出價時必須附上非交談式的零知識證明來證明出價的格式是符合規定的,我們使用了一個可信賴的第三者來分享密鑰,最後所有參與的競標者配合聯合解密來決定拍賣結果,整個競標過程符合可公開驗證性、私密性與不可否認性。
As internet technology advances, there are more and more electronic applications launched on the internet. The security issues of these applications become increasingly. In order to protect personal datas against improperly disclosing, the reseau lies on cryptography-technology, cryptosystems and their applications are roaming. In this thesis, we implement the Paillier[4] cryptosystem, propose a key- generator algorithm and supply some theorems and proofs which were missing in the original Paillier[4]’s paper. Then, we propose two applications based on Paillier cryptosystem : the secure voting protocol and the secure auction protocol. In the secure voting protocol, we propose an election scheme which is suitable for a small-scale meeting. It can decide the winning candidates without announcing vote-count for each candidate. We use a share-key scheme without a trusted third party, the correctness of each secret ballot is guaranteed by zero knowledge proofs. The privacy of each vote-count in a pairwise ciphertext comparison is maintained by the ‘mix-and-match’ sub-protocol. The whole voting process can be verified publicly ; In the secure auction protocol, we use a vector of homomorphic ciphertexts to represent the bidding of a bidder. Each bidder must append non-interactive zero knowledge proofs to prove that the submitted bidding is valid. We use a share-key scheme without a trusted third party. All participants join at the end of the auction decrypt as the protocol specifies. The whole auction process achieves the public verifiability, bidding privacy and undeniability.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M91570019
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