量子模糊傳輸及應用

模糊傳送是一種特殊的通訊協定, 被廣泛的應用在許多安全議題及密碼加密上, 例如: 秘密交換、丟銅板問題或簽合約問題等等。模糊傳送的定義是: 傳送者可以送兩段資訊給接收者, 接收者可以從兩個之中選一個, 接收到這個資訊的內容; 而另一個資訊則無法得知其內容。對於傳送者來說, 他並不知道接收者到底收到那一個資訊。也就是說, 這個通訊協定可以傳送若干資訊, 但又無法精確得知所傳送的資訊, 故稱模糊傳送。古典模糊傳送可以用數學的方法來實現, 例如RSA 演算法。然而這些數學方法是建構在困難的數學問題上, 安全性是屬於有條件的安全性(conditional security)。我們可以用量子的方法來破解之。為了解決這樣子的問題, 本計畫希望建立一個無條件的安全性(unconditional security), Popescu and Rohrlich 提出一個”non-locality machine” 簡稱 PR-Box。模糊傳送可以用PR-Box 來實現, 而PR-Box 亦可用量子纏繞的特性來建立, 其安全性是無條件的安全性。這樣的量子模糊傳送系統可以被用在許多應用上, 我們用這樣的系統發展一個簽合約的協定, 以及討論其安全性。

關鍵字

量子；密碼學；模糊傳輸；電子合約

並列摘要

Oblivious transfer, a special communication protocol, is widely used in various variants of security issue or cryptographic application such as Contrast Signing, Secrets Exchange, Coin Flipping and so on. Oblivious transfer allows a party to sent two messages to the receiver who can choose one of them and learn it, remaining ignorant about the other, while the sender who has no ideal about what the receiver choice. In other words, this is a protocol by which a sender sends some information to the receiver, but remains oblivious as to what is sent. Oblivious transfer has been developed in many different forms since it was introduced in 1981 by Michael O. Robin. The so-called Robin’s oblivious transfer means: sender sends information to receiver with probability 1/2, while the sender is not sure whether the receiver obtain it or not. And the form mentioned above, a more useful one, is called 1-2 oblivious transfer or 1-out-of-2 oblivious transfer. Besides, string and bit oblivious transfer is discussed in detail for implementation. All of these forms have been used in various problems of cryptography and implementation by mathematical method Nevertheless, mathematical method such as RSA scheme, which is based on difficult mathematical problem, is a conditional secure way. We can use quantum method to defeat these systems and it will not be secure any more. Therefore, we try to resolve this issue by quantum way. Popescu and Rohrlich have provided a ”non-locality machine” or ”PR machine,” which can realize oblivious transfer and we can build PR machine by quantum entanglement. This quantum oblivious transfer system, mentioned above, can be used in many applications. We present a contract signing protocol based on our system, quantum oblivious transfer, and discuss the security of this system.

並列關鍵字

Quantum ； Cryptography ； Oblivious Transfer ； Electronic Contract

參考文獻

[1] Ardehali, M. (1995), “Quantum oblivious transfer protocols based on epr

[2] Bellare, Mihir and Micali, Silvio (1990), “Non-interactive oblivious transfer

[3] Cr´epeau, Claude (1988), “Equivalence between two flavours of oblivious

transfers”, in CRYPTO87, volume 293.

mental game”, in Proceedings of the nineteenth annual ACM conference on

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量子模糊傳輸及應用

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