選擇性隱蔽傳輸協定的設計與分析

Abstract

選擇性隱蔽傳輸協定(Oblivious Transfer¸簡稱OT)是一種資訊傳輸的技術。當傳送者擁有一些秘密並且也願意讓接收者自由選擇並得知其中的一個秘密時¸運用選擇性隱蔽傳輸能確保接收者的選擇和傳送者的其他祕密均不會洩露。這種技術已經衍生出很多種類型和許多應用。例如: 將隱密資訊獲取協定(PIR)轉換到對等式隱密資訊獲取協定(SPIR) ¸選擇性隱蔽取樣¸資料庫查詢和選擇性隱蔽式的秘密運算等應用。 在本篇論文中¸我們提出了一種有效率的N中取1選擇性隱蔽傳輸協定¸在這個協定中¸我們對於接收秘密者的選擇做了以2為底的編碼。接著我們又發現改變編碼時的底數¸可以把協定過程中資料交換的數量減到最少。最後經過更改底數的N取1選擇性隱蔽傳輸協定需要三個回合的資料傳輸¸而交換的資料總數也縮小到N+7 +1。另外¸我們也可以經由平行的執行k份N取1選擇性隱蔽傳輸協定而建構出一個N中取K的選擇性隱蔽傳輸協定。

Oblivious transfer (OT) is a technique by which a party S owning some secrets , can transfer one of them to another party R. This is done in a way that does not release any information about the other secrets to R nor any information about R’s choice to S. The OT protocol has been developed into a number of types and has many practical applications, such as turning private information retrieval to symmetric private information retrieval, oblivious sampling, adaptive database query, and oblivious secure computation, etc. In this thesis we propose an efficient 1-out-of-N Oblivious Transfer scheme based on the binary expression of the index of the receiver’s choice. We then find if the index is expressed by ternary digits, the total number of messages exchanged can minimized. The resulting 1-out-of-N OT scheme requires 3 rounds, and the total number of messages exchanged is minimized to N+7 +1. A k-out-of-N OT scheme can be easily obtained by k parallel runs of the 1-out-of-N OT scheme.