本文選題：安全多方計算 + 計算幾何�。� 參考：《西安科技大學》2017年碩士論文

【摘要】：安全多方計算(Secure Multi-party Computation,SMC)是指在一個互相不信任的計算環(huán)境中,n個參與者利用各自的私有信息共同計算一個函數(shù)。計算結(jié)束后,每一方都能得到正確的結(jié)果,并且每一方除了自己的輸入和輸出外,不能得到其它方的任何數(shù)據(jù)。保護隱私的分布式計算都歸結(jié)于此,比如:統(tǒng)計分析、比較相等、科學計算、計算幾何、數(shù)據(jù)挖掘等。本文主要圍繞保密計算幾何中的兩類問題:幾何問題和集合問題,進行了研究。首先,針對幾何問題,研究了如何保護隱私的判斷空間位置關系。已存方案大多是通過轉(zhuǎn)化為距離或數(shù)據(jù)對應成比例問題解決的,計算復雜性較高、應用范圍受限且為計算性安全。針對這些問題,本文先將原問題轉(zhuǎn)化為一個點是否為一個方程的解,再利用一種簡單高效的內(nèi)積協(xié)議一次性解決了點線、點面、線線、線面、面面等5種空間位置關系的判定。本文方案沒有利用任何公鑰加密算法,取得了信息論安全。其次,針對集合問題,研究了如何保護隱私的判斷集合成員關系和如何計算集合交集的勢。已存方案大多是通過轉(zhuǎn)化為多次元素匹配查找、多次加密與多次調(diào)用內(nèi)積協(xié)議的問題來解決,計算繁瑣,效率低。針對這兩個問題,本文首先設計了一種新的0-1編碼,然后結(jié)合同態(tài)加密解決了集合成員判定問題。其次,又設計了其他兩種新的編碼:0-R編碼與1-0編碼,并分別結(jié)合同態(tài)加密、置換協(xié)議和內(nèi)積協(xié)議給出了解決集合交集勢的兩種方法。其中一種方法沒有利用任何公鑰加密算法,取得了信息論安全。最后,本文對所有協(xié)議的正確性、安全性和復雜性進行了理論分析,證明本文設計的協(xié)議是高效安全的,且具有實際意義。
[Abstract]:Secure Multi-party Computing (SMC) means that in a computing environment with mutual distrust, n participants use their private information to calculate a function together.After the calculation, each side can get the correct results, and each side can not get any data except their own input and output.The privacy of distributed computing is attributed to this, such as: statistical analysis, comparative equality, scientific computing, computational geometry, data mining and so on.This paper focuses on two kinds of problems in the geometry of secure computing: geometric problem and set problem.First of all, we study how to protect privacy to judge the spatial position relation for geometric problems.Most of the existing schemes are solved by transforming them into distance or data proportional problems, which have high computational complexity, limited application scope and computational security.In order to solve these problems, this paper first transforms the original problem into the solution of whether a point is an equation or not, and then uses a simple and efficient inner product protocol to determine the spatial position relationship of point line, point surface, line line, line surface and surface.This scheme does not use any public key encryption algorithm, and obtains information theory security.Secondly, for the set problem, we study how to protect the privacy of the set membership and how to calculate the potential of the set intersection.Most of the existing schemes are solved by transforming them into multiple element matching searching, multiple encryption and multiple calls to the inner product protocol. The calculation is tedious and the efficiency is low.In order to solve these two problems, a new 0-1 encoding is designed, and then the problem of judging set members is solved with homomorphic encryption.Secondly, we design two new codes: 0-R code and 1-0 code, and give two methods to solve the set intersection potential by combining homomorphic encryption, permutation protocol and inner product protocol, respectively.One of the methods does not use any public key encryption algorithm to obtain information theory security.Finally, the correctness, security and complexity of all the protocols are analyzed theoretically, which proves that the protocol designed in this paper is efficient and secure, and has practical significance.
【學位授予單位】：西安科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP309;O18

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本文編號：1770174