本文選題：安全多方計(jì)算 + 計(jì)算幾何　； 參考：《西安科技大學(xué)》2017年碩士論文

【摘要】：安全多方計(jì)算(Secure Multi-party Computation,SMC)是指在一個(gè)互相不信任的計(jì)算環(huán)境中,n個(gè)參與者利用各自的私有信息共同計(jì)算一個(gè)函數(shù)。計(jì)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(hù)隱私的分布式計(jì)算都?xì)w結(jié)于此,比如:統(tǒng)計(jì)分析、比較相等、科學(xué)計(jì)算、計(jì)算幾何、數(shù)據(jù)挖掘等。本文主要圍繞保密計(jì)算幾何中的兩類(lèi)問(wèn)題:幾何問(wèn)題和集合問(wèn)題,進(jìn)行了研究。首先,針對(duì)幾何問(wèn)題,研究了如何保護(hù)隱私的判斷空間位置關(guān)系。已存方案大多是通過(guò)轉(zhuǎn)化為距離或數(shù)據(jù)對(duì)應(yīng)成比例問(wèn)題解決的,計(jì)算復(fù)雜性較高、應(yīng)用范圍受限且為計(jì)算性安全。針對(duì)這些問(wèn)題,本文先將原問(wèn)題轉(zhuǎn)化為一個(gè)點(diǎn)是否為一個(gè)方程的解,再利用一種簡(jiǎn)單高效的內(nèi)積協(xié)議一次性解決了點(diǎn)線(xiàn)、點(diǎn)面、線(xiàn)線(xiàn)、線(xiàn)面、面面等5種空間位置關(guān)系的判定。本文方案沒(méi)有利用任何公鑰加密算法,取得了信息論安全。其次,針對(duì)集合問(wèn)題,研究了如何保護(hù)隱私的判斷集合成員關(guān)系和如何計(jì)算集合交集的勢(shì)。已存方案大多是通過(guò)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(wèn)題來(lái)解決,計(jì)算繁瑣,效率低。針對(duì)這兩個(gè)問(wèn)題,本文首先設(shè)計(jì)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(wèn)題。其次,又設(shè)計(jì)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(shì)的兩種方法。其中一種方法沒(méi)有利用任何公鑰加密算法,取得了信息論安全。最后,本文對(duì)所有協(xié)議的正確性、安全性和復(fù)雜性進(jìn)行了理論分析,證明本文設(shè)計(jì)的協(xié)議是高效安全的,且具有實(shí)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(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP309;O18

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本文編號(hào)：1770174