發(fā)布時間：2018-06-22 04:11

  本文選題：秘密共享 + 存取結(jié)構(gòu)�。� 參考：《陜西師范大學(xué)》2014年博士論文

【摘要】：秘密共享是密碼學(xué)中的重要工具。它是構(gòu)建許多安全協(xié)議和分布式計算,如安全多方計算、門限秘密、保密數(shù)據(jù)挖掘、訪問控制、通用不經(jīng)意傳輸、拜占庭協(xié)議等的基礎(chǔ)工具。在現(xiàn)代密碼學(xué)中占有重要的地位。盡管秘密共享為構(gòu)建上述安全協(xié)議提供了一種解決思路,但應(yīng)用環(huán)境的復(fù)雜性給利用秘密共享構(gòu)建其它安全協(xié)議帶來了極大的挑戰(zhàn),還有待進(jìn)一步研究。如在多秘密共享中可能存在分發(fā)者欺騙問題,需要進(jìn)行秘密和子份額的真?zhèn)悟炞C。特別是在安全多方計算和隱私保護(hù)數(shù)據(jù)挖掘的應(yīng)用領(lǐng)域中,多秘密共享方案中多秘密和子份額的有效驗證問題是急需解決的問題。 針對保密數(shù)據(jù)挖掘、安全多方計算以及無線網(wǎng)絡(luò)中密鑰管理等應(yīng)用場景的安全需求,研究了安全多方計算的相關(guān)知識,并給出了立體幾何問題的安全多方計算協(xié)議。結(jié)合橢圓曲線的離散對數(shù)和因子分解假設(shè)以及范德蒙行列式的性質(zhì)等,從安全性和實用性角度對如何構(gòu)造高效的可證的秘密共享方案進(jìn)行了相關(guān)研究。另外,判定秘密共享方案優(yōu)劣的一個重要指標(biāo)是確定給定的存取結(jié)構(gòu)秘密共享方案的信息率的大小。構(gòu)建信息率為1的理想秘密共享也是很重要的研究問題。結(jié)合非循環(huán)超圖的最長路徑和存取結(jié)構(gòu)的對應(yīng)關(guān)系,對如何構(gòu)建理想的秘密共享方案也進(jìn)行了相關(guān)研究。 文章的主要工作包括以下幾個方面： 1.針對理想秘密共享問題,通過構(gòu)造非循環(huán)超圖的最長路徑,利用向量空間構(gòu)造法和(t,t)門限體制相結(jié)合的思想設(shè)計了一個信息率為1的理想秘密共享方案。由于所有存取結(jié)構(gòu)與超圖之間存在一一對應(yīng)的關(guān)系。相比圖存取結(jié)構(gòu)而言,超圖對應(yīng)的存取結(jié)構(gòu)更為一般化；而且不局限于秩為2的情況。該內(nèi)容見第3章。 2.根據(jù)強(qiáng)t-一致性和可驗證的定義,利用范德蒙行列式的性質(zhì)構(gòu)建了一個高效強(qiáng)t-一致的可驗證秘密共享方案,與Harn和Lin的方案相比,該方案能抵抗并檢驗出Harn方案中出現(xiàn)的欺詐行為,而且無需選取κ個子多項式。因此,在保證秘密份額滿足強(qiáng)亡-一致定義的前提下具有較低的計算復(fù)雜度,能更好地滿足應(yīng)用需求。詳細(xì)內(nèi)容見第4章。 3.基于橢圓曲線的因子分解困難假設(shè)和離散對數(shù)困難假設(shè),提出可證的強(qiáng)(n,t,n)秘密共享方案,利用橢圓曲線的點乘運算將多項式和子份額點乘基點加密進(jìn)行公開驗證子秘密和子份額,不但滿足強(qiáng)t-一致性而且保證秘密的真實。通過對方案的性能和安全性等方面的分析,證明該方案具有較小的計算復(fù)雜度和通信復(fù)雜度。該內(nèi)容見第4章。 4.通過將參與者集合進(jìn)行劃分,每一部分作為一隔間。其中,隔間內(nèi)部的參與者共享次主密鑰,整個參與者集合共享主秘密,構(gòu)造了一個高效可驗證的層次秘密共享方案,利用雙變量單向函數(shù)實現(xiàn)了可驗證性,可防止不誠實欺詐行為。每個參與者只需持有一個較短的秘密份額即可重構(gòu)長度較大的主秘密,具有較高的信息率。該內(nèi)容見第5章。 5.在6章中,為了檢驗可驗證秘密共享方案的應(yīng)用,我們探討了其在無線傳感器網(wǎng)絡(luò)密鑰分發(fā)方案和隱私保護(hù)數(shù)據(jù)挖掘方案中的運用。驗證表明,這些方案可以用來作為構(gòu)建高效密鑰分配協(xié)議和隱私保護(hù)數(shù)據(jù)挖掘協(xié)議的基礎(chǔ)工具。 6.在7章中,研究了四面體體積的安全多方計算,提出了解決方案,并使用模擬范例證明該方案的保密性。然后基于四面體體積的安全多方計算,解決了：1)一個點與一個平面之間的關(guān)系；2)一條線和一個平面之間的關(guān)系；3)兩個平面之間的關(guān)系的三個安全多方計算問題,并給出解決方案。
[Abstract]:Secret sharing is an important tool in cryptography . It is a basic tool for building many security protocols and distributed computing , such as secure multi - party computing , threshold secret , secret data mining , access control , general - purpose inadvertent transmission , Byzting protocol , etc .

According to the security requirements of security data mining , secure multi - party computing and key management in wireless network , this paper studies the relevant knowledge of secure multi - party computing , and gives a secure multi - party computing protocol for three - dimensional geometric problems .

The main work of this article includes the following aspects :

1 . Aiming at the ideal secret sharing problem , by constructing the longest path of the non - cyclic hypergraph , an ideal secret sharing scheme with an information rate of 1 is designed by combining the idea of the vector space structure method and the ( t , t ) threshold system .
and is not limited to the case where the rank is 2 .

2 . According to the definition of strong t - consistency and verifiability , a highly efficient and strong t - consistent verifiable secret sharing scheme is constructed by using the property of van der - meng determinant . Compared with the schemes of Harn and Lin , this scheme can resist and verify the fraud behavior in Harn scheme , and it is not necessary to select the kappa number polynomial . Therefore , it has lower computational complexity under the premise of ensuring the secret share meets the definition of strong death - consistent definition , and can better meet the application requirements . See Chapter 4 for details .

3 . Based on the assumption of the difficult assumption and discrete logarithm difficulty assumption of the elliptic curve , a strong ( n , t , n ) secret sharing scheme is proposed , and the polynomial and the sub - share point are multiplied by the point multiplication operation of the elliptic curve to verify the sub - secret and the sub - share , which not only satisfies the strong t - consistency but also guarantees the truth of the secret . Through the analysis of the performance and the security of the scheme , the scheme proves that the scheme has smaller computing complexity and communication complexity .

4 . By dividing the participants ' collection , each part acts as a compartment . The participants in the compartment share the secondary master key , the whole participant set shares the main secret , constructs an efficient and verifiable hierarchical secret sharing scheme , realizes verifiability by using the bi - variable one - way function , and can prevent dishonest fraud .

5 . In Chapter 6 , in order to verify the application of verifiable secret sharing scheme , we discuss its application in wireless sensor network key distribution scheme and privacy protection data mining scheme . The verification shows that these schemes can be used as the base tool for constructing efficient key distribution protocol and privacy protection data mining protocol .

6 . In Chapter 7 , the security multi - party calculation of the tetrahedra volume is studied , the solution is put forward , and the security of the scheme is proved by using the simulation example . Then , the relation between one point and one plane is solved based on the security multi - party calculation of the tetrahedra volume ;
2 ) the relation between a line and a plane ;
3 ) Three security multi - party computing problems of the relationship between two planes , and the solution is given .
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN918.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前8條

1 劉文;羅守山;陳萍;;保護(hù)私有信息的點線關(guān)系判定協(xié)議及其應(yīng)用[J];北京郵電大學(xué)學(xué)報;2008年02期

2 羅永龍;黃劉生;徐維江;荊巍巍;;一個保護(hù)私有信息的多邊形相交判定協(xié)議[J];電子學(xué)報;2007年04期

3 李順東,司天歌,戴一奇;集合包含與幾何包含的多方保密計算[J];計算機(jī)研究與發(fā)展;2005年10期

4 羅永龍;黃劉生;荊巍巍;徐維江;;空間幾何對象相對位置判定中的私有信息保護(hù)[J];計算機(jī)研究與發(fā)展;2006年03期

5 Liu Liang;Wu Chunying;Li Shundong;;TWO PRIVACY-PRESERVING PROTOCOLS FOR POINT-CURVE RELATION[J];Journal of Electronics(China);2012年05期

6 Chen Ping;Ji Yimu;Wang Ruchuan;Huang Haiping;Zhang Dan;;A NEW PRIVACY-PRESERVING EUCLID-DISTANCE PROTOCOL AND ITS APPLICATIONS IN WSNS[J];Journal of Electronics(China);2013年02期

7 吳春英;李順東;;一類特殊超圖與理想秘密共享方案[J];計算機(jī)工程;2013年07期

8 ;A secure multi-party computation solution to intersection problems of sets and rectangles[J];Progress in Natural Science;2006年05期

，

本文編號：2051521