本文選題：序列密碼 + 半張量積��； 參考：《北京交通大學(xué)》2014年博士論文

【摘要】：密碼技術(shù)已經(jīng)被廣泛應(yīng)用于政治、軍事、外交、商務(wù)等各個領(lǐng)域,成為確保信息安全的重要手段。近年來隨著新技術(shù)與新的數(shù)學(xué)工具的出現(xiàn),密碼學(xué)研究出現(xiàn)了許多新的熱點。作為一門以數(shù)學(xué)為基礎(chǔ)學(xué)科,數(shù)學(xué)領(lǐng)域新的進展經(jīng)常能夠促進密碼學(xué)研究的發(fā)展。本論文將半張量積這種新的數(shù)學(xué)工具引入到密碼學(xué)的研究當中,主要做了以下兩方面的工作：一方面,基于半張量積的序列密碼的周期問題的研究；另一方面,基于半張量積運算構(gòu)建的靈活格基加密算法的研究。本文的主要研究工作如下： 1、研究了序列密碼設(shè)計中的常用器件：NFSR的狀態(tài)周期問題。給出了求解NFSR狀態(tài)空間的一般性方法。以往關(guān)于NFSR圈結(jié)構(gòu)的研究一直沒有很好的方法,本文給出了一種可以精確描述NFSR圈結(jié)構(gòu)、圈長度和分析NFSR非奇異性的方法,然后通過仿真實驗證明了所提方法的正確性。 2、研究了以NFSR器件為基礎(chǔ)的Grain型序列密碼算法的周期問題。分析了有外界輸入情況下,NFSR狀態(tài)的變化情況,給出有效輸入序列的判別條件和狀態(tài)可達性的判斷條件,并給出了構(gòu)建輸入序列的方法。提出有外界周期性輸入的情況下,NFSR狀態(tài)空間的描述的方法,并進行了實驗仿真。 3、研究另一類以NFSR器件為基礎(chǔ)的序列密碼算法—Trivium型算法的周期問題。建立了級聯(lián)NFSR的圈長度的求解方法。研究了有大量外界輸入的NFSR的狀態(tài)演變問題,給出縮小狀態(tài)矩陣規(guī)模的方法,并提出一種利用可達狀態(tài)矩陣對NFSR器件的狀態(tài)平衡性進行評測的方法。 4、研究了利用半張量積運算構(gòu)建靈活的格基加密算法。利用半張量積可以進行不同維度矩陣相乘的性質(zhì),以格基密碼中的重要困難問題：LWE問題為基礎(chǔ),提出了新的困難問題STP-LWE問題,并證明了新提出的困難問題的復(fù)雜性。在此基礎(chǔ)上,提出基于STP-LWE問題的公鑰加密方案,并證明了方案的安全性和正確性。此方案實現(xiàn)了在同一套安全參數(shù)下使用不同規(guī)模的密鑰進行加密。
[Abstract]:Cryptography technology has been widely used in political, military, diplomatic, commercial and other fields, and has become an important means to ensure information security. In recent years, with the emergence of new technologies and new mathematical tools, cryptography research has emerged many new hot spots. As a mathematics-based subject, new advances in mathematics can often promote the development of cryptography. In this paper, a new mathematical tool, semi-tensor product, is introduced into the research of cryptography, which mainly includes the following two aspects: on the one hand, the period problem of sequential cryptography based on semi-tensor product; on the other hand, The research of flexible lattice base encryption algorithm based on semi-tensor product operation. The main work of this paper is as follows: 1. The state period of the common device in the design of sequence cryptography:: NFSR is studied. A general method for solving NFSR state space is given. There has been no good method for the study of NFSR loop structure in the past. This paper presents a method that can accurately describe the NFSR cycle structure, cycle length and analysis of NFSR nonsingularity, and then proves the correctness of the proposed method by simulation experiments. 2. The periodic problem of Grain type sequence cipher algorithm based on NFSR device is studied. In this paper, the variation of NFSR state in the presence of external input is analyzed, and the conditions for judging the effective input sequence and the state reachability are given, and the method of constructing the input sequence is given. A description method of NFSR state space with periodic external input is proposed, and the experimental simulation is carried out. 3. The periodicity of another kind of sequential cipher algorithm-Trivium type algorithm based on NFSR devices is studied. A method to solve the cycle length of cascaded NFSR is established. The state evolution of NFSR with a large number of external inputs is studied. The method of reducing the size of state matrix is given. A method of evaluating the state balance of NFSR devices by using reachable state matrix is proposed. 4. Using semi-tensor product operation to construct flexible lattice-based encryption algorithm. By using the property of semi-tensor product to multiply different dimensional matrices, a new difficult problem STP-LWE problem is proposed based on the important difficult problem in lattice-base cryptosystem: LWE, and the complexity of the new difficult problem is proved. On this basis, a public key encryption scheme based on STP-LWE problem is proposed, and the security and correctness of the scheme are proved. This scheme implements encryption with different size keys under the same set of security parameters.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN918.1

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本文編號：1858535