本文選題：積分分析 + 分離特性　； 參考：《山東大學》2017年碩士論文

【摘要】：2015年的歐密會上,密碼學者Todo將傳統(tǒng)的積分分析進行推廣,提出了分離特性的概念。由于分離特性可以更加明確地刻畫介于"活躍"和"零和"之間的隱含性質,所以可以應用在使用了非雙射、比特級或低次數(shù)部件的分組密碼算法的分析中。同年的美密會上,Todo考慮S盒為公開函數(shù),首次在理論上成功地分析了 MISTY1的全輪算法。FSE2016,日本學者Todo和Morri提出比特級分離特性,更細致地利用了算法的內(nèi)部結構。之后,Sun和Wang將S盒的代數(shù)標準型和分離特性的定義相結合,提出了借助表的比特級分離特性。2016年的亞密會中,Xiang等將混合整數(shù)線性規(guī)劃的思想應用到比特級分離特性的搜索中。Sun等通過刻畫復雜線性層和模加運算中比特級分離特性的傳遞模型,分析了比特級分離特性在SPN算法和ARX類算法分析中的適用性,使得該方法能夠分析更為廣泛的分組密碼算法。本文主要研究了三種密碼算法在比特級分離特性分析下的安全程度。根據(jù)已知的發(fā)表文獻,本文首次研究了 Kuznyechik和Chaskey算法的分離特性,找到了輪數(shù)均為4的積分區(qū)分器。對于SPARX算法,其作者在設計之初就進行了分離特性分析。本文采用了比特級分離特性進行分析,得到了與設計文檔一致的分析結果,表明在比特級別上考慮分離特性不一定能夠改進分析結果。Kuznyechik算法為SPN結構,S盒為8比特的替換,線性層為有限域上的乘法。Chaskey和SPARX為ARX算法,由模加、循環(huán)移位和輪密鑰異或組成。本文通過分析比特級分離特性在這些算法模塊之間的傳遞方式,利用混合線性整數(shù)規(guī)劃搜索積分區(qū)分器。此外,對于Serpent、PRESENT和Noekeon等算法的已有較好積分區(qū)分器,本文通過綜合分析算法的結構模塊和密鑰生成方案進行了密鑰恢復分析,分別攻擊了12輪、9輪和7輪的相應算法。
[Abstract]:At the 2015 Euclidean meeting, cryptographer Todo extended the traditional integral analysis and proposed the concept of separation characteristics. Since the separation property can more clearly characterize the implicit properties between "active" and "zero sum", it can be applied to the analysis of block cipher algorithms using non-bijective, bit-level or low-order components. In the same year, considering S-box as an open function, Todo first successfully analyzed the full-wheel algorithm of MISTY1. FSE 2016. The Japanese scholars Todo and Morri put forward the characteristic of special order separation, and used the inner structure of the algorithm in more detail. Sun and Wang then combined the algebraic canonical form of the S-box with the definition of the separation property. The idea of mixed integer linear programming (MILP) is applied to the search of bitt order separation properties by characterizing complex linear layers and bit-gradations in modular addition operations by characterizing complex linear layers and modular addition. The transfer model of the separation characteristics, The applicability of bit-order separation in the analysis of SPN algorithm and ARX class algorithm is analyzed, which makes it possible to analyze a wider range of block cipher algorithms. This paper mainly studies the security degree of three cryptographic algorithms under the analysis of bit-level separation characteristics. Based on the known literatures, the separation characteristics of Kuznyechik and Chaskey algorithms are studied for the first time, and an integral discriminator with 4 wheels is found. For the SPARX algorithm, the author analyzed the separation characteristics at the beginning of the design. In this paper, we analyze the BST separation characteristics, and get the analysis results consistent with the design documents. It shows that considering the separation characteristics at the bit level is not necessarily able to improve the analysis result. Kuznyechik algorithm is an 8-bit replacement for the S-box with SPN structure. The linear layer is multiplication over finite fields. Chaskey and SPARX are ARX algorithms, which consist of modular addition, cyclic shift and wheel key XOR. In this paper, by analyzing the transfer of bit-order separation between these algorithms, the mixed linear integer programming is used to search the integral discriminator. In addition, for the existing better integral discriminators of Serpentine preset and Noekeon algorithms, this paper analyzes the key recovery by synthetically analyzing the structure module and the key generation scheme of the algorithm, and attacks the corresponding algorithms of 12 rounds, 9 rounds and 7 rounds, respectively.
【學位授予單位】：山東大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN918.1

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本文編號：1983593