本文選題：多變量公鑰密碼體制 + 非線性可逆映射��； 參考：《解放軍信息工程大學》2014年碩士論文

【摘要】：二十一世紀是信息的時代,繼電子信息科學技術之后,量子和生物等新型信息科學正在建立和發(fā)展。量子計算機的產生將會對目前廣泛使用的基于離散對數(包括橢圓曲線上的離散對數)和大數分解的公鑰密碼體制構成潛在的威脅。為此,基于抗量子的公鑰密碼體制成為密碼學中一個研究的熱點和重點。多變量公鑰密碼系統(tǒng)作為一種能有效抵抗未來的基于量子計算機攻擊方法的密碼體制,在近二十幾年受到越來越多的關注。多變量公鑰密碼被認為是后量子時代的一種安全的密碼體制的備選方案,其發(fā)展?jié)摿Σ蝗莺鲆�。但�?多變量公鑰密碼的整個體系尚未完整,隨著各種攻擊方法的提出,目前大部分多變量公鑰密碼體制均受到不同程度的攻擊。因此,提出新的安全的多變量方案、對已有算法進行改進增強其性能和安全性是值得研究的課題。本文把重點放在多變量公鑰密碼算法的研究,主要成果如下:1.為了有效抵抗線性攻擊和差分攻擊,分別基于溫順變換和“特殊油醋”思想設計出兩種不同的非線性可逆映射,利用擴展MQ(Multivariate Quadratic)公鑰體制的思想,將上述非線性可逆映射與MI(Matsumoto-Imai)方案結合,構造出擴展多變量公鑰密碼算法。接著,給出擴展方案對應的加密算法和簽名算法。分析結果顯示:擴展多變量公鑰密碼算法繼承了MI方案的高效性,克服了其不能抵抗線性攻擊和差分攻擊的缺陷,還能抵抗代數攻擊。2.在基于外部干擾的MFE簽名方案的基礎上,設計了新的外部干擾量,提出了一種優(yōu)化的基于外部干擾的簽名方案。優(yōu)化方案在保證安全性的同時,使得公私鑰空間大大縮小;接著,針對原MFE加密方案不能抵抗高階線性化攻擊,利用上述構造的外部干擾量,重構了中心映射,提出了一種基于外部干擾的改進簽名方案。改進方案保持了原MFE方案結構簡單、求逆容易的性質,具有較強的安全性。3.針對油醋簽名體制不能抵抗Kipnis-Shamir攻擊,將基于溫順變換的非線性可逆變換和油醋簽名體制結合,提出了一種改進的油醋簽名方案—L-油醋方案。L-油醋方案具備很小的公私鑰量,能夠抵抗窮舉攻擊,Kipnis-Shamir攻擊和代數攻擊,同時,滿足數字簽名的基本要求。4.結合Square體制和三角型密碼系統(tǒng),重構了中心映射,提出了一種混合多變量公鑰簽名方案—Tri-Square方案。分析結果表明,Tri-Square方案克服了Square體制和三角型密碼系統(tǒng)的缺陷,能夠抵抗線性攻擊,差分攻擊,最小秩攻擊和代數攻擊。
[Abstract]:The 21 century is the era of information. After electronic information science and technology, quantum and biological new information science is being established and developed. The generation of quantum computers will pose a potential threat to the widely used public key cryptosystems based on discrete logarithms (including discrete logarithms on elliptic curves) and large number decomposition. Therefore, the anti-quantum public key cryptosystem has become a hotspot and focus in cryptography. As a kind of cryptosystem based on quantum computer attack, multivariable public key cryptosystem has attracted more and more attention in recent twenty years. Multivariable public key cryptography is considered as an alternative to secure cryptosystem in the post-quantum era, and its development potential can not be ignored. However, the whole system of multivariable public key cryptosystem is not complete. With the development of various attack methods, most multivariable public key cryptosystems are attacked to varying degrees. Therefore, it is worth studying to propose a new secure multivariable scheme and improve the performance and security of existing algorithms. This paper focuses on the research of multivariable public key cryptography algorithm, the main results are as follows: 1. In order to effectively resist linear and differential attacks, two different nonlinear reversible mappings are designed based on docile transformation and "special oil and vinegar", respectively, and the idea of extended MQ(Multivariate Quadratic public key system is used. An extended multivariable public key cryptosystem is constructed by combining the above nonlinear reversible mapping with the MIG Matsumoto-Imai) scheme. Then, the encryption algorithm and signature algorithm corresponding to the extended scheme are given. The analysis results show that the extended multivariable public key cryptosystem inherits the high efficiency of MI scheme, and overcomes the defect that it can not resist linear attack and differential attack, and can resist algebraic attack. 2. Based on the MFE signature scheme based on external interference, a new external interference scheme is designed, and an optimized signature scheme based on external interference is proposed. The optimization scheme not only ensures security, but also reduces the public and private key space greatly. Then, for the original MFE encryption scheme can not resist high-order linearization attacks, the center map is reconstructed by using the external interference of the above structure. An improved signature scheme based on external interference is proposed. The improved scheme keeps the structure of the original MFE scheme simple and easy to reverse, and has strong security. 3. In view of the fact that the oil vinegar signature scheme can not resist the Kipnis-Shamir attack, a modified oil vinegar signature scheme, -L- oil vinegar scheme. L- oil vinegar scheme has a very small amount of public and private key, which combines the nonlinear reversible transformation based on docile transformation with the oil vinegar signature scheme. It can resist the exhaustive attack Kipnis-Shamir attack and algebraic attack. At the same time, it satisfies the basic requirement of digital signature. Combined with Square system and triangular cryptosystem, a hybrid multivariable public key signature scheme, Tri-Square scheme, is proposed by reconstructing the center map. The results show that the Tri-Square scheme overcomes the defects of Square system and triangular cryptosystem, and can resist linear attack, differential attack, minimum rank attack and algebraic attack.
【學位授予單位】：解放軍信息工程大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN918.1

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本文編號：1973525