Academic literature on the topic 'Multivariate quadratic cryptosystem'

Vehicular Ad-hoc Network (VANET) is a developing transmission system to abet in the everyday organization of vehicular traffic and safety of vehicles (nodes). Unsigned verification is one of the key necessities in VANET gives the confidentiality of the root of the message. Current security conventions in VANET’s gives unsigned verification depends on the two-tier architecture, comprises of two VANET components, particularly nodes and Roadside Units (RsU’s) functioning as the key developing server (KDS). This protocol depends densely on RsU’s to give unsigned identification to the nodes. In this paper, we propose the K-means Cluster Head algorithm which is utilized for guide assortment, for both personal-best (’pbest’) and global-best (’gbest’), are observed a tremendously successful and complete well evaluate to the before existing methods. Here, we also propose an asymmetric encryption algorithm, with emphasis on Multivariate Quadratic Quasigroups (MVQQ) algorithm, in a circumstance of VANET. We set forward prime pseudonyms reasonably make a long time cycle that are worn to interact with semi-confided in experts and alternate pseudonyms with a minor lifetime which are utilized to talk with different nodes.

Multivariate quadratic based public-key cryptography called MQ problem which based on calculation of a secure cryptography of multivariate equations and MQ cryptography security is based on the difficulty of the solution of multivariate equations. But computer and mathematician scientists put a lot of effort and a long time to research MQ cryptography and they have proved that MQ cryptography is NP complete problem. Therefore, before the P problem Equal to the NP problem we do not figure out selected multivariate equations by random in polynomial time. So we can use this feature to construct the relative safety method of the public key encryption. A new type of public-key cryptosystem has been brought up in this paper that one-way shell core function which has such advantages as more security and flexibility, and provides a more inclusive public-key cryptosystem.

The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.

Let K be the field GF(3). We calculate the growth of the ideal Aλ where A is the algebra of functions from Kn → Kn and λ is a quadratic function. Specifically we calculate dim Akλ where Ak is the space of polynomials of degree less than or equal to k. This question arises in the analysis of the complexity of Gröbner basis attacks on multivariate quadratic cryptosystems such as the Hidden Field Equation systems. We also prove analogous results over the associated graded ring [Formula: see text] and state conjectures for the case of a general finite field of odd order.

In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization.
 One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme.
 The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.

A Tamed Transformation Method (TTM) cryptosystem was proposed by T. T. Moh in 1999. We describe how the first implementation scheme of the TTM system can be defeated. The computational complexity of our attack is 233 computations on the finite field with 28 elements. The cipher of the TTM systems are degree 2 polynomial maps derived from composition of invertible maps of either total degree 2 or linear maps which can be easily calculated and can be easily inverted. To ensure the system to be of degree two, the key construction of the implementation schemes of the TTM systems is a multivariable polynomial Q8(x1,…,xn) and a set of linearly independent quadratic polynomials qi(x1,…,xm), i=1,…,n such that Q8(q1,…,qn) is again a degree 2 polynomials of x1,…,xm. In this paper, we study the first implementation scheme of the TTM systems [6]. We discovered that in this implementation scheme the specific polynomial Q8 can be decomposed further into a factorization in terms of composition. By taking powers of the equality satisfied by the new composition factors, we can actually derive a set of equations, that can produce linear equations satisfied by the plaintext. These linear equations lead us to find a way to defeat this implementation scheme.

AbstractT. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽

A new cryptanalytic application is proposed for a number theoretic tool Weil sum to the birthday attack against multivariate quadratic trapdoor function. This new customization of the birthday attack is developed by evaluating the explicit Weil sum of the underlying univariate polynomial and the exact number of solutions of the associated bivariate equation. I designed and implemented new algorithms for computing Weil sum values so that I could explicitly identify some class of weak Dembowski- Ostrom polynomials and the equivalent forms in the multivariate quadratic trapdoor function. This customized attack, also regarded as an equation solving algorithm for the system of some special quadratic equations over finite fields, is fundamentally different from the Grobner basis methods. The theoretical observations and experiments show that the required computational complexity of the attack on these weak polynomial instances can be asymptotically less than the square root complexity of the common birthday attack by a factor as large as 2^(n/8) in terms of the extension degree n of F2n. I also suggest a few open problems that any MQ-based short signature scheme must explicitly take into account for the basic design principles.

This thesis provides a survey of the attacks on multivariate cryptosystems. We begin by providing an outline of the general multivariate cryptosystem. Proceeding from there, we show that even with this level of detail, there are several attacks that are possible, including the method of Groebner bases, the XL method, and the recently announced method of Dixon resultants. Less general attack techniques also exist, such as MinRank attacks and differential analysis. These attacks lack the universality of the first three mentioned. In order to explore these less general attacks further, more details are required, so we present four different multivariate cryptosystems. Then, we attack them, using the less general attacks of MinRank, differential analysis and even an attack specific to one system. This concludes our study of the attacks themselves, and we move on to note that not all routes of attack are promising. Specifically, quantum computing does not seem to be helpful beyond the quadratic speed-up of Grover's algorithm. We also note that not all multivariate cryptosystems have been successfully attacked as of the writing of this thesis. We conclude with the fact that multivariate cryptography is gaining more and more active study.

Redes de sensores sem fio (RSSF) tipicamente consistem de nós sensores com limitação de energia, processamento, comunicação e memória. A segurança em RSSF está se tornando fundamental com o surgimento de aplicações que necessitam de mecanismos que permitam autenticidade, integridade e confidencialidade. Devido a limitações de recursos em RSSF, adequar criptossistemas de chaves públicas (PKC) para estas redes é um problema de pesquisa em aberto. Meados de 2008, Danilo Gligoroski et al. propuseram um novo PKC baseado em quase-grupos multivariados quadráticos (MQQ). Experimentos feitos por Gligoroski na plataforma FPGA mostram que MQQ executou em tempo menor que principais PKC (DH, RSA e ECC) existentes, tanto que alguns artigos afirmam que MQQ possui velocidade de uma típica cifra de bloco simétrica. Além disto, o MQQ exibiu o mesmo nível de segurança que outros PKC (DH, RSA e ECC) necessitando chaves menores. Outra propriedade que chama atenção no MQQ é o uso das operações básicas XOR, AND e deslocamento de bits nos processos de encriptação e decriptação, fato importante considerando que uma RSSF possui processamento limitado. Estas características tornam o MQQ promissor a levar um novo caminho na difícil tarefa de dotar redes de sensores sem fio de criptossistemas de chaves públicas. Neste contexto se insere este trabalho que analisa a viabilidade de implementar o algoritmo MQQ em uma plataforma de RSSF. Sendo importante considerar que este trabalho inova na proposta de levar para RSSF este novo PKC baseado quase-grupos multivariados quadráticos, além de contribuir com um método para reduzir o tamanho da chave pública utilizada pelo MQQ. Foram feitos testes com MQQ nas plataformas TelosB e MICAz, sendo que o MQQexibiu os tempos de 825; 1 ms para encriptar e 116; 6 ms para decriptar no TelosB e 445 ms para encriptar no MICAz.<br>Wireless sensor networks (WSN) typically consist of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in sensor networks, public key cryptosystems suit (PKC) for these networks is an open research problem. In 2008 Danilo Gligoroski et al. proposed a new PKC based on quasi-groups multivariate quadratic (MQQ). Experiments by Gligoroski on FPGA platform show that MQQ performed in less time than most popular PKC (DH, RSA and ECC), so that some papers say MQQ has a typical speed of symmetric block cipher. Moreover, the MQQ exhibited same level of security that other PKC (DH, RSA and ECC) requiring keys minors. Another property that draws attention in MQQ is the use of basic operations XOR, AND, and bit shifting in the processes of encryption and decryption, important fact considering that a WSN has limited processing. These features make the MQQ promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. Appears in this context that this study examines the feasibility of implementing MQQ a platform for WSN. Is important to consider this innovative work in the proposal to bring this new PKC for WSN based multivariate quadratic quasigroups, and contribute a method to reduce the size public key used by MQQ. Tests with MQQ on platforms TelosB and MICAz, the MQQ exhibited 825ms to encrypt and 116ms to decrypt on TelosB and 445 ms to encrypt on MICAz.

博士<br>國立臺灣大學<br>資訊工程學研究所<br>96<br>Many public key cryptosystems are based on univariate polynomials with low degree but the inverse of the polynomials are high degree polynomials. Thus it is time consuming to compute the inverse of the polynomials. Multivariate Quadratic Public Key Cryptosystem (MQPKC) can overcome this problem. The first MQPKC was proposed by Fell and Diffie [33]. Until now, there have been dozens of MQPKCs proposed. However most of them were broken. How to design a secure and practical MQPKC is still unknown. In order to study how to design a MQPKC, we survey the multivariate public key cryptosystems and the attacks against these cryptosystems. By studying the two algorithms for equations solving, we develop a more efficient algorithm for equations solving. Moreover, this algorithm can be used for examining the possible defects of MQPKCs. We also propose the attack against Multi-Sets UOV, e.g. TRMS, TTS, and Rainbow, and study the more efficient algorithm, XFLT , for solving the quadratic equations. Consequently, the minimum numbers of equations and variables for the security level 280 are 30 over GF(256) and 34 over GF(16). Finally we deduce and study criteria for building MQPKCs such that the new MQPKCs are examined systematically and are not attacked by the previous methods.