Lower bounds of shortest vector lengths in random knapsack lattices and random NTRU lattices

Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In the paper we study two types of random lattices in cryptography: the knapsack lattices and the NTRU lattices. For random knapsack lattices, we prove lower bounds of shortest vector lengths, which are very close to lengths predicted by the Gaussian heuristic. For a random NTRU lattice, we prove that with a overwhelming probability, the ratio between the length of the shortest vector and the length of the target vector, which corresponds to the secret key, is at least a constant, independent of the dimension of the lattice. The main technique we use is the incompressibility method from the theory of Kolmogorov complexity

Lower bounds of shortest vector lengths in random NTRU lattices

International audienceFinding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In this paper, we propose a general method to estimate lower bounds of the shortest vector lengths for random integral lattices in certain classes, which is based on the incompressibility method from the theory of Kolmogorov complexity. As an application, we can prove that for a random NTRU lattice, with an overwhelming probability, the ratio between the length of the shortest vector and the length of the target vector, which corresponds to the secret key, is at least a constant, independent of the rank of the lattice

Lattice-based Identity-Based Broadcast Encryption Scheme

Motivated by the lattice basis delegation technique due to [8], we propose an adaptively secure identity-based broadcast encryption(IBBE) scheme based on the hard worst-case lattice problems. Our construction can be generalized to obtain a hierarchical IBBE (HIBBE) scheme easily. To the best of the authors\u27 knowledge, our construction and its variants constitute the first adaptively secure IBBE schemes from lattices, which are believed secure in the post-quantum environment

Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields

International audienceWe present a deterministic 2O(t)qt-2/t-1 +o(1) algorithm to decide whether a univariate polynomial f, with exactly t monomial terms and degre

Cryptanalysis of two knapsack public-key cryptosystems

In this paper, we cryptanalyze two knapsack cryptosystems. The first one is proposed by Hwang et al [4], which is based on a new permutation algorithm named Permutation Combination Algorithm. We show that this permutation algorithm is useless to the security of the cryptosystem. Because of the special super increasing structure, we can break this cryptosystem use the method provided by Shamir at Crypto\u2782. The second one is provided by Su et al [16], which is based on the elliptic curve discrete logarithm and knapsack problem. We show that one can recover the plaintext as long as he solve a knapsack problem.Unfounately, this knapsack problem can be solved by Shamir\u27s method or the low density attack. Finally, we give a improved version of Su\u27s cryptosystem to avoid these attacks

Cryptanalysis of a homomorphic encryption scheme from ISIT 2008

International audienceAt ISIT 2008, Aguilar Melchor, Castagnos and Gaborit presented a lattice-based homomorphic encryption scheme (abbreviated as MCG). Its security is based on the Computational Knapsack Vector Problem. In this paper, we explore a secret linear relationship between the public keys and the secret keys, which can be used to construct a reduced-dimension lattice, and then we obtain a group of equivalent private keys by solving the Closest Vector Problem of the lattice. Moreover, our attack is practical on all the three settings of recommended parameters, and the running time to recover the equivalent private keys is only several hours on a single PC

ImplantaÃÃo e atuaÃÃo dos escritÃrios de projetos no setor pÃblico: o caso Estado do CearÃ.

nÃo hÃO interesse na gestÃo de projetos à um tema em ascenÃÃo em virtude dos efeitos da globalizaÃÃo que tornou os mercados muito mais competitivos, e tÃm obrigado os Estados a modernizarem a sua administraÃÃo, buscando maior eficiÃncia e eficÃcia na sua gestÃo em virtude da crise fiscal dos Estados. Isso implica numa transformaÃÃo da forma de gerir o Estado, pois conceitos antes aplicados somente no setor privado passam a ser utilizados como benchmarks com o objetivo de modernizar e tornar o serviÃo pÃblico mais eficiente, para melhor atender Ãs necessidades da sociedade. Este trabalho teve como objetivo estudar a implantaÃÃo e a atuaÃÃo dos escritÃrios de projetos no Estado do CearÃ, procurando entender quais os fatores que motivaram essa necessidade, como os escritÃrios de projetos controlam e influenciam a gestÃo do portfÃlio de projetos, analisar os obstÃculos da sua atuaÃÃo e quais os resultados que os escritÃrios de projetos tÃm proporcionado ao Estado do CearÃ. A metodologia caracterizou-se de um estudo de caso de natureza exploratÃria e de entrevistas em profundidade. A coleta de dados foi realizada por meio das entrevistas e coleta de outras informaÃÃes que foram colhidas durante as visitas ou em sites do Estado. Foram realizadas dez entrevistas com gestores da Seplag que participaram desde o inÃcio do processo de implementaÃÃo da cultura de gestÃo de projetos no Estado do Cearà que teve inÃcio em 2007. Decorrente da anÃlise dos dados, observou-se que a implementaÃÃo de uma cultura de gestÃo de projetos foi realizada como parte de uma reforma administrativa mais ampla que teve como objetivo uma melhoria do planejamento no Estado com a unificaÃÃo dos seus instrumentos de planejamento nas secretarias e a implantaÃÃo dos escritÃrios de projetos que criariam uma metodologia de gestÃo de projetos adequada Ãs necessidades do Estado para suportar a implantaÃÃo da GestÃo PÃblica por Resultados (GPR). Quanto ao controle e a influÃncia detectou-se que foram criados, um escritÃrio central que faz o papel do escritÃrio estratÃgico, escritÃrios setoriais que atuam de forma tÃtica e gestores de projetos que realizam a gestÃo operacional. Observou-se como maiores obstÃculos à atuaÃÃo dos escritÃrios de projetos, o desafio cultural, a falta de conhecimentos e experiÃncia em gestÃo de projetos e a falta de apoio por parte de alguns gestores. Como resultado, constatouse que a implementaÃÃo da cultura de gestÃo de projetos no Estado do Cearà tem trazido resultados positivos, pois tanto os gestores tem uma percepÃÃo positiva quanto à melhoria dos resultados, como tambÃm foi observado na anÃlise da GPR de algumas secretarias analisadas, que tem havido uma evoluÃÃo positiva na maioria dos indicadores no perÃodo analisado de 2007 a 2011, como resultado da implementaÃÃo de uma reforma administrativa com Ãnfase na gestÃo de projetos, o que tem permitido o alcance das metas e diretrizes estabelecidas na GPR pela Seplag e Governo. Conclui-se que mais e melhores serviÃos tÃm sido ofertados à sociedade pelo poder pÃblico, garantindo mais transparÃncia e melhores resultados no setor pÃblico.Interest in project management is an issue on the rise due to the effects of globalization that has made them much more competitive markets, and have forced States to modernize its administration, seeking greater efficiency and effectiveness in its management due to the fiscal crisis of the states. This implies a transformation of how to manage the state as concepts before applied only in the private sector come to be used as benchmarks for the purpose of modernize and make more efficient public service, to better meet societal needs. This work aimed to study the implantation and the role of project offices in the State of CearÃ, trying to understand what factors motivated this need, such as project management offices control and influence the project portfolio management, analyze the obstacles of his performance and what results the project offices have provided the State of CearÃ. The methodology was characterized a case study of exploratory and in-depth interviews nature. Data collection was conducted through interviews and collect other information that has collected during visits or state websites. Ten interviews were conducted Seplag with managers who participated since the beginning of the process implementation of project management culture in the state of Cearà which began in 2007. As a result of analyzing the data, it was observed that the implementation of a project management culture was performed as part of a reform wider administrative aimed to help better plan in State with the unification of the planning tools in departments and implementation of project management offices that would create a management methodology suitable projects to the state needs to support the implementation of Public Management by Results (GPR). As for the control and influence was detected they were created, a central office who plays the strategic office, sectoral offices that act tactically and project managers who perform operational management. It was noted as the biggest obstacles to the office of acting projects, cultural challenge, lack of knowledge and experience in management projects and the lack of support by some managers. As a result, I was evidenced that the implementation of project management culture in the state of Cearà has brought positive results, for both managers have a positive perception as the improvement of the results, as was also observed in the analysis of GPR some departments analyzed, there have been positive developments in Most indicators in the analyzed period 2007-2011 as a result of implementation of an administrative reform with an emphasis on project management, which has allowed the achievement of goals and guidelines established by the GPR Seplag and Government. It was concluded that more and better services have been offered the society by the government, ensuring greater transparency and better results in the public sector

Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem

Abstract. In this paper, we present an improvement of the Nguyen-Vidick heuristic sieve algorithm for shortest vector problem in general lattices, which time complexity is 2 0.3836n polynomial computations, and space complexity is 2 0.2557n. In the new algorithm, we introduce a new sieve technique with two-level instead of the previous one-level sieve, and complete the complexity estimation by calculating the irregular spherical cap covering

A new discrete gaussian sampler over orthogonal lattices

Discrete Gaussian is a cornerstone of many lattice-based cryptographic constructions. Aiming at the orthogonal lattice of a vector, we propose a discrete Gaussian rejection sampling algorithm, by modifying the dynamic programming process for subset sum problems. Within O(nq2) time, our algorithm generates a distribution statistically indistinguishable from discrete Gaussian at width s>ω(log n). Moreover, we apply our sampling algorithm to general high-dimensional dense lattices, and orthogonal lattices of matrices \matA\in\Z_q^{O(1)\times n}. Compared with previous polynomial-time discrete Gaussian samplers, our algorithm does not rely on the short basis