15 research outputs found
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
Rounding LLL: Finding Faster Small Roots of Univariate Polynomial Congruences
In a seminal work at EUROCRYPT \u2796, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time:
this has found many applications in public-key cryptanalysis and in a few security proofs.
However, the running time of the algorithm is a high-degree polynomial,
which limits experiments:
the bottleneck is an LLL reduction of a high-dimensional matrix with extra-large coefficients.
We present in this paper a polynomial speedup over Coppersmith\u27s algorithm.
Our improvement is based on a special property of the matrices used by Coppersmith\u27s algorithm,
which allows us to speed up the LLL reduction by rounding.
The exact speedup depends on the LLL algorithm used: for instance, the speedup is quadratic
in the bit-size of the small-root bound if one uses the Nguyen-Stehlé L^2 algorithm
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
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
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 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
ImplantaĂĂo e atuaĂĂo dos escritĂrios de projetos no setor pĂblico: o caso Estado do CearĂ.
nĂo hĂO interesse na gestĂo de projetos Ă um tema em ascenĂĂo em virtude dos efeitos da
globalizaĂĂo que tornou os mercados muito mais competitivos, e tĂm obrigado os
Estados a modernizarem a sua administraĂĂo, buscando maior eficiĂncia e eficĂcia
na sua gestĂo em virtude da crise fiscal dos Estados. Isso implica numa
transformaĂĂo 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 serviĂo pĂblico mais eficiente, para melhor atender Ăs
necessidades da sociedade. Este trabalho teve como objetivo estudar a implantaĂĂo
e a atuaĂĂo dos escritĂrios de projetos no Estado do CearĂ, procurando entender
quais os fatores que motivaram essa necessidade, como os escritĂrios de projetos
controlam e influenciam a gestĂo do portfĂlio de projetos, analisar os obstĂculos da
sua atuaĂĂo e quais os resultados que os escritĂrios de projetos tĂm proporcionado
ao Estado do CearĂ. A metodologia caracterizou-se de um estudo de caso de
natureza exploratĂria e de entrevistas em profundidade. A coleta de dados foi
realizada por meio das entrevistas e coleta de outras informaĂĂes que foram
colhidas durante as visitas ou em sites do Estado. Foram realizadas dez entrevistas
com gestores da Seplag que participaram desde o inĂcio do processo de
implementaĂĂo da cultura de gestĂo de projetos no Estado do CearĂ que teve inĂcio
em 2007. Decorrente da anĂlise dos dados, observou-se que a implementaĂĂo de
uma cultura de gestĂo de projetos foi realizada como parte de uma reforma
administrativa mais ampla que teve como objetivo uma melhoria do planejamento no
Estado com a unificaĂĂo dos seus instrumentos de planejamento nas secretarias e a
implantaĂĂo dos escritĂrios de projetos que criariam uma metodologia de gestĂo de
projetos adequada Ăs necessidades do Estado para suportar a implantaĂĂo da
GestĂo PĂblica por Resultados (GPR). Quanto ao controle e a influĂncia detectou-se
que foram criados, um escritĂrio central que faz o papel do escritĂrio estratĂgico,
escritĂrios setoriais que atuam de forma tĂtica e gestores de projetos que realizam a
gestĂo operacional. Observou-se como maiores obstĂculos Ă atuaĂĂo dos escritĂrios
de projetos, o desafio cultural, a falta de conhecimentos e experiĂncia em gestĂo de
projetos e a falta de apoio por parte de alguns gestores. Como resultado, constatouse
que a implementaĂĂo da cultura de gestĂo de projetos no Estado do CearĂ tem
trazido resultados positivos, pois tanto os gestores tem uma percepĂĂo positiva
quanto Ă melhoria dos resultados, como tambĂm foi observado na anĂlise da GPR
de algumas secretarias analisadas, que tem havido uma evoluĂĂo positiva na
maioria dos indicadores no perĂodo analisado de 2007 a 2011, como resultado da
implementaĂĂo de uma reforma administrativa com Ănfase na gestĂo 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 serviĂos tĂm sido ofertados Ă
sociedade pelo poder pĂblico, garantindo mais transparĂncia e melhores resultados
no setor pĂblico.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 CearĂ, 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 CearĂ. 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 CearĂ 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 CearĂ 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