54,989 research outputs found
On the complexity of Decomposition Attack
In recent researches, it is discovered that index calculus is
useful for solving the discrete logarithm problems (DLP) of the groups of the Jacobian of curves (including elliptic curve) over finite field, which are widely used to cryptosystems. In these cases, the probability that an element of the group is written by the summation of N elements of large primes and factor bases is O(1) where N is some pre-fixed constant. So the situation is little different to the normal index calculus and it is proposed that it should be called another name, ”decomposition attack”. In decomposition attack, first, some relations are collected and the graph, whose vertexes are the set of large primes and whose edges are the relations, is considered and the elimination of large prime is done by using this graph.
However, in the proposed algorithm, the randomness of the
graph, which is difficult to define, is needed. In this paper, we first formulate the decomposition attack and next propose a new algorithm, which does not require the randomness of the graph and its worst complexity can be estimated
Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups
Around two years ago, Roman\u27kov introduced a new type of attack called the nonlinear decomposition attack on groups with solvable membership search problem. To analyze the precise efficiency of the algorithm, we implemented the algorithm on two protocols: semidirect product protocol and Ko-Lee protocol. Because polycyclic groups were suggested as possible platform groups in the semidirect product protocol and polycyclic groups have a solvable membership search problem, we used poly- cyclic groups as the platform group to test the attack. While the complexity could vary regarding many different factors within the group, there was always at least one exponential factor in the complexity analysis of the algorithm
BlenX-based compositional modeling of complex reaction mechanisms
Molecular interactions are wired in a fascinating way resulting in complex
behavior of biological systems. Theoretical modeling provides a useful
framework for understanding the dynamics and the function of such networks. The
complexity of the biological networks calls for conceptual tools that manage
the combinatorial explosion of the set of possible interactions. A suitable
conceptual tool to attack complexity is compositionality, already successfully
used in the process algebra field to model computer systems. We rely on the
BlenX programming language, originated by the beta-binders process calculus, to
specify and simulate high-level descriptions of biological circuits. The
Gillespie's stochastic framework of BlenX requires the decomposition of
phenomenological functions into basic elementary reactions. Systematic
unpacking of complex reaction mechanisms into BlenX templates is shown in this
study. The estimation/derivation of missing parameters and the challenges
emerging from compositional model building in stochastic process algebras are
discussed. A biological example on circadian clock is presented as a case study
of BlenX compositionality
Robust Exponential Worst Cases for Divide-et-Impera Algorithms for Parity Games
The McNaughton-Zielonka divide et impera algorithm is the simplest and most
flexible approach available in the literature for determining the winner in a
parity game. Despite its theoretical worst-case complexity and the negative
reputation as a poorly effective algorithm in practice, it has been shown to
rank among the best techniques for the solution of such games. Also, it proved
to be resistant to a lower bound attack, even more than the strategy
improvements approaches, and only recently a family of games on which the
algorithm requires exponential time has been provided by Friedmann. An easy
analysis of this family shows that a simple memoization technique can help the
algorithm solve the family in polynomial time. The same result can also be
achieved by exploiting an approach based on the dominion-decomposition
techniques proposed in the literature. These observations raise the question
whether a suitable combination of dynamic programming and game-decomposition
techniques can improve on the exponential worst case of the original algorithm.
In this paper we answer this question negatively, by providing a robustly
exponential worst case, showing that no intertwining of the above mentioned
techniques can help mitigating the exponential nature of the divide et impera
approaches.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
Algorithms and Complexity Results for Persuasive Argumentation
The study of arguments as abstract entities and their interaction as
introduced by Dung (Artificial Intelligence 177, 1995) has become one of the
most active research branches within Artificial Intelligence and Reasoning. A
main issue for abstract argumentation systems is the selection of acceptable
sets of arguments. Value-based argumentation, as introduced by Bench-Capon (J.
Logic Comput. 13, 2003), extends Dung's framework. It takes into account the
relative strength of arguments with respect to some ranking representing an
audience: an argument is subjectively accepted if it is accepted with respect
to some audience, it is objectively accepted if it is accepted with respect to
all audiences. Deciding whether an argument is subjectively or objectively
accepted, respectively, are computationally intractable problems. In fact, the
problems remain intractable under structural restrictions that render the main
computational problems for non-value-based argumentation systems tractable. In
this paper we identify nontrivial classes of value-based argumentation systems
for which the acceptance problems are polynomial-time tractable. The classes
are defined by means of structural restrictions in terms of the underlying
graphical structure of the value-based system. Furthermore we show that the
acceptance problems are intractable for two classes of value-based systems that
where conjectured to be tractable by Dunne (Artificial Intelligence 171, 2007)
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