94,101 research outputs found
On Distributional Collision Resistant Hashing
Collision resistant hashing is a fundamental concept that is the basis for many of the important cryptographic primitives and protocols. Collision resistant hashing is a family of compressing functions such that no efficient adversary can find any collision given a random function in the family.
In this work we study a relaxation of collision resistance called distributional collision resistance, introduced by Dubrov and Ishai (STOC \u2706). This relaxation of collision resistance only guarantees that no efficient adversary, given a random function in the family, can sample a pair where is uniformly random and is uniformly random conditioned on colliding with .
Our first result shows that distributional collision resistance can be based on the existence of multi-collision resistance hash (with no additional assumptions). Multi-collision resistance is another relaxation of collision resistance which guarantees that an efficient adversary cannot find any tuple of inputs that collide relative to a random function in the family. The construction is non-explicit, non-black-box, and yields an infinitely-often secure family. This partially resolves a question of Berman et al. (EUROCRYPT \u2718). We further observe that in a black-box model such an implication (from multi-collision resistance to distributional collision resistance) does not exist.
Our second result is a construction of a distributional collision resistant hash from the average-case hardness of SZK. Previously, this assumption was not known to imply any form of collision resistance (other than the ones implied by one-way functions)
Matrix-geometric solution of infinite stochastic Petri nets
We characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such on approach are that very efficient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. We first characterize the class of stochastic Petri nets of interest by formally defining a number of constraints that have to be fulfilled. We then discuss the matrix geometric solution technique that can be employed and present some boundary conditions on tool support. We illustrate the practical usage of the class of stochastic Petri nets with two examples: a queueing system with delayed service and a model of connection management in ATM network
The time resolution of the St. Petersburg paradox
A resolution of the St. Petersburg paradox is presented. In contrast to the
standard resolution, utility is not required. Instead, the time-average
performance of the lottery is computed. The final result can be phrased
mathematically identically to Daniel Bernoulli's resolution, which uses
logarithmic utility, but is derived using a conceptually different argument.
The advantage of the time resolution is the elimination of arbitrary utility
functions.Comment: 20 pages, 1 figur
Comparison between the two definitions of AI
Two different definitions of the Artificial Intelligence concept have been
proposed in papers [1] and [2]. The first definition is informal. It says that
any program that is cleverer than a human being, is acknowledged as Artificial
Intelligence. The second definition is formal because it avoids reference to
the concept of human being. The readers of papers [1] and [2] might be left
with the impression that both definitions are equivalent and the definition in
[2] is simply a formal version of that in [1]. This paper will compare both
definitions of Artificial Intelligence and, hopefully, will bring a better
understanding of the concept.Comment: added four new section
Incremental Sampling-based Algorithms for Optimal Motion Planning
During the last decade, incremental sampling-based motion planning
algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown
to work well in practice and to possess theoretical guarantees such as
probabilistic completeness. However, no theoretical bounds on the quality of
the solution obtained by these algorithms have been established so far. The
first contribution of this paper is a negative result: it is proven that, under
mild technical conditions, the cost of the best path in the RRT converges
almost surely to a non-optimal value. Second, a new algorithm is considered,
called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost
of the best path in the RRG converges to the optimum almost surely. Third, a
tree version of RRG is introduced, called the RRT algorithm, which
preserves the asymptotic optimality of RRG while maintaining a tree structure
like RRT. The analysis of the new algorithms hinges on novel connections
between sampling-based motion planning algorithms and the theory of random
geometric graphs. In terms of computational complexity, it is shown that the
number of simple operations required by both the RRG and RRT algorithms is
asymptotically within a constant factor of that required by RRT.Comment: 20 pages, 10 figures, this manuscript is submitted to the
International Journal of Robotics Research, a short version is to appear at
the 2010 Robotics: Science and Systems Conference
Quantum Lightning Never Strikes the Same State Twice
Public key quantum money can be seen as a version of the quantum no-cloning
theorem that holds even when the quantum states can be verified by the
adversary. In this work, investigate quantum lightning, a formalization of
"collision-free quantum money" defined by Lutomirski et al. [ICS'10], where
no-cloning holds even when the adversary herself generates the quantum state to
be cloned. We then study quantum money and quantum lightning, showing the
following results:
- We demonstrate the usefulness of quantum lightning by showing several
potential applications, such as generating random strings with a proof of
entropy, to completely decentralized cryptocurrency without a block-chain,
where transactions is instant and local.
- We give win-win results for quantum money/lightning, showing that either
signatures/hash functions/commitment schemes meet very strong recently proposed
notions of security, or they yield quantum money or lightning.
- We construct quantum lightning under the assumed multi-collision resistance
of random degree-2 systems of polynomials.
- We show that instantiating the quantum money scheme of Aaronson and
Christiano [STOC'12] with indistinguishability obfuscation that is secure
against quantum computers yields a secure quantum money schem
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