118 research outputs found
11 x 11 Domineering is Solved: The first player wins
We have developed a program called MUDoS (Maastricht University Domineering
Solver) that solves Domineering positions in a very efficient way. This enables
the solution of known positions so far (up to the 10 x 10 board) much quicker
(measured in number of investigated nodes).
More importantly, it enables the solution of the 11 x 11 Domineering board, a
board up till now far out of reach of previous Domineering solvers. The
solution needed the investigation of 259,689,994,008 nodes, using almost half a
year of computation time on a single simple desktop computer. The results show
that under optimal play the first player wins the 11 x 11 Domineering game,
irrespective if Vertical or Horizontal starts the game.
In addition, several other boards hitherto unsolved were solved. Using the
convention that Vertical starts, the 8 x 15, 11 x 9, 12 x 8, 12 x 15, 14 x 8,
and 17 x 6 boards are all won by Vertical, whereas the 6 x 17, 8 x 12, 9 x 11,
and 11 x 10 boards are all won by Horizontal
Decay of Correlations in a Topological Glass
In this paper we continue the study of a topological glassy system. The state
space of the model is given by all triangulations of a sphere with nodes,
half of which are red and half are blue. Red nodes want to have 5 neighbors
while blue ones want 7. Energies of nodes with other numbers of neighbors are
supposed to be positive. The dynamics is that of flipping the diagonal between
two adjacent triangles, with a temperature dependent probability. We consider
the system at very low temperatures.
We concentrate on several new aspects of this model: Starting from a detailed
description of the stationary state, we conclude that pairs of defects (nodes
with the "wrong" degree) move with very high mobility along 1-dimensional
paths. As they wander around, they encounter single defects, which they then
move "sideways" with a geometrically defined probability. This induces a
diffusive motion of the single defects. If they meet, they annihilate, lowering
the energy of the system. We both estimate the decay of energy to equilibrium,
as well as the correlations. In particular, we find a decay like
Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance
Parameters of LDPC codes, such as minimum distance, stopping distance,
stopping redundancy, girth of the Tanner graph, and their influence on the
frame error rate performance of the BP, ML and near-ML decoding over a BEC and
an AWGN channel are studied. Both random and structured LDPC codes are
considered. In particular, the BP decoding is applied to the code parity-check
matrices with an increasing number of redundant rows, and the convergence of
the performance to that of the ML decoding is analyzed. A comparison of the
simulated BP, ML, and near-ML performance with the improved theoretical bounds
on the error probability based on the exact weight spectrum coefficients and
the exact stopping size spectrum coefficients is presented. It is observed that
decoding performance very close to the ML decoding performance can be achieved
with a relatively small number of redundant rows for some codes, for both the
BEC and the AWGN channels
An iterative algorithm for parametrization of shortest length shift registers over finite rings
The construction of shortest feedback shift registers for a finite sequence
S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is
presented that yields a parametrization of all shortest feedback shift
registers for the sequence of numbers S_1,...,S_N, thus solving an open problem
in the literature. The algorithm iteratively processes each number, starting
with S_1, and constructs at each step a particular type of minimal Gr\"obner
basis. The construction involves a simple update rule at each step which leads
to computational efficiency. It is shown that the algorithm simultaneously
computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte
On Weak Keys and Forgery Attacks Against Polynomial-Based MAC Schemes
Abstract. Universal hash functions are commonly used primitives for fast and secure message authentication in the form of Message Authentication Codes (MACs) or Authenticated Encryption with Associated Data (AEAD) schemes. These schemes are widely used and standardised, the most well known being McGrew and Viega’s Galois/Counter Mode (GCM). In this paper we identify some properties of hash functions based on polynomial evaluation that arise from the underlying algebraic structure. As a result we are able to describe a general forgery attack, of which Saarinen’s cycling attack from FSE 2012 is a special case. Our attack removes the requirement for long messages and applies regardless of the field in which the hash function is evaluated. Furthermore we provide a common description of all published attacks against GCM, by showing that the existing attacks are the result of these algebraic properties of the polynomial-based hash function. We also greatly expand the number of known weak GCM keys and show that almost every subset of the keyspace is a weak key class. Finally, we demonstrate that these algebraic properties and corresponding attacks are highly relevant to GCM/2 +, a variant of GCM designed to increase the efficiency in software
Complexity of token swapping and its variants
AbstractIn the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is W[1]-hard parameterized by the length k of a shortest sequence of swaps. In fact, we prove that, for any computable function f, it cannot be solved in time f(k)no(k/logk) where n is the number of vertices of the input graph, unless the ETH fails. This lower bound almost matches the trivial nO(k)-time algorithm. We also consider two generalizations of the Token Swapping, namely Colored Token Swapping (where the tokens have colors and tokens of the same color are indistinguishable), and Subset Token Swapping (where each token has a set of possible destinations). To complement the hardness result, we prove that even the most general variant, Subset Token Swapping, is FPT in nowhere-dense graph classes. Finally, we consider the complexities of all three problems in very restricted classes of graphs: graphs of bounded treewidth and diameter, stars, cliques, and paths, trying to identify the borderlines between polynomial and NP-hard cases
A Traceable Ring Signature Scheme based on Coding Theory
Traceable ring signatures are a variant of ring signatures which allows the identity of a user to be revealed, when it signs two different messages with respect to the same group of users. It has applications in e-voting and in cryptocurrencies, such as the well-known Monero. We propose the first traceable ring signature scheme whose security is based on the hardness of the Syndrome Decoding problem, a problem in coding theory which is conjectured to be unsolvable by both classical and quantum algorithms. To construct the scheme, we use a variant of Stern\u27s protocol and, by applying the Fiat-Shamir transform to it in an ingenious way, we obtain a ring signature that allows traceability. We prove that the resulting protocol has the standard security properties for traceable ring signatures in the random oracle model: tag-linkability, anonymity and exculpability. As far as we know, this is the first proposal for a traceable ring signature scheme in the post-quantum setting
Optimal Forgeries Against Polynomial-Based MACs and GCM
Polynomial-based authentication algorithms, such as GCM and Poly1305, have seen widespread adoption in practice. Due to their importance, a significant amount of attention has been given to understanding and improving both proofs and attacks against such schemes. At EUROCRYPT 2005, Bernstein published the best known analysis of the schemes when instantiated with PRPs, thereby establishing the most lenient limits on the amount of data the schemes can process per key. A long line of work, initiated by Handschuh and Preneel at CRYPTO 2008, finds the best known attacks, advancing our understanding of the fragility of the schemes. Yet surprisingly, no known attacks perform as well as the predicted worst-case attacks allowed by Bernstein\u27s analysis, nor has there been any advancement in proofs improving Bernstein\u27s bounds, and the gap between attacks and analysis is significant. We settle the issue by finding a novel attack against polynomial-based authentication algorithms using PRPs, and combine it with new analysis, to show that Bernstein\u27s bound, and our attacks, are optimal
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