13,463 research outputs found
A new class of codes for Boolean masking of cryptographic computations
We introduce a new class of rate one-half binary codes: {\bf complementary
information set codes.} A binary linear code of length and dimension
is called a complementary information set code (CIS code for short) if it has
two disjoint information sets. This class of codes contains self-dual codes as
a subclass. It is connected to graph correlation immune Boolean functions of
use in the security of hardware implementations of cryptographic primitives.
Such codes permit to improve the cost of masking cryptographic algorithms
against side channel attacks. In this paper we investigate this new class of
codes: we give optimal or best known CIS codes of length We derive
general constructions based on cyclic codes and on double circulant codes. We
derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all
be classified in small lengths by the building up construction. Some
nonlinear permutations are constructed by using -codes, based on the
notion of dual distance of an unrestricted code.Comment: 19 pages. IEEE Trans. on Information Theory, to appea
Complexity classifications for different equivalence and audit problems for Boolean circuits
We study Boolean circuits as a representation of Boolean functions and
consider different equivalence, audit, and enumeration problems. For a number
of restricted sets of gate types (bases) we obtain efficient algorithms, while
for all other gate types we show these problems are at least NP-hard.Comment: 25 pages, 1 figur
Generalized Satisfiability Problems via Operator Assignments
Schaefer introduced a framework for generalized satisfiability problems on
the Boolean domain and characterized the computational complexity of such
problems. We investigate an algebraization of Schaefer's framework in which the
Fourier transform is used to represent constraints by multilinear polynomials
in a unique way. The polynomial representation of constraints gives rise to a
relaxation of the notion of satisfiability in which the values to variables are
linear operators on some Hilbert space. For the case of constraints given by a
system of linear equations over the two-element field, this relaxation has
received considerable attention in the foundations of quantum mechanics, where
such constructions as the Mermin-Peres magic square show that there are systems
that have no solutions in the Boolean domain, but have solutions via operator
assignments on some finite-dimensional Hilbert space. We obtain a complete
characterization of the classes of Boolean relations for which there is a gap
between satisfiability in the Boolean domain and the relaxation of
satisfiability via operator assignments. To establish our main result, we adapt
the notion of primitive-positive definability (pp-definability) to our setting,
a notion that has been used extensively in the study of constraint satisfaction
problems. Here, we show that pp-definability gives rise to gadget reductions
that preserve satisfiability gaps. We also present several additional
applications of this method. In particular and perhaps surprisingly, we show
that the relaxed notion of pp-definability in which the quantified variables
are allowed to range over operator assignments gives no additional expressive
power in defining Boolean relations
The Connectivity of Boolean Satisfiability: Dichotomies for Formulas and Circuits
For Boolean satisfiability problems, the structure of the solution space is
characterized by the solution graph, where the vertices are the solutions, and
two solutions are connected iff they differ in exactly one variable. In 2006,
Gopalan et al. studied connectivity properties of the solution graph and
related complexity issues for CSPs, motivated mainly by research on
satisfiability algorithms and the satisfiability threshold. They proved
dichotomies for the diameter of connected components and for the complexity of
the st-connectivity question, and conjectured a trichotomy for the connectivity
question. Recently, we were able to establish the trichotomy [arXiv:1312.4524].
Here, we consider connectivity issues of satisfiability problems defined by
Boolean circuits and propositional formulas that use gates, resp. connectives,
from a fixed set of Boolean functions. We obtain dichotomies for the diameter
and the two connectivity problems: on one side, the diameter is linear in the
number of variables, and both problems are in P, while on the other side, the
diameter can be exponential, and the problems are PSPACE-complete. For
partially quantified formulas, we show an analogous dichotomy.Comment: 20 pages, several improvement
Session Types in a Linearly Typed Multi-Threaded Lambda-Calculus
We present a formalization of session types in a multi-threaded
lambda-calculus (MTLC) equipped with a linear type system, establishing for the
MTLC both type preservation and global progress. The latter (global progress)
implies that the evaluation of a well-typed program in the MTLC can never reach
a deadlock. As this formulated MTLC can be readily embedded into ATS, a
full-fledged language with a functional programming core that supports both
dependent types (of DML-style) and linear types, we obtain a direct
implementation of session types in ATS. In addition, we gain immediate support
for a form of dependent session types based on this embedding into ATS.
Compared to various existing formalizations of session types, we see the one
given in this paper is unique in its closeness to concrete implementation. In
particular, we report such an implementation ready for practical use that
generates Erlang code from well-typed ATS source (making use of session types),
thus taking great advantage of the infrastructural support for distributed
computing in Erlang.Comment: This is the original version of the paper on supporting programming
with dyadic session types in AT
A Sound and Complete Axiomatization of Majority-n Logic
Manipulating logic functions via majority operators recently drew the
attention of researchers in computer science. For example, circuit optimization
based on majority operators enables superior results as compared to traditional
logic systems. Also, the Boolean satisfiability problem finds new solving
approaches when described in terms of majority decisions. To support computer
logic applications based on majority a sound and complete set of axioms is
required. Most of the recent advances in majority logic deal only with ternary
majority (MAJ- 3) operators because the axiomatization with solely MAJ-3 and
complementation operators is well understood. However, it is of interest
extending such axiomatization to n-ary majority operators (MAJ-n) from both the
theoretical and practical perspective. In this work, we address this issue by
introducing a sound and complete axiomatization of MAJ-n logic. Our
axiomatization naturally includes existing majority logic systems. Based on
this general set of axioms, computer applications can now fully exploit the
expressive power of majority logic.Comment: Accepted by the IEEE Transactions on Computer
The complexity of approximately counting in 2-spin systems on -uniform bounded-degree hypergraphs
One of the most important recent developments in the complexity of
approximate counting is the classification of the complexity of approximating
the partition functions of antiferromagnetic 2-spin systems on bounded-degree
graphs. This classification is based on a beautiful connection to the so-called
uniqueness phase transition from statistical physics on the infinite
-regular tree. Our objective is to study the impact of this
classification on unweighted 2-spin models on -uniform hypergraphs. As has
already been indicated by Yin and Zhao, the connection between the uniqueness
phase transition and the complexity of approximate counting breaks down in the
hypergraph setting. Nevertheless, we show that for every non-trivial symmetric
-ary Boolean function there exists a degree bound so that for
all the following problem is NP-hard: given a
-uniform hypergraph with maximum degree at most , approximate the
partition function of the hypergraph 2-spin model associated with . It is
NP-hard to approximate this partition function even within an exponential
factor. By contrast, if is a trivial symmetric Boolean function (e.g., any
function that is excluded from our result), then the partition function of
the corresponding hypergraph 2-spin model can be computed exactly in polynomial
time
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