951 research outputs found
Applications of Multilinear Forms to Cryptography
We study the problem of finding efficiently computable non-degenerate multilinear maps from to , where and are groups of the same prime order, and where computing discrete logarithms in is hard. We present several applications to cryptography, explore directions for building such maps, and give some reasons to believe that finding examples with may be difficult
Unbounded violation of tripartite Bell inequalities
We prove that there are tripartite quantum states (constructed from random
unitaries) that can lead to arbitrarily large violations of Bell inequalities
for dichotomic observables. As a consequence these states can withstand an
arbitrary amount of white noise before they admit a description within a local
hidden variable model. This is in sharp contrast with the bipartite case, where
all violations are bounded by Grothendieck's constant. We will discuss the
possibility of determining the Hilbert space dimension from the obtained
violation and comment on implications for communication complexity theory.
Moreover, we show that the violation obtained from generalized GHZ states is
always bounded so that, in contrast to many other contexts, GHZ states do in
this case not lead to extremal quantum correlations. The results are based on
tools from the theories of operator spaces and tensor norms which we exploit to
prove the existence of bounded but not completely bounded trilinear forms from
commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more
accessible for a non-specialized reade
Regular and almost universal hashing: an efficient implementation
Random hashing can provide guarantees regarding the performance of data
structures such as hash tables---even in an adversarial setting. Many existing
families of hash functions are universal: given two data objects, the
probability that they have the same hash value is low given that we pick hash
functions at random. However, universality fails to ensure that all hash
functions are well behaved. We further require regularity: when picking data
objects at random they should have a low probability of having the same hash
value, for any fixed hash function. We present the efficient implementation of
a family of non-cryptographic hash functions (PM+) offering good running times,
good memory usage as well as distinguishing theoretical guarantees: almost
universality and component-wise regularity. On a variety of platforms, our
implementations are comparable to the state of the art in performance. On
recent Intel processors, PM+ achieves a speed of 4.7 bytes per cycle for 32-bit
outputs and 3.3 bytes per cycle for 64-bit outputs. We review vectorization
through SIMD instructions (e.g., AVX2) and optimizations for superscalar
execution.Comment: accepted for publication in Software: Practice and Experience in
September 201
A Closer Look at the Multilinear Cryptography using Nilpotent Groups
In a previous paper we generalized the definition of a multilinear map to
arbitrary groups and introduced two multiparty key-exchange protocols using
nilpotent groups. In this paper we have a closer look at the protocols and will
address some incorrect cryptanalysis which have been proposed
Foundations and applications of program obfuscation
Code is said to be obfuscated if it is intentionally difficult for humans to understand.
Obfuscating a program conceals its sensitive implementation details and
protects it from reverse engineering and hacking. Beyond software protection, obfuscation
is also a powerful cryptographic tool, enabling a variety of advanced applications.
Ideally, an obfuscated program would hide any information about the original
program that cannot be obtained by simply executing it. However, Barak et al.
[CRYPTO 01] proved that for some programs, such ideal obfuscation is impossible.
Nevertheless, Garg et al. [FOCS 13] recently suggested a candidate general-purpose
obfuscator which is conjectured to satisfy a weaker notion of security called indistinguishability
obfuscation.
In this thesis, we study the feasibility and applicability of secure obfuscation:
- What notions of secure obfuscation are possible and under what assumptions?
- How useful are weak notions like indistinguishability obfuscation?
Our first result shows that the applications of indistinguishability obfuscation go
well beyond cryptography. We study the tractability of computing a Nash equilibrium
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of a game { a central problem in algorithmic game theory and complexity theory.
Based on indistinguishability obfuscation, we construct explicit games where a Nash
equilibrium cannot be found efficiently.
We also prove the following results on the feasibility of obfuscation. Our starting
point is the Garg at el. obfuscator that is based on a new algebraic encoding scheme
known as multilinear maps [Garg et al. EUROCRYPT 13].
1. Building on the work of Brakerski and Rothblum [TCC 14], we provide the first
rigorous security analysis for obfuscation. We give a variant of the Garg at el.
obfuscator and reduce its security to that of the multilinear maps. Specifically,
modeling the multilinear encodings as ideal boxes with perfect security, we prove
ideal security for our obfuscator. Our reduction shows that the obfuscator resists
all generic attacks that only use the encodings' permitted interface and do not
exploit their algebraic representation.
2. Going beyond generic attacks, we study the notion of virtual-gray-box obfusca-
tion [Bitansky et al. CRYPTO 10]. This relaxation of ideal security is stronger
than indistinguishability obfuscation and has several important applications
such as obfuscating password protected programs. We formulate a security
requirement for multilinear maps which is sufficient, as well as necessary for
virtual-gray-box obfuscation.
3. Motivated by the question of basing obfuscation on ideal objects that are simpler
than multilinear maps, we give a negative result showing that ideal obfuscation
is impossible, even in the random oracle model, where the obfuscator is given access
to an ideal random function. This is the first negative result for obfuscation
in a non-trivial idealized model
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