24,708 research outputs found
Statistical Signatures of Structural Organization: The case of long memory in renewal processes
Identifying and quantifying memory are often critical steps in developing a
mechanistic understanding of stochastic processes. These are particularly
challenging and necessary when exploring processes that exhibit long-range
correlations. The most common signatures employed rely on second-order temporal
statistics and lead, for example, to identifying long memory in processes with
power-law autocorrelation function and Hurst exponent greater than .
However, most stochastic processes hide their memory in higher-order temporal
correlations. Information measures---specifically, divergences in the mutual
information between a process' past and future (excess entropy) and minimal
predictive memory stored in a process' causal states (statistical
complexity)---provide a different way to identify long memory in processes with
higher-order temporal correlations. However, there are no ergodic stationary
processes with infinite excess entropy for which information measures have been
compared to autocorrelation functions and Hurst exponents. Here, we show that
fractal renewal processes---those with interevent distribution tails ---exhibit long memory via a phase transition at .
Excess entropy diverges only there and statistical complexity diverges there
and for all . When these processes do have power-law
autocorrelation function and Hurst exponent greater than , they do not
have divergent excess entropy. This analysis breaks the intuitive association
between these different quantifications of memory. We hope that the methods
used here, based on causal states, provide some guide as to how to construct
and analyze other long memory processes.Comment: 13 pages, 2 figures, 3 appendixes;
http://csc.ucdavis.edu/~cmg/compmech/pubs/lrmrp.ht
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
Hard isogeny problems over RSA moduli and groups with infeasible inversion
We initiate the study of computational problems on elliptic curve isogeny
graphs defined over RSA moduli. We conjecture that several variants of the
neighbor-search problem over these graphs are hard, and provide a comprehensive
list of cryptanalytic attempts on these problems. Moreover, based on the
hardness of these problems, we provide a construction of groups with infeasible
inversion, where the underlying groups are the ideal class groups of imaginary
quadratic orders.
Recall that in a group with infeasible inversion, computing the inverse of a
group element is required to be hard, while performing the group operation is
easy. Motivated by the potential cryptographic application of building a
directed transitive signature scheme, the search for a group with infeasible
inversion was initiated in the theses of Hohenberger and Molnar (2003). Later
it was also shown to provide a broadcast encryption scheme by Irrer et al.
(2004). However, to date the only case of a group with infeasible inversion is
implied by the much stronger primitive of self-bilinear map constructed by
Yamakawa et al. (2014) based on the hardness of factoring and
indistinguishability obfuscation (iO). Our construction gives a candidate
without using iO.Comment: Significant revision of the article previously titled "A Candidate
Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the
constructions by giving toy examples, added "The Parallelogram Attack" (Sec
5.3.2). 54 pages, 8 figure
On the security of the Blockchain Bix Protocol and Certificates
The BIX protocol is a blockchain-based protocol that allows distribution of
certificates linking a subject with his public key, hence providing a service
similar to that of a PKI but without the need of a CA. In this paper we analyze
the security of the BIX protocol in a formal way, in four steps. First, we
identify formal security assumptions which are well-suited to this protocol.
Second, we present some attack scenarios against the BIX protocol. Third, we
provide a formal security proof that some of these attacks are not feasible
under our previously established assumptions. Finally, we show how another
attack may be carried on.Comment: 16 pages, 1 figur
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory
The present survey reports on the state of the art of the different
cryptographic functionalities built upon the ring learning with errors problem
and its interplay with several classical problems in algebraic number theory.
The survey is based to a certain extent on an invited course given by the
author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other
authors/ comment of the author: quotation has been added to Theorem 5.
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