789 research outputs found
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
Factorizing Numbers with the Gauss Sum Technique: NMR Implementations
Several physics-based algorithms for factorizing large number were recently
published. A notable recent one by Schleich et al. uses Gauss sums for
distinguishing between factors and non-factors. We demonstrate two NMR
techniques that evaluate Gauss sums and thus implement their algorithm. The
first one is based on differential excitation of a single spin magnetization by
a cascade of RF pulses. The second method is based on spatial averaging and
selective refocusing of magnetization for Gauss sums corresponding to factors.
All factors of 16637 and 52882363 are successfully obtained.Comment: 4 pages, 4 figures; Abstract and Conclusion are slightly modified.
References added and formatted with Bibte
Keyword-Based Delegable Proofs of Storage
Cloud users (clients) with limited storage capacity at their end can
outsource bulk data to the cloud storage server. A client can later access her
data by downloading the required data files. However, a large fraction of the
data files the client outsources to the server is often archival in nature that
the client uses for backup purposes and accesses less frequently. An untrusted
server can thus delete some of these archival data files in order to save some
space (and allocate the same to other clients) without being detected by the
client (data owner). Proofs of storage enable the client to audit her data
files uploaded to the server in order to ensure the integrity of those files.
In this work, we introduce one type of (selective) proofs of storage that we
call keyword-based delegable proofs of storage, where the client wants to audit
all her data files containing a specific keyword (e.g., "important"). Moreover,
it satisfies the notion of public verifiability where the client can delegate
the auditing task to a third-party auditor who audits the set of files
corresponding to the keyword on behalf of the client. We formally define the
security of a keyword-based delegable proof-of-storage protocol. We construct
such a protocol based on an existing proof-of-storage scheme and analyze the
security of our protocol. We argue that the techniques we use can be applied
atop any existing publicly verifiable proof-of-storage scheme for static data.
Finally, we discuss the efficiency of our construction.Comment: A preliminary version of this work has been published in
International Conference on Information Security Practice and Experience
(ISPEC 2018
Detecting brute-force attacks on cryptocurrency wallets
Blockchain is a distributed ledger, which is protected against malicious
modifications by means of cryptographic tools, e.g. digital signatures and hash
functions. One of the most prominent applications of blockchains is
cryptocurrencies, such as Bitcoin. In this work, we consider a particular
attack on wallets for collecting assets in a cryptocurrency network based on
brute-force search attacks. Using Bitcoin as an example, we demonstrate that if
the attack is implemented successfully, a legitimate user is able to prove that
fact of this attack with a high probability. We also consider two options for
modification of existing cryptocurrency protocols for dealing with this type of
attacks. First, we discuss a modification that requires introducing changes in
the Bitcoin protocol and allows diminishing the motivation to attack wallets.
Second, an alternative option is the construction of special smart-contracts,
which reward the users for providing evidence of the brute-force attack. The
execution of this smart-contract can work as an automatic alarm that the
employed cryptographic mechanisms, and (particularly) hash functions, have an
evident vulnerability.Comment: 10 pages, 2 figures; published versio
Probing F-theory With Multiple Branes
We study multiple 3-branes on an F theory orientifold. The world-volume
theory of the 3-branes is d=4, N=2 Sp(2k) gauge theory with an antisymmetric
tensor and four flavors of matter in the fundamental. The solution of this
gauge theory is found for vanishing bare mass of the antisymmetric tensor
matter, and massive fundamental matter. The integrable system underlying this
theory is constructed.Comment: 9 pages, harvma
On rationality of the intersection points of a line with a plane quartic
We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case;
Conjecture 1 from the previous version is proved wron
The Saito-Kurokawa lifting and Darmon points
Let E_{/_\Q} be an elliptic curve of conductor with and let
be its associated newform of weight 2. Denote by the -adic
Hida family passing though , and by its -adic
Saito-Kurokawa lift. The -adic family of Siegel modular forms
admits a formal Fourier expansion, from which we can define a family of
normalized Fourier coefficients indexed by positive
definite symmetric half-integral matrices of size . We relate
explicitly certain global points on (coming from the theory of
Stark-Heegner points) with the values of these Fourier coefficients and of
their -adic derivatives, evaluated at weight .Comment: 14 pages. Title change
A note on q-Bernoulli numbers and polynomials
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials
of higher order.Comment: 8 page
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