685 research outputs found
Small generic hardcore subsets for the discrete logarithm: short secret DL-Keys
Abstract Let G be a group of prime order q with generator g. We study hardcore subsets H ⊂ G of the discrete logarithm (DL) log g in the model of generic algorithms. In this model we count group operations such as multiplication and division, while computations with non-group data are for free. It is known from Nechaev [Math. Notes 55 (1994
Arithmetic complexity via effective names for random sequences
We investigate enumerability properties for classes of sets which permit
recursive, lexicographically increasing approximations, or left-r.e. sets. In
addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably,
Schnorr, and Kurtz random sets, weakly 1-generics and their complementary
classes, we find that there exist characterizations of the third and fourth
levels of the arithmetic hierarchy purely in terms of these notions.
More generally, there exists an equivalence between arithmetic complexity and
existence of numberings for classes of left-r.e. sets with shift-persistent
elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz
non-randoms) have left-r.e. numberings, there is no canonical, or acceptable,
left-r.e. numbering for any class of left-r.e. randoms.
Finally, we note some fundamental differences between left-r.e. numberings
for sets and reals
A Machine-Checked Formalization of the Generic Model and the Random Oracle Model
Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode
Sustainable Energy Storage
This Final Design Review document covers the work we, students at California Polytechnic State University – San Luis Obispo, have performed in collaboration with Mr. Harish Bhutani and Dr. Mohammad Noori. The project’s intent is to create an energy storage system for off-grid and developing region applications using alternative technologies to lithium-ion battery storage. We plan to manufacture and assemble a scale model of the energy storage system to prove effectiveness and practicality. This system will store enough energy to power basic appliances and essential devices for a house or community. The chosen design direction will be a flywheel, as it is very energy dense and is less complex than other options. The following will outline the entire design process, including the ideas we created, the design challenges, and the testing of our physical build. To meet climate change goals set around the globe, our world needs to head towards a more sustainable future, and the energy sector is no exception. This project aims to help with the research and design of this new field and present a final product that will have a meaningful impact on our world
Amplification by stochastic interference
A new method is introduced to obtain a strong signal by the interference of
weak signals in noisy channels. The method is based on the interference of 1/f
noise from parallel channels. One realization of stochastic interference is the
auditory nervous system. Stochastic interference may have broad potential
applications in the information transmission by parallel noisy channels
The invertibility of the XOR of rotations of a binary word
We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.
Universal fluctuations in subdiffusive transport
Subdiffusive transport in tilted washboard potentials is studied within the
fractional Fokker-Planck equation approach, using the associated continuous
time random walk (CTRW) framework. The scaled subvelocity is shown to obey a
universal law, assuming the form of a stationary Levy-stable distribution. The
latter is defined by the index of subdiffusion alpha and the mean subvelocity
only, but interestingly depends neither on the bias strength nor on the
specific form of the potential. These scaled, universal subvelocity
fluctuations emerge due to the weak ergodicity breaking and are vanishing in
the limit of normal diffusion. The results of the analytical heuristic theory
are corroborated by Monte Carlo simulations of the underlying CTRW
Slide reduction, revisited—filling the gaps in svp approximation
We show how to generalize Gama and Nguyen's slide reduction algorithm [STOC
'08] for solving the approximate Shortest Vector Problem over lattices (SVP).
As a result, we show the fastest provably correct algorithm for
-approximate SVP for all approximation factors . This is the range of approximation factors most
relevant for cryptography
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