837 research outputs found
On an Improved Correlation Analysis of Stream Ciphers Using Muti-Output Boolean Functions and the Related Generalized Notion of Nonlinearity
We investigate the security of -bit to -bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In this paper, we introduce a new approach for analyzing vector Boolean functions called generalized correlation analysis. It is based on approximate equations which are linear in the input but of free degree in the output . The complexity for computing the generalized nonlinearity for this new attack is reduced from to . Based on experimental results, we show that the new generalized correlation attack gives linear approximation with much higher bias than the Zhang-Chan and usual correlation attack. We confirm this with a theoretical upper bound for generalized nonlinearity, which is much lower than for the unrestricted nonlinearity (for Zhang-Chan\u27s attack) and {\em a fortiori} for usual nonlinearity. We also prove a lower bound for generalized nonlinearity which allows us to construct vector Boolean functions with high generalized nonlinearity from bent and almost bent functions. We derive the generalized nonlinearity of some known secondary constructions for secure vector Boolean functions. Finally, we prove that if a vector Boolean function has high nonlinearity or even a high unrestricted nonlinearity, it cannot ensure that it will have high generalized nonlinearity
Octal Bent Generalized Boolean Functions
In this paper we characterize (octal) bent generalized Boolean functions
defined on \BBZ_2^n with values in \BBZ_8. Moreover, we propose several
constructions of such generalized bent functions for both even and odd
Vaex: Big Data exploration in the era of Gaia
We present a new Python library called vaex, to handle extremely large
tabular datasets, such as astronomical catalogues like the Gaia catalogue,
N-body simulations or any other regular datasets which can be structured in
rows and columns. Fast computations of statistics on regular N-dimensional
grids allows analysis and visualization in the order of a billion rows per
second. We use streaming algorithms, memory mapped files and a zero memory copy
policy to allow exploration of datasets larger than memory, e.g. out-of-core
algorithms. Vaex allows arbitrary (mathematical) transformations using normal
Python expressions and (a subset of) numpy functions which are lazily evaluated
and computed when needed in small chunks, which avoids wasting of RAM. Boolean
expressions (which are also lazily evaluated) can be used to explore subsets of
the data, which we call selections. Vaex uses a similar DataFrame API as
Pandas, a very popular library, which helps migration from Pandas.
Visualization is one of the key points of vaex, and is done using binned
statistics in 1d (e.g. histogram), in 2d (e.g. 2d histograms with colormapping)
and 3d (using volume rendering). Vaex is split in in several packages:
vaex-core for the computational part, vaex-viz for visualization mostly based
on matplotlib, vaex-jupyter for visualization in the Jupyter notebook/lab based
in IPyWidgets, vaex-server for the (optional) client-server communication,
vaex-ui for the Qt based interface, vaex-hdf5 for hdf5 based memory mapped
storage, vaex-astro for astronomy related selections, transformations and
memory mapped (column based) fits storage. Vaex is open source and available
under MIT license on github, documentation and other information can be found
on the main website: https://vaex.io, https://docs.vaex.io or
https://github.com/maartenbreddels/vaexComment: 14 pages, 8 figures, Submitted to A&A, interactive version of Fig 4:
https://vaex.io/paper/fig
A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking
In this paper, a new chaotic pseudo-random number generator (PRNG) is
proposed. It combines the well-known ISAAC and XORshift generators with chaotic
iterations. This PRNG possesses important properties of topological chaos and
can successfully pass NIST and TestU01 batteries of tests. This makes our
generator suitable for information security applications like cryptography. As
an illustrative example, an application in the field of watermarking is
presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information
Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211,
October 201
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