8,109 research outputs found
Algebraic Attack on the Alternating Step(r,s)Generator
The Alternating Step(r,s) Generator, ASG(r,s), is a clock-controlled sequence
generator which is recently proposed by A. Kanso. It consists of three
registers of length l, m and n bits. The first register controls the clocking
of the two others. The two other registers are clocked r times (or not clocked)
(resp. s times or not clocked) depending on the clock-control bit in the first
register. The special case r=s=1 is the original and well known Alternating
Step Generator. Kanso claims there is no efficient attack against the ASG(r,s)
since r and s are kept secret. In this paper, we present an Alternating Step
Generator, ASG, model for the ASG(r,s) and also we present a new and efficient
algebraic attack on ASG(r,s) using 3(m+n) bits of the output sequence to find
the secret key with O((m^2+n^2)*2^{l+1}+ (2^{m-1})*m^3 + (2^{n-1})*n^3)
computational complexity. We show that this system is no more secure than the
original ASG, in contrast to the claim of the ASG(r,s)'s constructor.Comment: 5 pages, 2 figures, 2 tables, 2010 IEEE International Symposium on
Information Theory (ISIT2010),June 13-18, 2010, Austin, Texa
Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics
Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics
The Scalar Curvature Problem on the Four Dimensional Half Sphere
In this paper, we consider the problem of prescribing the scalar curvature
under minimal boundary conditions on the standard four dimensional half sphere.
We provide an Euler-Hopf type criterion for a given function to be a scalar
curvature to a metric conformal to the standard one. Our proof involves the
study of critical points at infinity of the associated variational problem.Comment: 19 page
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