219 research outputs found
On the Design of LIL Tests for (Pseudo) Random Generators and Some Experimental Results
NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo)
random generators to detect deviations of a binary sequence from randomness. On
the one hand, as a counter example to NIST SP800-22 test suite, it is easy to
construct functions that are considered as GOOD pseudorandom generators by NIST
SP800-22 test suite though the output of these functions are easily
distinguishable from the uniform distribution. Thus these functions are not
pseudorandom generators by definition. On the other hand, NIST SP800-22 does
not cover some of the important laws for randomness. Two fundamental limit
theorems about random binary strings are the central limit theorem and the law
of the iterated logarithm (LIL). Several frequency related tests in NIST
SP800-22 cover the central limit theorem while no NIST SP800-22 test covers
LIL.
This paper proposes techniques to address the above challenges that NIST
SP800-22 testing suite faces. Firstly, we propose statistical distance based
testing techniques for (pseudo) random generators to reduce the above mentioned
Type II errors in NIST SP800-22 test suite. Secondly, we propose LIL based
statistical testing techniques, calculate the probabilities, and carry out
experimental tests on widely used pseudorandom generators by generating around
30TB of pseudorandom sequences. The experimental results show that for a sample
size of 1000 sequences (2TB), the statistical distance between the generated
sequences and the uniform distribution is around 0.07 (with for
statistically indistinguishable and for completely distinguishable) and the
root-mean-square deviation is around 0.005
Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes
This paper compares the efficiency of various algorithms for implementing
quantum resistant public key encryption scheme RLCE on 64-bit CPUs. By
optimizing various algorithms for polynomial and matrix operations over finite
fields, we obtained several interesting (or even surprising) results. For
example, it is well known (e.g., Moenck 1976 \cite{moenck1976practical}) that
Karatsuba's algorithm outperforms classical polynomial multiplication algorithm
from the degree 15 and above (practically, Karatsuba's algorithm only
outperforms classical polynomial multiplication algorithm from the degree 35
and above ). Our experiments show that 64-bit optimized Karatsuba's algorithm
will only outperform 64-bit optimized classical polynomial multiplication
algorithm for polynomials of degree 115 and above over finite field
. The second interesting (surprising) result shows that 64-bit
optimized Chien's search algorithm ourperforms all other 64-bit optimized
polynomial root finding algorithms such as BTA and FFT for polynomials of all
degrees over finite field . The third interesting (surprising)
result shows that 64-bit optimized Strassen matrix multiplication algorithm
only outperforms 64-bit optimized classical matrix multiplication algorithm for
matrices of dimension 750 and above over finite field . It should
be noted that existing literatures and practices recommend Strassen matrix
multiplication algorithm for matrices of dimension 40 and above. All our
experiments are done on a 64-bit MacBook Pro with i7 CPU and single thread C
codes. It should be noted that the reported results should be appliable to 64
or larger bits CPU architectures. For 32 or smaller bits CPUs, these results
may not be applicable. The source code and library for the algorithms covered
in this paper are available at http://quantumca.org/
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