Twisting generators for pseudorandom numbers may use a congruential array to simulate stochastic sequences. Typically, the computer program controls the quantity of elements in array to limit the random access memory. This technique may have limitations in situations where the stochastic sequences have an insufficient size for some application tasks, ranging from theoretical mathematics and tec...

The ns-2 is a widely used network simulation tool which implements a fairly old and weak random number generator (RNG). As the RNG component is used by a variety of other components, it can be seen as one of the most important core components of the ns-2. In this paper we explore weaknesses of this RNG and demonstrate its shortcomings in context with a simple simulation example (M/D/1) which pr...

This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined when p is a Mersenne pri...

In this article, we show how to prove that an odd perfect number with eight distinct prime factors is divisible by 5. A perfect number N is equal to twice the sum of its divisors: σ(N) = 2N . The theory of perfect numbers when N is even is well known: Euclid proved that if 2 − 1 is prime, then 2p−1(2p − 1) is perfect, and Euler proved that every one is of this type. These numbers have seen a gr...

We propose two stream ciphers based on a non-secure pseudorandom number generator (called the mother generator). The mother generator is here chosen to be the Mersenne Twister (MT), a widely used 32-bit integer generator having 19937 bits of internal state and period 219937 − 1. One proposal is CryptMT, which computes the accumulative product of the output of MT, and use the most significant 8 ...

In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number p = 2 − 1, where n is a prime, a positive integer h , and two n -bit integers T,R , find two n -bit integers F,G each of Hamming weight at most h such that T = F ·R+G modulo p , under the promise that they exist.

A q query Locally Decodable Code (LDC) encodes an n-bit message x as an N -bit codeword C(x), such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword C(x), even after some constant fraction of codeword bits has been corrupted. We give new constructions of three query LDCs of vastly shorter length than that of previous constructions. Specific...