On the Use of Reducible Polynomials as Random Number Generators
نویسندگان
چکیده
The randomness properties and the hierarchy of correlation coefficients are studied of approximate-maximum-length sequences, for which the characteristic polynomial is a product of several primitive polynomials. The randomness properties are almost the same as for maximum-length sequences characterized by a primitive polynomial with many terms and of the same degree. Reducible characteristic polynomials have acceptable figures of merit and can be of extremely high degree. Since they are also easily constructed and implemented, reducible polynomials are strong candidates for reliable random number generation, especially at the bit rates needed in large-scale Monte Carlo simulations.
منابع مشابه
Reducible cubic CNS polynomials
The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are tr...
متن کاملCounting Reducible Matrices, Polynomials, and Surface and Free Group Automorphisms
A. We give upper bounds on the numbers of various classes of polynomials reducible over Z and over Z/pZ, and on the number of matrices in SL(n),GL(n) and Sp(2n) with reducible characteristic polynomials, and on polynomials with non-generic Galois groups. We use our result to show that a random (in the appropriate sense) element of the mapping class group of a closed surface is pseudo-Ano...
متن کاملOn Classifications of Random Polynomials
Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...
متن کاملDesign of low power random number generators for quantum-dot cellular automata
Quantum-dot cellular automata (QCA) are a promising nanotechnology to implement digital circuits at the nanoscale. Devices based on QCA have the advantages of faster speed, lower power consumption, and greatly reduced sizes. In this paper, we are presented the circuits, which generate random numbers in QCA. Random numbers have many uses in science, art, statistics, cryptography, gaming, gambli...
متن کامل