Distribution of Special Sequences modulo a Large Prime
نویسنده
چکیده
As it was indicated in [5], A. Odlyzko asks for which values of N the set A contains all residue classes (modp). The conjecture is that one can take N to be as small as p1/2+ε, for any positive ε and p > c with some c = c(ε). From the result of Rudnick and Zaharescu [4] it follows that in Odlyzko’s problem one can take N = c0p logp for some absolute constant c0. One of the main results of [5] is that for the exceptional set of Odlyzko’s problem we have
منابع مشابه
A Class of Random Sequences for Key Generation
This paper investigates randomness properties of sequences derived from Fibonacci and Gopala-Hemachandra sequences modulo m for use in key distribution applications. We show that for sequences modulo a prime a binary random sequence B(n) is obtained based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). For the more general case of arbitrary m, we use the property if the peri...
متن کاملA Comparative S-Index in Factoring RSA Modulus via Lucas Sequences
General Lucas sequences are practically useful in cryptography. In the past quarter century, factoring large RSA modulo into its primes is one of the most important and most challenging problems in computational number theory. A factoring technique on RSA modulo is mainly hindered by the strong prime properties. The success of factoring few large RSA modulo within the last few decades has been ...
متن کاملLinear Complexity of a Family of Pseudorandom Discrete Logarithm Threshold Sequences
We discuss the linear complexity of a family of binary threshold sequence defined by the discrete logarithm of integers modulo a large prime. It is proved that the linear complexity is at least the half of their period and under some special conditions the linear complexity can achieve maximal.
متن کاملCompleteness results for metrized rings and lattices
The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...
متن کاملOn Periods modulo a Prime of Some Classes of Sequences of Integers
Theorem 1: Let un, n > 0, be the general term of a given sequence of integers and define the transformation T^yk)(un) as T^xyJc){un) = xun+lc +yun for every n > 0, A: being a positive integer. Then, if x mdy are nonzero integers and there exists a positive prime number/? which divides T(x,y,k)(n) f° every n>0 and is relatively prime to x, the distribution of the residues of (un) modulo p is eit...
متن کامل