相关论文: Narayana Sequences for Cryptographic Applications
A recursive random number generator using prime reciprocals is described.
We examine the linear complexity and the autocorrelation properties of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential…
The combined processes of anodization and electrodeposition lead to highly ordered arrays of cylindrical nanowires. This template-based self-assembly fabrication method yields nanowires embedded in alumina. Commonly, chemical etching is…
Wall-Sun-Sun primes (shortly WSS primes) are defined as those primes $p$ such that the period of the Fibonacci recurrence is the same modulo $p$ and modulo $p^2.$ This concept has been generalized recently to certain second order…
We prove, without recourse to the Extended Riemann Hypothesis, that the projection modulo $p$ of any prefixed polynomial with integer coefficients can be completely factored in deterministic polynomial time if $p-1$ has a $(\ln…
If $p$ is prime, a sequence of prime numbers $\{p, 2p+1, 4p+3,...,2^{n-1}(p+1)-1\}$ is called a Cunningham chain. These are finite sequences of prime numbers, for which each element but the last is a Sophie Germain prime. It is conjectured…
Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very…
Let p>3 be a prime number and let r be an integer with 1<r<p-1. For each r, let moreover G_r denote the unique quotient of the maximal class pro-p group of size p^{r+1}. We show that the mod-p cohomology ring of G_r has depth one and that,…
Let b be an odd integer such that b=+/-1 (mod 8) and let q be a prime with primitive root 2 such that q does not divide b. We show that if (p(k)) is a sequence of odd primes, with 0<=k<=q-2 such that p(k)=2p(k-1)+b for all 1<=k<=q-2, then…
The generating functions of some sequences of Catalan numbers and Narayana polynomials have simple expansions as continued fractions of Jacobi type. We give an overview of these facts and prove analogous results for q-Narayana polynomials…
In this paper we construct a pseudorandom multisequence $(x_{n_1,...,n_r})$ based on $k$th-order linear recurrences modulo $p$, such that the discrepancy of the $s$-dimensional multisequence $(x_{n_1+i_1,...,n_r+i_r})_{1 \leq i_j \leq s_j,…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Suppose that $p$ is an odd prime and $\genfrac{(}{)}{}{}{\cdot}{p}$ denotes the Legendre symbol modulo $p$. If $p$ is has the form $p= n^2+1$ then one easily verifies that $\genfrac{(}{)}{}{}{a}{p} = \genfrac{(}{)}{}{}{-a}{p}$ for all $a\in…
Linear recursions of degree $k$ are determined by evaluating the sequence of Generalized Fibonacci Polynomials, $\{F_{k,n}(t_1,...,t_k)\}$ (isobaric reflects of the complete symmetric polynomials) at the integer vectors $(t_1,...,t_k)$. If…
In this short note, we develop a novel idea of a bilinear cryptosystem using the discrete logarithm problem in matrices. These matrices come from a linear representation of a finite $p$-group of class 2. We discuss an example at the end.
The prime numbers look like a randomly chosen sequence of natural numbers, but there is still no strict theory to determine 'Randomness'. In these years, cryptography has developed a battery of statistical tests for randomness. In this…
According to the Wagstaff heuristic, the probability that a Mersenne number $M_p = 2^p-1$ is prime mainly depends on the size of the exponent $p$. We investigate whether the secondary arithmetic structure in $p-1$ is linked to noticeable…
This paper proposes a computational method for obtaining the length of the cycle that arises from the Fibonacci series taken mod m (some number) and mod p (some prime number).
Goldbach partitions can be used in creation of ellipses and circles on the number line. We extend this work and determine the count and other properties of concentric Goldbach circles for different values of n. The autocorrelation function…