Related papers: Binary GH Sequences for Multiparty Communication
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…
This paper investigates the randomness and cryptographic properties of the Narayana series modulo p, where p is a prime number. It is shown that the period of the Narayana series modulo p is either p*p+p+1 (or a divisor) or p*p-1 (or a…
Let $1<g_1<\ldots<g_{\varphi(p-1)}<p-1$ be the ordered primitive roots modulo~$p$. We study the pseudorandomness of the binary sequence $(s_n)$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod 2$, $n=0,1,\ldots$. In particular, we study the…
This paper proposes the use of the binary primes sequence to strengthen pseudorandom (PN) decimal sequences for cryptography applications. The binary primes sequence is added to the PN decimal sequence (where one can choose from many…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…
For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive…
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…
In this work, a classical problem of the digital sequence design, or more precisely, finding binary sequences with optimal peak sidelobe level (PSL), is revisited. By combining some of our previous works, together with some mathematical…
The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference functions of span one to define q-ary sequences that generalize…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
This paper presents a twist to the generation of binary random sequences by starting with decimal sequences. Rather than representing the prime reciprocal sequence directly in base 2, we first right the prime reciprocal in base 10 and then…
In this paper we obtain some sophisticated combinatorial congruences involving binomial coefficients and confirm two conjectures of the author and Davis. They are closely related to our investigation of the periodicity of the sequence…
A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Henon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
We present a method for obtaining congruences modulo powers of a prime number~$p$ for combinatorial sequences whose generating function satisfies an algebraic differential equation. This method generalises the one by Kauers and the authors…