Related papers: Binary Prime Tableau Sequences
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…
This paper investigates cross correlation properties of sequences derived from GH sequences modulo p, where p is a prime number and presents comparison with cross correlation properties of pseudo noise sequences. For GH sequences modulo…
Primitive Pythagorean triples (PPT) may be put into different equivalence classes using residues with respect to primes. We show that the probability that the smaller odd number associated with the PPT triple is divisible by prime p is…
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…
Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design.…
This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D…
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 presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…
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…
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…
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…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and…
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…
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…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
A general construction of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic and this construction, several classes of binary sequences with optimal autocorrelation and other…
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…
We present those properties of planar doodles, especially when regarded as 4-valent graphs, that enable us to classify them into {\it prime} and {\it super prime} doodles by analogy to a knot sum. We describe a method for partially…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…