Prime Reciprocal Digit Frequencies and the Euler Zeta Function

Some open questions related to prime reciprocal digit frequencies with potential applications to cryptography are presented.Comment: 6 page

Visual Secret Sharing Scheme using Grayscale Images

Pixel expansion and the quality of the reconstructed secret image has been a major issue of visual secret sharing (VSS) schemes. A number of probabilistic VSS schemes with minimum pixel expansion have been proposed for black and white (binary) secret images. This paper presents a probabilistic (2, 3)-VSS scheme for gray scale images. Its pixel expansion is larger in size but the quality of the image is perfect when it's reconstructed. The construction of the shadow images (transparent shares) is based on the binary OR operation.Comment: 6 pages, 2 figure

A New Result on the Random Residue Sequence Algorithm

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 by the author. This makes it possible to obtain many more random sequences than was possible to do by the previous algorithm. Experimental results are presented on a variety of sequences of length 16 and 24. To obtain a variety of RR sequences of a specific length can have obvious applications in cryptography.Comment: 6 pages,2 table

Generating Primes Using Partitions

This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested using either Miller Rabin or AKS primality tests.Comment: 9 pages, 7 figure

Testing Kak's Conjecture on Binary Reciprocal of Primes and Cryptographic Applications

This note considers reciprocal of primes in binary representation and shows that the conjecture that 0s exceed 1s in most cases continues to hold for primes less one million. The conjecture has also been tested for ternary representation with similar results. Some applications of this result to cryptography are discussed.Comment: 5 pages, 4 figure

Binary Random Sequences Obtained From Decimal 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 convert it into the binary form. The autocorrelation and cross-correlation properties of these binary random (BRD) sequences are discussed.Comment: 10 page

New Class of Pseudorandom D-sequences to Generate Cryptographic Keys

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 then replacing 2 in the expansion with either the string 01 or 10 based on the preceding bit, which represents a general mapping. We show that the resulting pseudorandom sequences have excellent autocorrelation properties. Such a method can be extended to inverse prime expansions to any base.Comment: 8 pages, 6 figure

Indexing Properties of Primitive Pythagorean Triples for Cryptography Applications

This paper presents new properties of Primitive Pythagorean Triples (PPT) that have relevance in applications where events of different probability need to be generated and in cryptography.Comment: 8 page

A Wireless System Using Random Residue Sequences

This paper describes the architecture of wireless communication system using random residue sequences. The basic scheme is that of spread spectrum but instead of using PN sequences for coding, we use random residue sequences. Such a system can provide cryptographic security whose strength would depend on the number of code sequences being used.Comment: 3 figure

Goldbach Circles and Balloons and Their Cross Correlation

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 of this sequence with respect to even and odd values suggests that it has excellent randomness properties. Cross correlation properties of ellipse and circle sequences are provided that indicate that these sequences have minimal dependencies and, therefore, they can be used in spread spectrum and other cryptographic applications.Comment: 9 pages, 7 figure