Introduced CPT scheme as a block-based hiding scheme based on the ring of the integers modulo 2 r , which permits to embed r = log2(k+1) secret bits in F by changing at most two entries, while the highest number of secret bits in any CPT-based schemes is MSDR2 = log2(1+k (k+1)/2), approximately 2r-1. This ratio can be reached approximately in our proposed CPTE1 scheme by using modules on th...

We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual ...

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo p . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N , and quasi-linea...

Deene the MOD m-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments ~ x, F(~ x) = 0 ii P(~ x) = 0. By exploring the periodic property of the binomial coeecients modulo m, two new lower bounds on the MOD m-degree of the MOD l and :MOD m functions are proved, where m is any composite integer and l has ...

Memory devices based on floating-gate transistor have recently become dominant technology for non-volatile storage like USB flash drives, memory cards, solid-state disks, etc. In contrast to many communication channels, the errors observed in device use are not random but of special, mainly asymmetric, type. Integer codes which proved their efficiency cases with asymmetric can be applied succes...

where N p (a,b) is the number of positive integers x{ax , and {m} m∈ℤ least nonnegative residue m modulo p.

A helpful starting point is the paper entitled "Fibonacci Series Modulo m by D. D. Wall [3]. With Wall, we let /„ denote the n member of the sequence of integers fQ = a, f1 = b9 ..., where fn + 1 = fn + f n _ r The symbol h(m) will denote the length of the period of the sequence resulting from reducing each /„ modulo w. The basic Fibonacci sequence will be given by uQ = 0, ux = 1, ... and the L...

For a commutative ring R with unity, the associate graph, denoted by AG(R), is simple graph vertices as nonzero elements of and two distinct are adjacent if they associates. The AG(R) contains components equal in number to orbits, except for orbit an element 0. Moreover, each component complete graph. An important finding that this class strongly perfect graphs. In article we describe structure...