Pseudo-random Subset Of Modulus

With the development of computer network, pseudo random subset have been widely used in many fileds. Especially, it plays a very important role in the study of the security of the cryptosystem. Let m be a modulus of "RSA type", i.e., it is the product of two primes not far apart, say, m pq, p, q are primes, p<q<2p. In this paper, we study composite model of pseudo random subset and obtain results as follows1. A construction using polynomials and additive characters.Let f(x)∈Z[x], r∈Z, s∈N, s<m/2, define U={n:1≤n≤m,(?)h∈{r, r+1,…, r+s-1} with f(n)≡h(modm)}. and study the pseudorandomness.2. Construction of pseudorandom subsets of the set{1,2,…,m} using polynomials and multiplicative inverse.Let f(x) E Z[x], r E Z, s∈N, s<m/2. define and study the pseudorandomness.3. A Construction using power residues. and study its good pseudorandomness.