On The Pseudorandomness Of The Subsets Constructed By Using Quadratic Residues And Quadratic Non-residues

The sets of quadratic residues or quadratic non-residues enjoy good distribution properties and have important applications in cryptography.The wellknown the Rabin public-key cryptosystem and the Goldwasser-Micali probabilistic public-key cryptosystem are both based on the pseudorandom properties of quadratic residues and non-residues above.A set of integer in the form of a+r ,where a is any integer and r is the quadratic residue,which plays an important role in constructing a cryptosystem.Perron first studied the distribution of quadratic residues and quadratic non-residues in the set of integers of the form a+r under the prime modulus,but many applications of quadratic residues in cryptography need to be considered in the composite modulus.Tiplea,Iftene,Teseleanu and Nica,etc.,based on the work of Perron,studied the properties of the series subsets related to quadratic residues and quadratic non-residues composite modulus,and presented applications of the subsets to Cocks' identity-based encryption scheme.In this paper we shall further study the pseudorandom properties of these subsets by using the estimates for character sums.The main research contents are as follows:In the case of prime modulus and composite modulus,starting from the uniform distribution measure and correlation measure,study the pseudorandom properties of the quadratic residues and quadratic non-residues generated series subsets in the set composed of integers of the form a+r by using knowledge of the estimates for character sums and trigonometric identity,etc.