A primality test is an algorithm to decide whether an input number is prime. Some primality tests are deterministic. They always correctly decide if a number is prime or composite.The fastest known deterministic primality test was invented in 2004. There are three computer scientists, such as Agrawal, Kayal, and Saxena, ... Read More

Euler's theorem is a generalization of Fermat's little theorem handling with powers of integers modulo positive integers. It increase in applications of elementary number theory, such as the theoretical supporting structure for the RSA cryptosystem.This theorem states that for every a and n that are relatively prime −$$\mathrm{a^{\phi \left ( ... Read More

S-Box Substitution is a procedure that accepts the 48-bit input from the XOR operation containing the compressed key and expanded RPT and creates a 32-bit output utilizing the substitution technique.The substitution is implemented by the eight substitution boxes (also known as the S-boxes). Each 8-S-boxes has a 6-bit input and ... Read More

Modular arithmetic is a structure of arithmetic for integers, where numbers "wrap around" upon reaching a specific value. Modular arithmetic enables us to simply make groups, rings and fields which are the basic constructing piece of most modern public-key cryptosystems.For instance, Diffie-Hellman need the multiplicative group of integers modulo a ... Read More

The public key cryptography is treated as the most secure cryptography to make digital signatures and to implement encryption process. The management of digital signature will be treated as the most secured service in future for on-line communications. Therefore, it can perform secure online communications the public key cryptography plays ... Read More

Public-key cryptography is also known as asymmetric cryptography. It is a form of cryptography in which a user has a set of cryptographic keys including public key and a private key. The functions of Public key Cryptography are as follows −Encryption − The encryption application supports the confidentiality and integrity ... Read More

A public-key cryptosystem is that the messages is encrypted with one key and can only be decrypted with a second key, etc. A strong public-key system is one in which control of both the algorithm and the one key provides no beneficial information about the other key and thus no ... Read More

Let G be a finite cyclic set with n elements. It consider that the group is written multiplicatively. Let b be a generator of G and thus each element g of G can be written in the form g = bk for some integer k.Moreover, any two such integers defining ... Read More

Random numbers are the numbers which play an essential role for various network security applications. There are some approaches that are used to generating random numbers including pseudorandom number generator and linear congruent generator also cryptographically generated random numbers etc.The main objective of the Chinese Reminder Theorem is to generating ... Read More

Fermat's little theorem is a fundamental theorem in elementary number theory, which provides compute powers of integers modulo prime numbers. It is a specific case of Euler's theorem, and is essential in applications of elementary number theory, such as primality testing and public-key cryptography. This is referred to as Fermat’s ... Read More