A basic small scale Java program that generates Public and Private keys for RSA encryption/decryption. Developed with the intent to test mathematical algorithms involved in RSA encryption/decryption such as the Extended Euclidean Algorithm and a square left to right multiply algorithm.

Simply compile using javac RSAystem.java

generateKeys(int p, int q, int e) Generates an array of RSA public and private keys for the given prime numbers.

• p and q and a number e relatively prime to (p-1)*(q-1).
• The returned integer array has the following form: {n, e, d} where n is the product of p and q, e is the public exponent, and d is the private exponent.
• Returns null if the input parameters are invalid.

isPrime(int e) is a naive calculation that checks whether the given integer e is a prime number or not.

• A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.

getEulerTotient(int n, List<Integer> factorsList) Calculates the Euler totient function of the given integer n, using the prime factors provided in the factorsList.

• The Euler totient function, also known as Euler's phi function, is defined as the number of positive integers that are relatively prime to n.

getPrimeFactorisation(int n) Calculates the prime factorization of the given positive integer n.

• Prime factorization is the process of finding the prime factors of a number, which are the prime numbers that can divide the number exactly without leaving a remainder.

getModularInverse(int r0, int r1, int n) Calculates the modular inverse of r1 modulo n using the Extended Euclidean Algorithm.

• The Extended Euclidean Algorithm is an algorithm that calculates the greatest common divisor (GCD) of two integers, as well as the coefficients x and y of the Bezout's identity, which is an equation of the form ax + by = gcd(a, b).
• In the case of calculating a modular inverse, the coefficients x and y can be used to find the inverse of r1 modulo n, if it exists.