W3Schools: The Ultimate Coding Companion

  Introduction Prime numbers are fundamental to cryptography, ensuring secure communication over digital networks. Two key mathematical principles used in cryptographic systems are Euler’s Theorem and primality testing , both of which play a crucial role in encryption, authentication, and key exchange protocols, particularly in RSA encryption . Understanding Prime Numbers A prime number is a number greater than 1 that has only two factors: 1 and itself. Cryptography relies on large prime numbers because they are difficult to factorize, making encryption methods secure. Euler’s Theorem Euler’s Theorem states that for any integer a that is coprime to n : where φ(n) (Euler’s totient function) counts the number of integers less than n that are coprime to it. This theorem generalizes Fermat’s Little Theorem and is a key principle in RSA encryption, ensuring efficient modular exponentiation. Primality Testing in Cryptography Primality testing helps in identifying large prime numbers...

  Introduction Prime numbers play a crucial role in modern cryptography, ensuring secure communication over digital networks. One of the key mathematical principles used in cryptographic systems is Fermat’s Little Theorem (FLT) , which helps in encryption, authentication, and key exchange protocols. Understanding Prime Numbers A prime number is a number greater than 1 that has only two factors: 1 and itself. Cryptography relies on large prime numbers because they are difficult to factorize, making encryption methods secure. Fermat’s Little Theorem (FLT) Fermat’s Little Theorem states that if p is a prime number and a is any integer not divisible by p , then: This theorem is widely used in cryptographic applications such as primality testing , RSA encryption , and digital signatures . Real-World Applications RSA Encryption : Uses large prime numbers and modular exponentiation for secure data encryption. Diffie-Hellman Key Exchange : Establishes secure communication between two pa...