Understanding RSA - The Math behind modern encryption

RSA is an asymmetric encryption algorithm that uses public and private keys for secure communication. Steve encrypts a message with his public key, and only Cathy, with her private key, can decrypt it. The core of RSA lies in mathematical principles, specifically prime factorization. The process involves selecting two prime numbers, calculating the modulus (n), and finding Euler's totient. A public exponent (e) and a private exponent (d) are then derived using mathematical formulas. Encryption is performed by raising the message (m) to the power of the public exponent (e) modulo n. Decryption uses the cipher text, raises it to the power of the private exponent (d) modulo n to retrieve the original message. The security of RSA hinges on the difficulty of factoring large numbers into their prime factors. Cracking RSA is computationally challenging, requiring extensive computing power and time, making it a robust encryption method. RSA's strength comes from this mathematical problem, making it extremely difficult to break even with current technology. With its reliance on prime factorization, RSA provides strong encryption, hence its widespread use. The public key consists of (e, n), while the private key comprises (d, n).