RSA Encryption:

RSA encryption is a widely used asymmetric encryption algorithm named after its inventors, Ron Rivest, Adi Shamir, and Leonard Adleman. It’s based on the mathematical properties of large prime numbers.

Here’s a brief overview of how RSA encryption works:

a. Key Generation:

• Choose two distinct prime numbers, (p) and (q).
• Compute their product, (n = p \times q), which is used as the modulus for both the public and private keys.
• Calculate Euler’s totient function, (\phi(n) = (p-1) \times (q-1)), which represents the count of positive integers less than (n) that are coprime with (n).
• Choose an integer (e) such that (1 < e < \phi(n)), and (e) is coprime with (\phi(n)). This (e) is the public exponent.
• Compute the private exponent (d) as the modular multiplicative inverse of (e) modulo (\phi(n)).

b. Encryption:

• To encrypt a message (M), the sender uses the recipient’s public key ((n, e)).
• The ciphertext (C) is calculated as (C \equiv M^e \pmod{n}).

c. Decryption:

• To decrypt the ciphertext (C) and recover the original message (M), the recipient uses their private key (d).
• The plaintext (M) is calculated as (M \equiv C^d \pmod{n}).

RSA encryption is widely used for secure communication, digital signatures, and key exchange protocols. Its security relies on the difficulty of factoring the modulus (n) into its prime factors (p) and (q), which becomes increasingly difficult with larger key sizes. As computing power increases, longer key lengths are required to maintain security against brute-force attacks and advances in factoring algorithms.