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RSA is a widely used encryption algorithm that ensures secure communication. It involves generating keys, encrypting messages, and decrypting ciphertexts. This article provides a step-by-step overview of implementing RSA in practical scenarios.
Generating RSA Keys
The first step in RSA implementation is creating a pair of keys: a public key and a private key. This process involves selecting two large prime numbers, calculating their product, and determining encryption and decryption exponents.
Steps include:
- Select two large prime numbers, p and q.
- Calculate n = p * q.
- Compute Euler’s totient, φ(n) = (p – 1) * (q – 1).
- Choose an encryption exponent, e, such that 1 < e < φ(n) and e is coprime with φ(n).
- Calculate the decryption exponent, d, such that d * e ≡ 1 mod φ(n).
The public key consists of (n, e), while the private key is (n, d).
Encryption Process
To encrypt a message, convert it into a numerical format compatible with RSA. Using the public key, the encryption process involves exponentiation and modular arithmetic.
The encryption formula is:
Ciphertext = message^e mod n
For example, if the message is represented as m, then the encrypted message c is calculated as c = m^e mod n.
Decryption Process
Decryption involves using the private key to retrieve the original message from the ciphertext. The process is similar to encryption but uses the decryption exponent d.
The decryption formula is:
Message = ciphertext^d mod n
Applying this formula restores the original message, completing the encryption-decryption cycle.