1. What is RSA Encryption?

RSA is a public-key cryptosystem that is widely used for secure data transmission. It is based on the practical difficulty of factoring the product of two large prime numbers.

2. How Does RSA Encryption Work?

The RSA encryption formula is:

Where:

• \( m \) — The original message (as integer)
• \( e \) — Public exponent
• \( n \) — Modulus (product of two primes)
• \( c \) — Resulting ciphertext

Explanation: The message is converted to a number, then raised to the power of the public exponent modulo n to produce the ciphertext.

3. Importance of RSA Encryption

Details: RSA is fundamental to secure web browsing (HTTPS), email encryption, and many other secure communication protocols. Its security relies on the computational difficulty of factoring large integers.

4. Using the Calculator

Tips: Enter the message as an integer, along with the public exponent and modulus. The calculator will compute the ciphertext using modular exponentiation.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for e and n?
A: Common values for e are 3, 5, 17, 257, or 65537. n is typically a very large number (hundreds of digits) that is the product of two large primes.

Q2: How secure is RSA?
A: RSA is considered secure when using sufficiently large key sizes (currently 2048 bits or more). The security relies on the difficulty of factoring large numbers.

Q3: Can this calculator handle very large numbers?
A: The calculator uses PHP's bcpowmod function which can handle arbitrarily large integers, limited only by PHP's memory constraints.

Q4: What's the difference between RSA encryption and signing?
A: Encryption uses the public key to encode a message, while signing uses the private key to create a verifiable signature.

Q5: Why is RSA called an asymmetric algorithm?
A: Because it uses different keys for encryption (public key) and decryption (private key), unlike symmetric algorithms that use the same key for both.