1. What is RSA Decryption?

RSA decryption is the process of converting ciphertext back to plaintext using a private key in the RSA cryptosystem. It's based on the mathematical properties of modular exponentiation and prime factorization.

2. How Does the Calculator Work?

The calculator uses the RSA decryption formula:

Where:

• \( m \) — Decrypted message (plaintext)
• \( c \) — Encrypted message (ciphertext)
• \( d \) — Private exponent
• \( n \) — Modulus (product of two primes)

Explanation: The formula performs modular exponentiation to reverse the encryption process using the private key components.

3. Importance of RSA Decryption

Details: RSA decryption is fundamental to secure communications, digital signatures, and various cryptographic protocols that protect data confidentiality.

4. Using the Calculator

Tips: Enter valid integers for ciphertext (c), private exponent (d), and modulus (n). All values must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of values this calculator can handle?
A: The calculator can handle very large integers thanks to PHP's bcpowmod function, which is designed for arbitrary precision mathematics.

Q2: Why is modular exponentiation used in RSA?
A: Modular exponentiation provides a one-way function that's easy to compute in one direction but hard to reverse without the private key.

Q3: What are typical sizes for RSA keys?
A: Modern RSA implementations typically use 2048-bit or 4096-bit keys, corresponding to 617-digit or 1234-digit numbers in decimal.

Q4: Can this calculator be used for real cryptographic operations?
A: While the math is correct, this is for educational purposes only. Real cryptographic operations require proper security implementations.

Q5: What happens if I enter invalid values?
A: The calculator will either show an error or produce incorrect results. Always ensure your inputs are valid RSA parameters.