Unlock the secrets of public-key cryptography with our RSA Key Generation Calculator. Input your distinct prime numbers p and q, along with your chosen public exponent e, to quickly compute the modulus n, Euler's totient φ(n), and the crucial private exponent d needed for secure communications. This tool is perfect for students and developers understanding RSA key generation!
Formula:
The RSA key generation process involves the following mathematical steps:
- Choose two distinct large prime numbers, p and q.
- Compute the modulus: n = p × q
- Compute Euler's totient function: φ(n) = (p - 1) × (q - 1)
- Choose a public exponent e such that 1 < e < φ(n) and gcd(e, φ(n)) = 1.
- Compute the private exponent d such that d × e ≡ 1 (mod φ(n)). This means d is the modular multiplicative inverse of e modulo φ(n).
Our calculator simplifies finding n, φ(n), and d when you provide p, q, and e.