RSA Private Exponent Calculator
Enter the public exponent e and the totient φ(n) to compute the private exponent d.
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
RSA key generation picks a public exponent e and computes the private exponent d as its modular inverse with respect to Euler's totient of the modulus: d ≡ e⁻¹ (mod φ(n)), meaning d is the unique value satisfying e·d ≡ 1 (mod φ(n)). It's found using the extended Euclidean algorithm rather than by simple division.
Cryptography students and instructors use this calculator to work through RSA key generation by hand and verify their arithmetic, and security engineers use it to sanity-check a manually constructed key pair or to understand exactly how e, φ(n) and d relate before implementing RSA in code.
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