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Educational RSA Arithmetic Calculator — result sheet
Build a small textbook RSA key pair from two primes, calculate the private exponent, encrypt a numeric message, and decrypt it for learning.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: n = pq; φ(n) = (p−1)(q−1); ed ≡ 1 (mod φ(n)); c = mᵉ mod n; m′ = cᵈ mod n.
This page demonstrates the small-number RSA arithmetic relationship between a public exponent, a private modular inverse, and modular exponentiation. It deliberately exposes the mathematics rather than presenting a production cryptography implementation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Prime p — minimum 2; maximum 1000000
- Prime q — minimum 2; maximum 1000000
- Public exponent e — minimum 3; maximum 1000000000000
- Numeric message m — minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Prime p | 61 |
| Prime q | 53 |
| Public exponent e | 17 |
| Numeric message m | 65 |
n = 3233, φ(n) = 3120, d = 2753, ciphertext c = 2790, and textbook decryption returns 65.
Assumptions and limits
- p and q are distinct prime integers and the demonstration uses the two-prime textbook construction.
- The public exponent is between 1 and φ(n) and coprime with φ(n), so a modular inverse exists.
- The message is an integer from 0 through n−1; the handler uses exact BigInt modular arithmetic after validating the bounded numeric inputs.
- No OAEP/PSS padding, hashing, side-channel protection, key serialization, secure randomness, large-key security, or production encryption claim is provided.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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