Modular Exponentiation Calculator
Modular exponentiation b^e mod m
Client-side computation for analysis, verification, and learning. Do not paste production secrets into untrusted sites; prefer local tooling for key material.
Educational / engineering use. RSA mode uses tiny primes for illustration only—not for real key generation.
Base b
Exponent e
Modulus m
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What is Modular Exponentiation Calculator?
Computes the result of raising a base to a large exponent within a modulus efficiently. A core operation in cryptographic systems like RSA and Diffie-Hellman where direct exponentiation would be computationally infeasible.
Modular Exponentiation Formula
result = b^e mod m
Computed efficiently using repeated squaring:
Step-by-Step
- Enter base b, exponent e, modulus m.
- Convert exponent to binary.
- Repeatedly square and reduce modulo m.
- Multiply terms where exponent bit is 1.
- Return final reduced result.
Worked Example
Where Modular Exponentiation Calculator Is Applied
- Core computation inside RSA encryption/decryption
- Diffie-Hellman key exchange
- ElGamal encryption scheme
- Primality testing (Miller-Rabin algorithm)
- Generating cryptographic keys
- Zero-knowledge proof systems
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