Frequently Asked Questions
What is modular exponentiation?
Computing a to the b mod m efficiently using exponentiation by squaring. It is the backbone of public-key cryptography.
Why is it useful in cryptography?
RSA encryption requires raising messages to large exponents modulo huge primes. Direct computation would overflow; modular exponentiation keeps numbers bounded by m at every step.
Can I use a negative exponent?
Only when a has a modular inverse, that is gcd(a, m) is one. Then a to the minus 1 is the modular inverse and a to the minus n is its n-th power. Otherwise, the inverse does not exist.
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