Compute using integers:

Rational exponent:

Gaussian integers:

Compute for large numbers:

PowerMod threads over lists:

TraditionalForm Formatting:

Use Reduce to simplify expressions:

Use FindInstance to find solutions to expressions containing PowerMod

Use PowerMod in a sum:

Find a PrimitiveRoot of 9:

Use PowerMod to generate all coprime integers modulo 9:

Recognize base pseudoprimes:

Find all base 2 pseudoprimes below 1000:

Find all base 5 pseudoprimes below 1000:

Build an RSA-like toy encryption scheme. Start with the modulus:

Find the universal exponent of the multiplication group modulo n:

Private key:

Public key:

Encrypt a message:

Decrypt it:

Build an RSA-like toy encryption scheme:

Perform a cycling attack. One of the outputs will be the plaintext:

Alice and Bob publicly agree on a prime number and a primitive root modulo that prime :

Then Alice and Bob each choose private keys:

Then Alice sends Bob mod while Bob sends Alice mod :

Bob then computes mod and Alice computes mod :

This is their secret number which they now both share:

Create a random number generator that uses the current time as a seed:

Choose a modulus and base:

Compute random numbers between and :