The RSA cryptosystem is a public-key system based on modular exponentiation and the difficulty of factoring a product of two large primes.
To generate keys, choose primes 
and 
, set 
, choose an encryption exponent 
relatively prime to 
, and choose 
such that 
. The pair 
is public, while 
and the factorization of 
are private.
For a message representative 
, RSA encryption computes
, and decryption recovers
. RSA signatures reverse
the private and public exponents: a signer computes a representative 
, and verification checks 
. Practical RSA uses encoding and padding schemes
rather than applying these textbook operations directly to a message.
