Public Key Cryptography – The RSA cryptosystem uses a public key e and N ,where N is a product of two primes, and the private key d which is the multiplicative inverse of e \bmod \phi(N). A message M is encrypted by e, M^e \bmod N = E and decrypted using d, E^d \bmod N = M.

The RSA encryption system is practical since it doesn’t require messages to have their own communication line and computing d with only e and N takes a very long time. Computing d requires one to factor N which can take a computer anywhere from decades to centuries and even millenniums.

Computing – Data structures such as stacks and hash tables can be created by using the modulo operation to reference indexes.

Other Applications can be found in number theory and abstract algebra.


  1. What is Modular Arithmetic?
  2. Basic Operations
  3. Multiplicative Inverse
  4. Fermat’s Little Theorem
  5. Euler’s Totient Function
  6. Applications

Filed under : Crash Courses, Mathematics

Sources Used

  • Elementary Number Theory by James K. Strayer
  • Data Abstraction and Problem Solving with C++, Walls and mirrors by Frank M. Carrano

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