Applications

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.

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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