= RSA =

RSA is an asymetric encryption algorithm based on the difficulty of factoring
large prime numbers.

== algoirthm ==

1) choose some `p` and `q`
   * where `p` and `q` are very large primes
   * `n = p * q`
2) T = (p-1)(q-1)
   * known as eulers totient
3) choose 2 values e and d
   * where (e * d) mod T = 1
   * where e < T
   * [[relative_prime]] with T and N
4) we now have our keys
   * n and e are public keys
   * n and d are private keys

=== encryption ===

`(plaintext value)^e mod N = ciphertext value`

=== decryption ===

`(ciphertext value)^d mod N = plaintext vlaue`

=== example ===

`p = 2; q = 7`

therefore,

`n = 14; T = 6`

Due to restrictions, choose e = 5

Then choose d from pool of canidiates satisfying `(e * d) mod T = 1`

For example then, choose 14 as d

Private key `(11,14)` and public key `(5,14)`

For example Encrypt B

`2^5 mod 14 = 4` or `D`

Decrypt value

`4^11 mod 14 = 2` or our original `B`

== Also see ==

* [[Eliptic_Curve]]