vimwiki/tech/RSA.wiki

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= 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
* [[../math/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`