# One Time Pad 一次性密碼本
[TOC]
## What is OPT ?
- Aka Vernam Cipher
- the improvement to Vernam Cipher (key is reused)
- it produces random output

### History
- Frank Miller v.s Gilbert Vernam
- straight-forward ciphers & superenciphered codes

### Features
- Key
- As long as the total set of messages
- Absolutely random
- Never re-used
- Unbreakable(if used correctly)
- For the cipher to be 100% secure, the following requirements apply:
1. The key must be truly random
2. The key must be at least as long as the plaintext
3. The key must never be reused (not even a part of it)
4. The key must be kept completely secret

### Why is it Unbreakable?
1. The key is as long as the given message.
2. The key is truly random and specially auto-generated.
3. Key and plain text calculated as modulo 10/26/2.
4. Each key should be used once and destroyed by both sender and receiver.
5. There should be two copies of key: one with the sender and other with the receiver.

### Disadvantage
- **Unbreakable(if used correctly) but weak**
- Key management is at best difficult, often completely impossible.
- It is useful primarily for low-bandwidth channels.
- It is highly vulnerable to a **substitution attack**.

## History
- Gilbert Vernam

## How to encrypt ?
modular addition (refer. the standard Vigenère cipher)
1. assign each letter a numerical value (e.g. `a` is `0`, `b` is `1`, and so on)
2. (message) alphabet -> number
3. cipher = (message + key) mod 26
4. (ciphertext) number -> alphabet

- True randomness
- $c = p \oplus k$

## How to decrypt ?
plaintext = ciphertext – key (mod 26)

## Reference
- [Wikipedia - One-time pad](https://en.wikipedia.org/wiki/One-time_pad)
- [OPT - FAQ](http://www.ranum.com/security/computer_security/papers/otp-faq/)
- [FreeS/WAN - Discussion](https://www.freeswan.org/freeswan_trees/freeswan-2.06/doc/glossary.html#OTP)
- [Wikipedia - Gilbert Vernam](https://en.wikipedia.org/wiki/Gilbert_Vernam)
- [Youtube - One Time Pad](https://www.youtube.com/watch?v=6iYqHn3q8sY&ab_channel=NesoAcademy)
- [擁有 Perfect Secrecy 的加密函式 One Time Pad](https://medium.com/fcamels-notes/%E6%93%81%E6%9C%89-perfect-secrecy-%E7%9A%84-one-time-pad-d9ad353f2af1)
- [Tutorialpoints - One Time Pad Cipher](https://www.tutorialspoint.com/cryptography_with_python/cryptography_with_python_one_time_pad_cipher.htm)
- [MAT - One-time Pad (OTP)](https://www.nku.edu/~christensen/1402%20one%20time%20pads.pdf)