# Cryptography

The power behind secrets.

Published at 2018-06-20, Updated at 2013-02-26.### Introduction to Cryptography

Posted in Cryptography at 2011-10-25 by #care-crewCryptography tries to solve a common problem. The problem of secure communication using a unsecured transport. In this series we will use three Persons in our examples. Jack wants to communicate with Jones without Jane being able to read. The definition of a...

### Symmetric Cryptography

Posted in Cryptography at 2011-10-25 by #care-crewThe example in the introduction used the same key for encryption and decryption. This is called Symmetric Cryptography. It is very fast, but Jack and Jones need to find a way to exchange their secret keys without Jane listening. The advantages of symmetric cr...

### Asymmetric Cryptography

Posted in Cryptography at 2011-10-25 by #care-crewAsymmetric Cryptography is also called public-key cryptography. The big advantage is that there is no need to share a secret key anymore, because we are able to generate two keys. A public key: Used to encrypt plain text. A private key: Used to decrypt the ci...

### Permutation

Posted in Cryptography at 2011-10-25 by #care-crewA very simple form of Cryptography is based on Permutation. We only use A-Z in this example, because it is easier to read for us. Jack uses the secret key "awesomeness". We remove all duplicate chars from the key and get "awesomn". We start at a and fill th...

### Shift

Posted in Cryptography at 2011-10-25 by #care-crewShit cryptography is often called "Caesar cipher", cause he was one of the first users. It shifts elements of the public vocabulary. In order to reveal the power of shift cryptography, one must think of A-Z as a ring. We have 26 elements and after the last...

### Vigenere Cryptosystem

Posted in Cryptography at 2011-10-25 by #care-crewVigenere is a poly alphabetic Cryptosystem, it changes the representation of the vocabulary in order to be less vulnerable to security attacks. Vigenere uses a fixed length secret key and it splits the public key in parts of the length of the secret key. The ...

### Hill Cryptosystem

Posted in Cryptography at 2011-10-25 by #care-crewHill is a poly alphabetic cryptosystem that is based on matrix calculation using finite rings. The finite ring in the example uses 26 elements (A-Z), cause it is easier to read for us. The plain text message is converted to a matrix. the matrix and the secret...

### Attacking Crypto Systems

Posted in Cryptography at 2011-10-25 by #care-crewA crypto system is secure, if the algorithm is public accessible and the secret key is only obtainable by the brute force method (or getting it from a human person). The following elements can help breaking a crypto system. Knowledge of plain text Knowled...

### RSA Crypto System

Posted in Cryptography at 2011-10-25 by #care-crewThe RSA Crypto System was released 1978 by Ronald Rivest, Adi Shamir and Leonard Adleman. It is the most known and used public-key-crypto system, so you better learn how it works. Preparations 1) Choose two huge prime numbers: p and q; 2) Calculate: m= p*q;...

### Diffie Hellman Key Exchange

Posted in Cryptography at 2011-10-25 by #care-crewThe Diffie Hellman Key Exchanges enables secure communication over a insecure transport system by creating a private key without ever sending it over the transport system. the diffie hellman procedure //Sender 1) select and publish a primitive Element: g in...

### Knapsack Crypto System

Posted in Cryptography at 2011-10-25 by #care-crewThe Knapsack Crypto System is based on the subset sum problem. It is easy to learn, but is not secure, cause the subset sum problem is broken. knapsack You have a empty knapsack "s" and want to fill it as good as possible with elements "a0...an". It is possi...

### ElGamal Crypto System

Posted in Cryptography at 2011-10-25 by #care-crewThe ElGamal Crypto System is a public key crypto system which allows to send a message over a insecure transport system. ElGamal procedure 1) Choose a prime number: p; 2) Choose a number: a in {2,...,p-2}; 3) Select a number: g with g mod p; 4) Calculate:...