Introduction to Cryptography Concepts and History

What is Cryptography NOUN: 1) The process or skill of communicating in or deciphering secret writings or ciphers. 2) Secret writing.

What is Cryptography Cryptography (or cryptology; derived from word kryptós which means "hidden," and the verb gráfo, which means write "write" is the study of message secrecy.

What is Cryptography Now that you have seen a few dictionary definitions of cryptography, lets synthesize a complete definition: Cryptography is the science of altering communication so that it cannot be understood without having the key.

Some Basic Terminology plaintext - original message ciphertext - coded message cipher - algorithm for transforming plaintext to ciphertext key - info used in cipher known only to sender/receiver Key space – number of possible keys encipher (encrypt) - converting plaintext to ciphertext decipher (decrypt) - recovering ciphertext from plaintext cryptography - study of encryption principles/methods cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext without knowing key cryptology - field of both cryptography and cryptanalysis

History Hidden or secret writing is very old. People have been practicing hidden writing for at least 3000 years. There has always been a need to have hidden communications. Until the latter part of the 20th century, this was almost exclusively for the military and government purposes. In this section we will focus on those historical cryptographic methods that led to today's modern cryptography. There are many historical ciphers that one can study, we will be focusing on a select group of those that have been the most influential in the history of cryptography.

Mono-alphabet substitution These are among the most primitive of cryptographic algorithms. These algorithms simply substitute one character of cipher text for each character of plain text. Some examples are: Atbash cipher Caesar cipher Rot13

Single substitution Weaknesses While single cipher cryptography algorithms may have been adequate when the bulk of the population was illiterate, they are totally inadequate today. There are a few reasons they are so easy to break. The most important reason is that all languages have a certain letter and word frequency. For example in English the words’ the and and are the two most common three letter words. The most common single letter words are I and a. If you see two of the same letters together in a word, it is most likely ee or oo. All single alphabet substitution ciphers preserve the underlying letter and word frequency and are thus vulnerable to cryptanalysis.

Atbash Cipher Hebrew scribes copying the book of Jeremiah used this cipher. It is very simple, just reverse the alphabet. This is, by modern standards, a very primitive and easy to break cipher. But it will help you get a feel for how cryptography works. The ATBASH cipher is a Hebrew code which substitutes the first letter of the alphabet for the last and the second letter for the second to the last, etc. It simply reverses the alphabet. A becomes Z, B becomes Y, C becomes X, etc.

Atbash Cipher Example A cat sleeps Becomes Z xzg hovvkh This is obviously a rather simple cipher and not used in modern times. However it illustrates the basic concept of cryptography. That is to perform some permutation on the plain text to render it difficult to read by those who don’t have the key to ‘un scramble’ the cipher text.

Caesar Cipher This cipher was first used by Julius Caesar. Every letter is shifted a fixed number of spaces to the left or the right in the alphabet. Caesar purportedly shifted 3 to the right, but you can apply this with any type of shift you prefer. The shifting is the ‘key’ for this algorithm The shift is often called the ‘alphabet’ being used. So the Caesar Cipher is an example of a single alphabet substitution since all letters are shifted the same amount.

Caesar Cipher Example Example: Shifting One to the Left

ROT 13 This is another single alphabet substitution cipher. All characters are rotated 13 characters through the alphabet. The phrase A CAT Becomes N PNG

Scytale Pronounced “skit a lee” A cylinder tool used by Spartans for substitution encryption.

Playfair The Playfair cipher is a bit more complex than most historical ciphers. It also encrypts two letters rather than one. It was invented in 1854 by Charles Wheatstone. It was named after Lord Playfair who promoted the use of the cipher. The Playfair cipher uses a 5 by 5 table containing a key word or phrase. To generate the key table, one would first fill in the spaces in the table with the letters of the keyword (dropping any duplicate letters), then fill the remaining spaces with the rest of the letters of the alphabet in order. People often omitted Q from the list. To encrypt a message, youwould break the message into groups of 2 letters. For example, “CheeseBurger" becomes “Ch ee se Bu rg er", and map them out on the key table. If both letters are the same (or only one letter is left), add an "X" after the first letter. Encrypt the new pair and continue. If the letters appear on the same row of your table, replace them with the letters to their immediate right . If the letters appear on the same column of your table, replace them with the letters immediately below . While this is rather complex and cumbersome it is not any more secure then other classic ciphers such as Vigenere.

Playfair Key Matrix a 5X5 matrix of letters based on a keyword fill in letters of keyword (sans duplicates) fill rest of matrix with other letters eg. using the keyword MONARCHY M O N A R C H Y B D E F G I/J K L P Q S T U V W X Z

Encrypting and Decrypting plaintext is encrypted two letters at a time if a pair is a repeated letter, insert filler like 'X’ if both letters fall in the same row, replace each with letter to right (wrapping back to start from end) if both letters fall in the same column, replace each with the letter below it (wrapping to top from bottom) otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair

Rail Fence cipher This is a transposition cipher. Rather than changing letters, their position is changed. The process is as follows: write message letters out diagonally over a number of rows then read off cipher row by row eg. write message out as: L n a t e e c a d t h b a h giving ciphertext lnateecadthbah

Poly-alphabetic Substitution The obvious way to make substitution ciphers (like atbash and Caesar) stronger, is to rotate through various alphobets. Any substitution using multiple alphabets. Such using three alphabets like: +1 -1 +2. Then the phrase A CAT Becomes B BCA The first letter is add 1, then the second is subtract 1 the third is add two then for the fourth letter you start over.

Poly-alphabetic Subsitution These ciphers break up the letter and word frequency making them harder to break than single substitution ciphers. In fact for a human using a pen and paper, it may be too difficult to crack. Examples of poly-alphabetic substitution include: Cipher Disk Vigenère Cipher Enigma Machine

Cipher Disk The cipher disk was invented by Leon Alberti in 1466. The cipher disk was polyalphabetic, each time you turned the disk you used a new cipher. It was literally a disk you turned to encrypt plain text.

Vigenère Cipher Perhaps the most widely known poly-alphabet cipher is the Vigenère cipher. This cipher was invented in 1553 by Giovan Battista Bellaso. It is a method of encrypting alphabetic text by using a series of different mono-alphabet ciphers selected based on the letters of a keyword. This algorithm was later misattributed to Blaise de Vigenère, and so it is now known as the "Vigenère cipher“, even though Vigenère did not really invent it.

Vigenère Cipher Example Match the letter of your keyword on the top with the letter of your Plain text on the left to find the cipher text.

Vigenère Cipher Example Using the previous chart if you are encrypting the word ‘cat’ and your key word is ‘horse’ then: the cipher text is jok

Vigenère Cipher Example This is a very effective multi-alphabet cipher and prior to the advent of computers was considered quite strong. It should be noted that the longer the keyword, the more alphabets used to encrypt the message, and thus the stronger the encryption. In fact one does not even need to use a real word. Any serious of letters will work.

Breaking the Vigenère Cipher In 1863 Friedrich Kasiski was the first person to publish a successful general attack on the Vigenère cipher. Previous attacks on this cipher relied on knowledge of the plaintext (i.e. they where ‘known plaintext’ attacks, which we will discuss in depth in cryptanalysis).

Electro-Mechanical Rotor Ciphers Electro-mechanical rotor ciphers invented and patented by 4 people in 4 countries after WW1 Most famous was the German Enigma machine Current went through multiple rotors to change each letter several times. Basically a mechanical poly-alphabet cipher Key was the selection and order of rotors with addition of plugboard for Enigma Enigma was broken by Polish, then British and US code-breakers, significantly shortening WW2 2003 discovery - electro-mechanical rotor cipher was first invented in 1915 by 2 Dutch Naval Officers, but kept secret

The Enigma Machine In World War II, the Germans made use of a mechanical rotor based cipher system known as Enigma machine. It was essentially a typewriter that implemented a polyalphabet substitution cipher. There were multiple variations on this machine. The machine was designed so that when the operator pressed a key the encrypted cipher text for that plain text was altered each time. So if the operator pressed the “A” key, he or she might generate a “E” in the cipher text, and the next time it might be a “S”. Essentially this was a multi-alphabet cipher consisting of 26 possible alphabets.

Identify Friend or Foe Cipher Wheels Invention of radar and faster planes required pilots to identify enemy aircraft before visual sighting IFF radios were invented in WW2, but cryptology was needed to prevent the enemy from using the radio from a downed plane Germans were the first to use IFF which included encryption keys, but the British made a device to locate the German plane, so the IFF was not used First US IFF radio was the ABA-1, used a cipher wheel inserted into the dynamotor of the radio Crypto was crude but effective, one of 10 wheels was selected for use that day IFF later developed into the transponder, which is in every aircraft today