IntroductionIntroduction toto CryptographyCryptography Dr. Arjan Durresi Louisiana State University Baton Rouge, LA 70810 [email protected] These slides are available at: http://www.csc.lsu.edu/~durresi/csc4601_04/ Louisiana State University 5- Introduction to Cryptography - 1 CSC4601 F04 OverviewOverview Definitions Secret keys Public keys Hash functions Louisiana State University 5- Introduction to Cryptography - 2 CSC4601 F04 CommunicationCommunication SecrecySecrecy The history of codes and ciphers is the story of centuries-old battle between codemakers and codebreakers Evolution of codes. Always under attack from codebreakers. Analogous to the situation of a strain of infectious bacteria under the attack of antibiotics Technologies involved from mathematics to linguistics, from information theory to quantum theory Louisiana State University 5- Introduction to Cryptography - 3 CSC4601 F04 TheThe EvolutionEvolution ofof SecretSecret WritingWriting In The histories, Herodotus, “the father of history”, chronicled the conflicts between Greece and Persia in the fifth century B.C. The art of secret writing saved the Greece Demaratus send information to Greece about Persian preparation using secret messages: scraping the wax off a pair of wooden folding tablets, writing on the wood underneath and then covering the message with wax again. Herodotus chronicled also the story of Histaiaeus who wanted to encaurage Aristagoras of Miletus to revolt against Persians To convey his instructions securely, Histaiaeus shaved the head of his messenger, wrote the message on his scalp, and then waited for the hair to grow. It seems this period of history tolerated a certain lack of urgency. Hiding a message is known as steganography derived from the Greek word steganos meaning “covered” and graphein–“to write”. Louisiana State University 5- Introduction to Cryptography - 4 CSC4601 F04 TheThe EvolutionEvolution ofof SecretSecret WritingWriting In the two thousand years since Herodotus, various forms of steganography has been used. The ancient Chinese wrote messages on fine silk, which then was scrunched into a tiny ball and covered in wax and swallowed by a messenger. In the 16th century, the Italian scientist Giovanni Porta described how to conceal a message within a hard-boiled egg by making an ink from mixture of alum and pint vinegar and then write on the shell. The solution penetrates the shell and leaves the message on the egg inside and can be read when the shell is removed. Today write messages on pictures posted on the web Louisiana State University 5- Introduction to Cryptography - 5 CSC4601 F04 TheThe EvolutionEvolution ofof SecretSecret WritingWriting The longevity of steganography illustrates that can offer security, but it suffers from a fundamental weakness. If the message is found the secret is revealed. Hence in parallel with steganography, there was the evolution of Cryptography, derived from the Greek word kryptos – “hidden”. The aim of cryptography is not to hide the existence of the message, but rather hide its meaning, a process known as encryption. To render the message unintelligible, it is scrambled according a particular protocol agreed beforehand between the sender and the intended recipient. The advantage of cryptography is that if the enemy intercepts an encrypted message, then the message is unreadable. Louisiana State University 5- Introduction to Cryptography - 6 CSC4601 F04 CryptographyCryptography Possible to combine cryptography and steganography. For example, during Second World War, German agents in Latin America would photographically shrink a page of text down to a dot less than 1 mm and then hide it in a letter. Sometimes they also scrambled the text before reducing it. Cryptography is more powerful because of this ability to prevent the information from falling into enemy hands. Louisiana State University 5- Introduction to Cryptography - 7 CSC4601 F04 CryptographyCryptography Cryptography can be divided into: transposition and substitution. In transposition, the letters of the message are simply rearranged. For very short messages, such as a single word, this method is relatively insecure. “For example, consider this short sentence.” 35 letters with more than 50 *1030 distinct arrangements. If each person would check one arrangement per second, it would take all people more than thousand time the life of universe to check all arrangements. This seems unbreakable, but there is a drawback. If letter are randomly jumbled without rule, then unscrambling the text will be impossible for the enemy as well as for the recipient. Louisiana State University 5- Introduction to Cryptography - 8 CSC4601 F04 CryptographyCryptography Have a history of at least 4000 years Ancient Egyptians enciphered some of their hieroglyphic writing on monuments Louisiana State University 5- Introduction to Cryptography - 9 CSC4601 F04 SpartanSpartan ScytaleScytale Wrap a strip of paper around a tube of specific size, then write your message sideways (generally one letter per strip). Only someone with same size tube can read your message. Louisiana State University 5- Introduction to Cryptography - 10 CSC4601 F04 CryptographyCryptography Ancient Hebrews enciphered certain words in the scriptures 2000 years ago Julius Ceasar used a simple substitution cipher, now known as the Caesar cipher Roger Bacon described several methods in 1200s Geoffrey Chaucer included several ciphers in his works Leon Alberti devised a cipher wheel, and described the principles of frequency analysis in the 1460s Blaise de Vigenère published a book on cryptology in 1585, & described the polyalphabetic substitution cipher Increasing use, esp in diplomacy & war over centuries Louisiana State University 5- Introduction to Cryptography - 11 CSC4601 F04 SubstitutionSubstitution CiphersCiphers Make a table for all the letters of the alphabet. Pick a new code letter to stand for each one. Go through your message, and replace each letter with its code letter from the table. Only someone with the table could decode your message. bed Original a b c d e f g h i j Code Letter D F I Q K X M Z R P FKQ Louisiana State University 5- Introduction to Cryptography - 12 CSC4601 F04 CaesarCaesar CipherCipher akaaka DecoderDecoder RingsRings Caesar used a simple substitution cipher. He just “shifted” the alphabet. But since there’s only 26 ways to shift, these codes are easy to break (just try all 26 ways). Image: Old Time Radio Premiums Original a b c d e f g h i j ... Code Letter D E F G H I J K L M ... Louisiana State University 5- Introduction to Cryptography - 13 CSC4601 F04 KKāāmama--SSūūtratra SecretSecret WritingWriting A harder-to-break cipher can be designed by instead of just shifting the letters of the alphabet, you assign each letter a totally random code letter. This form of secret-writing is one of the 64 arts explained in the Kāma-Sūtra. Original a b c d e f g h i j Code Letter D F I Q K X M Z R P Louisiana State University 5- Introduction to Cryptography - 14 CSC4601 F04 NewspaperNewspaper CryptogramsCryptograms Why don’t we all just use this approach to hide our information? Because people can figure out how to decode it! In fact, substitution ciphers are behind the cryptogram puzzles you see in the newspaper. People solve these in an afternoon… Computers make them even easier to solve. Louisiana State University 5- Introduction to Cryptography - 15 CSC4601 F04 DefinitionsDefinitions Process data into unintelligible form, reversible, without data loss Usually one-to-one (not compression) Analog cryptography example: voice changers Other services: Integrity checking: no tampering Authentication: not an imposter Plaintext encryption→ ciphertext decryption → plaintext Louisiana State University 5- Introduction to Cryptography - 16 CSC4601 F04 SecretSecret KeyKey CryptographyCryptography Originally a way to keep secret data private Encode a message using a secret “key” A long and colorful history Today, it has many uses Privacy Authentication – verifying someone (something’s) identity Data Integrity – reassuring the recipient of the message that the message has not been altered since it was generated by a legitimate source Louisiana State University 5- Introduction to Cryptography - 17 CSC4601 F04 WhatWhat isis Encryption?Encryption? You and I agree on a secret way to transform data Later, we use that transform on data we want to pass over an unsafe communications channel Instead of coming up with new transforms, design a common algorithm customized with a “key” Louisiana State University 5- Introduction to Cryptography - 18 CSC4601 F04 SecretSecret KeyKey EncryptionEncryption forfor PrivacyPrivacy Key Key PlaintextEncrypt CiphertextDecrypt Plaintext Louisiana State University 5- Introduction to Cryptography - 19 CSC4601 F04 HowHow SecureSecure isis Encryption?Encryption? An attacker who knows the algorithm we’re using could try all possible keys Security of cryptography depends on the limited computational power of the attacker A fairly small key (e.g. 64 bits) represents a formidable challenge to the attacker Algorithms can also have weaknesses, independent of key size Louisiana State University 5- Introduction to Cryptography - 20 CSC4601 F04 HowHow dodo wewe knowknow howhow goodgood anan algorithmalgorithm is?is? A problem of mathematics: it is very hard to prove a problem is hard It’s never impossible to break a cryptographic algorithm - we want it to be as hard as trying all keys