Cryptography

What is cryptography? kryptos – “hidden” grafo – “write” Keeping messages secret  Usually by making the message unintelligible to anyone that intercepts it

The Problem BobAlice Eve Private Message Eavesdropping

The Solution BobAlice Eve Scrambled Message Eavesdropping EncryptionDecryption Private Message

What do we need? Bob and Alice want to be able to encrypt/decrypt easily But no one else should be able to decrypt How do we do this?  Keys!

Using Keys Plaintext Ciphertext DecryptionEncryption Plaintext Nonsense

The Shift Cipher We “shift” each letter over by a certain amount ILYH UHG EDOORRQV five red balloons f + 3 = I i + 3 = L v + 3 = Y … Plaintext Ciphertext Encryption Key = 3

The Shift Cipher cont. To decrypt, we just subtract the key five red balloons I - 3 = f L - 3 = i Y - 3 = v … Plaintext Decryption Key = 3 ILYH UHG EDOORRQV Ciphertext

What’s wrong with the shift cipher? Not enough keys! If we shift a letter 26 times, we get the same letter back  A shift of 27 is the same as a shift of 1, etc.  So we only have 25 keys (1 to 25) Eve just tries every key until she finds the right one

The Substitution Cipher Rather than having a fixed shift, change every plaintext letter to an arbitrary ciphertext letter aG bX cN dS eD …… zQ PlaintextCiphertext

The Substitution Cipher cont. aG bX cN dS eD fA gF hV iL jM kC lO mE ALRD HDS XGOOYYBW five red balloons f = A i = L v = R … Plaintext Ciphertext Encryption Key = nB oY pZ qP rH sW tI uJ vR wU xK yT zQ

The Substitution Cipher cont. To decrypt we just look up the ciphertext letter in the table and then write down the matching plaintext letter How many keys do we have now?  A key is just a permutation of the letters of the alphabet  There are 26! permutations

Frequency Analysis In English (or any language) certain letters are used more often than others If we look at a ciphertext, certain ciphertext letters are going to appear more often than others It would be a good guess that the letters that occur most often in the ciphertext are actually the most common English letters

Letter Frequency This is the letter frequency for English The most common letter is ‘e’ by a large margin, followed by ‘t’, ‘a’, and ‘o’ ‘J’, ‘q’, ‘x’, and ‘z’ hardly occur at all

Frequency Analysis in Practice Suppose this is our ciphertext  dq lqwurgxfwlrq wr frpsxwlqj surylglqj d eurdg vxuyhb ri wkh glvflsolqh dqg dq lqwurgxfwlrq wr surjudpplqj. vxuyhb wrslfv zloo eh fkrvhq iurp: ruljlqv ri frpsxwhuv, gdwd uhsuhvhqwdwlrq dqg vwrudjh, errohdq dojheud, gljlwdo orjlf jdwhv, frpsxwhu dufklwhfwxuh, dvvhpeohuv dqg frpslohuv, rshudwlqj vbvwhpv, qhwzrunv dqg wkh lqwhuqhw, wkhrulhv ri frpsxwdwlrq, dqg duwlilfldo lqwhooljhqfh.

Ciphertext distributionEnglish distribution In our ciphertext we have one letter that occurs more often than any other (h), and 6 that occur a good deal more than any others (d, l, q, r, u, and w) There is a good chance that h corresponds to e, and d, l, q, r, u, and w correspond to the 6 next most common English letters

Frequency Analysis cont. If we replace ‘e’ with ‘h’ and the 6 next most common letters with their matches, the ciphertext becomes  an intro???tion to ?o?p?tin? pro?i?in? a ?roa? ??r?e? o? t?e ?i??ip?ine an? an intro???tion to pro?ra??in?. ??r?e? topi?? ?i?? ?e ??o?en ?ro?: ori?in? o? ?o?p?ter?, ?ata repre?entation an? ?tora?e, ?oo?ean a??e?ra, ?i?ita? ?o?i? ?ate?, ?o?p?ter ar??ite?t?re, a??e???er? an? ?o?pi?er?, operatin? ???te??, net?or?? an? t?e internet, t?eorie? o? ?o?p?tation, an? arti?i?ia? inte??i?en?e.

Classical to Modern Cryptography Classical cryptography  Everything up until around WWII  Encryption/decryption done by hand Modern cryptography  Computers to encrypt and decrypt  Same principles, but automation allows ciphers to become much more complex

The Enigma Machine German encryption and decryption machine used in WWII Essentially a complex, automated substitution cipher

How did Enigma work? Rotors have different wiring connecting input to output Rotors move after each keypress The key is the initial position of the three rotors

Breaking the Enigma Britain set up its cryptanalysis team in Bletchley Park They consistently broke German codes throughout the war  Provided the intelligence codenamed ULTRA Important location in the history of computing  Alan Turing  COLOSSUS

Cryptography in the Computer Age Working with binary instead of letters We can do things many, many times  Think of an Enigma machine that has pairs of symbols on each rotor, and 20 rotors Other than that, the basic principles are the same as classical cryptography

Modern Ciphers We design one relatively simple scrambling method (called a round) and repeat it many times  Think of each round as a rotor on the Enigma  One round may be easy to break, but when you put them all together it becomes very hard Almost all ciphers follow one of two structures  SPN (Substitution Permutation Network)  Feistel Network  These describe the basic structure of a round

Modern Ciphers in Practice Follow SPN/Feistel structure in general, but with added twists for security There are two important ciphers in the history of modern cryptography  DES (Data Encryption Standard)  AES (Advanced Encryption Standard)

DES U.S. Government recognized the need to have a standardized cipher for secret documents DES was developed by IBM in 1976 Analysis of DES was the beginning of modern cryptographic research

Controversy Surrounding DES Development process was hidden from public  Suspicions that the government had put in a “backdoor” Government attempted to shut down research in cryptography

Breaking DES The key length of DES was too short  If a key is 56 bits long, that means there are 2 56 possible keys  “DES Cracker” machines were designed to simply try all possible keys

Breaking DES cont. DES was further weakened by the discovery of differential cryptanalysis  Biham and Shamir in 1990  The most significant advance in cryptanalysis since frequency analysis Ideally a ciphertext should be completely random, there should be no connection to its matching plaintext  Differential analysis exploits the fact that this is never actually the case  Uses patterns between plaintext and ciphertext to discover the key There is evidence that IBM knew about differential cryptanalysis back when they were designing DES in 1976

Developing the AES With DES effectively broken, a new standard was needed U.S. Government made it an open application/review process this time, and received many submissions In 2001, after five years, the Rijndael cipher was selected to become the Advanced Encryption Standard

The Problem of Symmetric Key Cryptography Up until now we’ve been talking about symmetric key cryptography  Alice and Bob are using the same key to encrypt/decrypt Problem: How does Bob get the key to Alice when Eve is eavesdropping? Up until 1976 the only solution was to physically give Alice the key in a secure environment

Public Key Cryptography Diffie and Hellman published a paper in 1976 providing a solution We use one key for encryption (the public key), and a different key for decryption (the private key) Everyone knows Alice’s public key, so they can encrypt messages and send them to her  But only Alice has the key to decrypt those messages No one can figure out Alice’s private key even if they know her public key

Using Public Keys Plaintext Ciphertext DecryptionEncryption Plaintext Nonsense

Public Key Cryptography in Practice The problem is that public key algorithms are too slow to encrypt large messages  Instead Bob uses a public key algorithm to send Alice the symmetric key, and then uses a symmetric key algorithm to send the message The best of both worlds!  Security of public key cryptography  Speed of symmetric key cryptography

Sending a Message What’s your public key? Bob picks a symmetric key and encrypts it using Alice’s public key Alice decrypts the symmetric key using her private key Bob encrypts his message using the symmetric key Then sends the key to Alice Then sends the message to Alice Alice decrypts the message using the symmetric key hi

The RSA Public Key Cipher The most popular public key cipher is RSA, developed in 1977  Named after its creators: Rivest, Shamir, and Adleman Uses the idea that it is really hard to factor large numbers  Create public and private keys using two large prime numbers  Then forget about the prime numbers and just tell people their product  Anyone can encrypt using the product, but they can’t decrypt unless they know the factors  If Eve could factor the large number efficiently she could get the private key, but there is no known way to do this

Are we all secure now? Unfortunately not, there are still many problems that need to be dealt with  How does Bob know that he’s really talking to Alice?  How does Alice know that the message she receives hasn’t been tampered with?  How does Alice know the message was sent by Bob? These are questions addressed by other areas of cryptography

The End