Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering. Apr Cryptography Slide 1

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1 Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering Apr Cryptography Slide 1

2 About This Presentation This presentation belongs to the lecture series entitled Ten Puzzling Problems in Computer Engineering, devised for a ten-week, one-unit, freshman seminar course by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. The material can be used freely in teaching and other educational settings. Unauthorized uses, including any use for financial gain, are prohibited. Behrooz Parhami Edition Released Revised Revised Revised Revised First Apr Apr Apr Apr Apr Apr Apr Apr Apr Cryptography Slide 2

3 Puzzles and Cryptograms in Archeology Apr Cryptography Slide 3

4 Secret Codes Are as Old as Forts and they serve the same purpose Providing security! Apr Cryptography Slide 4

5 Some Simple Cryptograms Cipher: YHPARGOTPYRC OT EMOCLEW Plain: WELCOME TO CRYPTOGRAPHY Cipher: EHT YPS WSI RAE GNI LBA CEU TAO Plain: THE SPY ISW EAR ING ABL UEC OAT Cipher: ICCRAANCTKBEEDLTIHEIVSECYOODUE Plain: I C A N T B E L I E V E Y O U C R A C K E D T H I S C O D E Cipher: SSA PSE TJX SME CRE STO THI GEI Plain: --- THI --- SME --- SSA --- GEI --- STO --- PSE --- CRE TJX --- Key: Cipher: AMY TAN S TWINS ARE CUTE KIDS Plain: A T T A C K Apr Cryptography Slide 5

6 Simple Substitution Ciphers Decipher the following text, which is a quotation from a famous scientist. Clue: Z stands for E CEBA YUC YXSENM PDZ SERSESYZ, YXZ QESOZDMZ PEJ XQKPE MYQGSJSYA, PEJ S K ECY MQDZ PLCQY YXZ RCDKZD. PBLZDY ZSEMYZSE CEBA YUC YXSENM PDZ SERSESYZ, YXZ QESOZDMZ PEJ XQKPE O NL Y T WO T HIN G S AR E IN F INIT E, T HE U NI V E RS E AN D HUM AN MYQGSJSYA, PEJ S K ECY MQDZ PLCQY YXZ RCDKZD. ST UP I D IT Y, AN D I M N O T S U R E AB OU T T HE FO R M E R. PBLZDY ZSEMYZSE X stands for H? ALBE RT E INSTEIN Contextual information facilitated the deciphering of this example Apr Cryptography Slide 6

7 Breaking Substitution Ciphers The previous puzzle, with punctuation and other give-aways removed: CEBA YUC YXSENM PDZ SERSESYZ YXZ QESOZDMZ PEJ XQKPE MYQGSJSYA PEJ SK ECY MQDZ PLCQY YXZ RCDKZD Letter frequencies in the cipher: A N B O C P D Q E R F S G T H U I V J W K X L Y M Z Letter frequencies in the English language ABCDEFGH IJKLMNOPQ RSTUVW XYZ Most frequently used 3-letter words: THE AND FOR WAS HIS Most frequently used letter pairings: TH HE AN IN ER ON RE ED Apr Cryptography Slide 7

8 The Pigpen Cipher Encoded message: T H I S I H S S S S This is a substitution cipher, with all the weaknesses of such ciphers Apr Cryptography Slide 8

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10 More Sophisticated Substitution Ciphers The letter A has been replaced by C, D, X, or E in different positions The letter T has been replaced by M, W, or X in different positions Message Cipher 25 rotating wheels Apr Cryptography Slide 10

11 The German Enigma Encryption Machine Reflector Three rotors Entry disk (4) Connection goes through the 3 rotors, is reflected, returns through the 3 rotors, leads to plugboard Light array (5) Eventually, the I light is illuminated Keyboard Q W E R T Z U I O A S D F G H J K P Y X C V B N M L (1) W pressed on keyboard Plugboard (2) Battery now connected to W on plugboard... (3)... which is wired to X plug Source: Apr Cryptography Slide 11

12 Alan Turing and the Enigma Project Alan M. Turing The Mansion at Bletchley Park (England s wartime codebreaking center) The German Enigma encryption machine Enigma s rotor assembly Source: Apr Cryptography Slide 12

13 More on the Enigma and the Turing Biopic Brief demo of Enigma (the London Science Museum) The Imitation Game movie trailer How accurate is The Imitation Game biopic? _fact_vs_fiction_how_true_the_new_movie_is_to_alan_turing.html Apr Cryptography Slide 13

14 A Simple Key-Based Cipher A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Agreed upon secret key: ourkey Plain text: Secret key: A T T A C K A T D A W N o u r k e y o u r k e y Sum: Modulo 26 sum: Cipher text: O N K K G I O N U K A L Secret key: Difference: Modulo 26 diff.: Recovered text: A T T A C K A T D A W N One can break such key-based ciphers by doing letter frequency analysis with different periods to determine the key length The longer the message, the more successful this method of attack Apr Cryptography Slide 14

15 Decoding a Key-Based Cipher A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Agreed upon secret key: freshman Cipher text: Secret key: Difference: Modulo 26 diff.: Plain text: B Y E L P E Y B Z I R S T Q f r e s h m a n f r e s h m W H A T I S Y O U R N A M E Decipher the coded message and provide a reply to it using the same key Reply: Secret key: J O H N S M I T H f r e s h m a n f Sum: Modulo 26 sum: Cipher text: O F L F Z Y I G M Apr Cryptography Slide 15

16 Key-Based Cipher with Binary Messages A B C D E F G H I J K L M N O P Q R S T U V W X Y Z * & % $ Agreed upon secret key (11 bits): = H 04 = E 24 = Y Plain text: Secret key: XOR: (mod-2 add) 15 = P 25 = Z 28 = # Secret key: XOR: Symmetric: Encoding and decoding algorithms are the same Apr Cryptography Slide 16

17 Data Encryption Standard (DES) Input Permutation Feistel block: The data path is divided into left (m i 1 ) and right (m i ) halves. A function f of m i and a key k i is computed and the result is XORed with m i 1. Right and left halves are then interchanged. m i 1 + f m i m i m i+1 k m 0 m f m 1 m 2 f m 2 m 3 + f k 1 k 2 k 3 The f function is fairly complicated, but it has an efficient hardware realization Feistel twisted ladder, Preceded and followed by permutation blocks form DES s encryption, decryption algorithms m 3 m 4 + f m 4 m 5 Reverse Permutation k 4 Apr Cryptography Slide 17

18 Use of Backdoors in Cryptography Plaintext x Complicated transformation f Cipher f(x) f(x) f 1 Inverse function is a backdoor... x Like a hidden latch that releases a magician s handcuffs Apr Cryptography Slide 18

19 Alice Alice Public-Key Cryptography Encryption and decryption are asymmetric. Knowledge of the public key does not allow one to decrypt a message. Bob Alice Alice Bob Electronic signature (authentication) Bob E.g., key for symmetric communication Source: Wikipedia Apr Cryptography Slide 19

20 Analogy for Public-Key Cryptography Bob Alice Bob s padlocks Carol s padlocks Dave s padlocks Alice sends a secret message to bob by putting the message in a box and using one of Bob s padlocks to secure it. Only Bob, who has a key to his padlocks, can open the box to read the message. Erin s padlocks Apr Cryptography Slide 20

21 RSA Public Key Algorithm Choose large primes p and q Compute n = pq Compute m = (p 1)(q 1) Choose small e coprime to m Find d such that de = 1 mod m Publish n and e as public key Keep n and d as private key p = 7, q = 19 n = 7 19 = 133 m = 6 18 = 108 e = 5 d = 65 Public key: 133, 5 Private key: 133, 65 Security of RSA is due to the difficulty of factoring large numbers Therefore, p and q must be very large: 100s of bits Encryption example: y = x e mod n = 6 5 mod 133 = 7776 mod 133 = 62 Decryption example: x = y d mod n = mod 133 = 62(3844) 32 mod 133 = 62(120) 32 mod 133 =... = 6 Apr Cryptography Slide 21