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


About This Presentation: 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


Some Simple Cryptograms:   Some Simple Cryptograms Cipher: YHPARGOTPYRC OT EMOCLEW Plain: ----------------------- Cipher: EHT YPS WSI RAE GNI LBA CEU TAO Plain: --- --- --- --- --- --- --- --- 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 1 2 3 4 5 6 7 8 Key: 7 4 1 8 6 2 5 3 SME SSA GEI STO PSE CRE TJX Cipher: AMY TAN’S TWINS ARE CUTE KIDS Plain: A T T A C K


Simple Substitution Ciphers:   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 ALB RT INST IN X stands for H? Contextual information facilitated the deciphering of this example


Breaking Substitution Ciphers:   Breaking Substitution Ciphers CEBA YUC YXSENM PDZ SERSESYZ YXZ QESOZDMZ PEJ XQKPE MYQGSJSYA PEJ SK ECY MQDZ PLCQY YXZ RCDKZD The previous puzzle, with punctuation and other give-aways removed: 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 |||||||| Most frequently used 3-letter words: THE AND FOR WAS HIS Most frequently letter pairings: TH HE AN IN ER ON RE ED


The Pigpen Cipher:   The Pigpen Cipher Encoded message: T This is a substitution cipher, with all the weaknesses of such ciphers


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More Sophisticated Substitution Ciphers:   More Sophisticated Substitution Ciphers The letter A has been replaced by C, D, X, or E in different positions The letter T has been replaced by M, W, or X in different positions 25 rotating wheels


The German Enigma Encryption Machine:   The German Enigma Encryption Machine (1) W pressed on 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 (2) Battery now connected to W on plugboard . . . (3) . . . which is wired to X plug (4) Connection goes through the 3 rotors, is “reflected”, returns through the 3 rotors, leads to plugboard (5) Eventually, the “I” light is illuminated Source: http://www.codesandciphers.org.uk/enigma/index.htm Entry disk Reflector Three rotors Light array Keyboard Plugboard


Alan Turing and the Enigma Project:   Alan Turing and the Enigma Project Source: http://www.ellsbury.com/enigmabombe.htm The Mansion at Bletchley Park (England’s wartime codebreaking center) Alan M. Turing 1912-1954 The German Enigma encryption machine Enigma’s rotor assembly


A Simple Key-Based Cipher:   A Simple Key-Based Cipher Plain text: A T T A C K A T D A W N 00 19 19 00 02 10 00 19 03 00 22 13 Secret key: o u r k e y o u r k e y 14 20 17 10 04 24 14 20 17 10 04 24 Sum: 14 39 36 10 06 34 14 39 20 10 26 37 Modulo 26 sum: 14 13 10 10 06 08 14 13 20 10 00 11 Cipher text: O N K K G I O N U K A L 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 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Agreed upon secret key: ourkey Secret key: 14 20 17 10 04 24 14 20 17 10 04 24 Difference: 00 -7 -7 00 02-16 00 -7 03 00 -4-13 Modulo 26 diff.: 00 19 19 00 02 10 00 19 03 00 22 13 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


Decoding a Key-Based Cipher:   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 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Agreed upon secret key: freshman 09 14 07 13 18 12 08 19 07 Secret key: f r e s h m a n f 05 17 04 18 07 12 00 13 05 Sum: 14 31 11 31 25 24 08 32 12 Modulo 26 sum: 14 05 11 05 25 24 08 06 12 Cipher text: O F L F Z Y I G M Decipher the coded message and provide a reply to it using the same key Cipher text: B Y E L P E Y B Z I R S T Q 01 24 04 11 15 04 24 01 25 08 17 18 19 16 Secret key: f r e s h m a n f r e s h m 05 17 04 18 07 12 00 13 05 17 04 18 07 12 Difference: Modulo 26 diff.: Plain text: Reply: J O H N S M I T H -4 07 00 -7 08 -8 24-12 20 -9 13 00 12 04 22 07 00 19 08 18 24 14 20 17 13 00 12 04 W H A T I S Y O U R N A M E


Key-Based Cipher with Binary Messages:   Key-Based Cipher with Binary Messages Agreed upon secret key (11 bits): 0 1 0 0 0 1 1 1 0 1 0 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 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 * & # @ % $ 26 27 28 29 30 31 Symmetric: Encoding and decoding algorithms are the same


Data Encryption Standard (DES):   Data Encryption Standard (DES) Feistel block: The data path is divided into left (mi–1) and right (mi) halves. A function f of mi and a key ki is computed and the result is XORed with mi–1. Right and left halves are then interchanged. The f function is fairly complicated, but it has an efficient hardware realization


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


Analogy for Public-Key Cryptography: Analogy for Public-Key Cryptography 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. Bob’s padlocks Alice Bob Carol’s padlocks Dave’s padlocks Erin’s padlocks