Ciphers: Making and Breaking
|
|
|
- Lora Morris
- 5 years ago
- Views:
Transcription
1 Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford Smithsonian Institute October 31, 2009
2 2009 Ralph Morelli You are free to reuse and remix this presentation under a creative commons license provided you give credit to the author. This presentation was created using Open Office 3.0, free and open source software.
3 Part II: Cryptology in Transition
4 Outline Polyalphabetic Substitution Alberti Cipher Vigenère Cipher Le Chiffre Indéchiffrable Kasiski Decipherment Mechanical Ciphers The Enigma Machine WWII
5 Leon Battista Alberti ( )
6 Leon Battista Alberti ( ) Renaissance man. Architect, author, artist, poet, philosopher. Father of Modern Cryptography First western exposition of frequency analysis. Invention of polyalphabetic cipher. Courtyard of the Uffizi Palace
7 Alberti the Architect Santa Maria Novella Florence
8 De Cifris First comprehensive account of cryptanalysis in the West. Invention of the polyalphabetic cipher.
9 Alberti Cipher Disk Outer disk stationary with regular alphabet. Inner disk moveable with permuted alphabet. An inner disk letter (k) is picked as index, and aligned with some letter on outer disk (B). The index is changed every 3 or 4 words and inserted into the message. Ciao amici might be encrypted as BlvgyCeztkt.
10 Compare Letter Frequencies Plain Caesar Simple Polyalphabetic
11 Polyalphabetic Development Alberti (~ 1472): devised genuine polyalphabetic cipher with mixed alphabet plus a practical cipher disk device. Abbot Trithemius (~ 1508): used tables of regular alphabets to be used in fixed order. Giovanni Battista Belaso (~ 1550 ): invented principle of a key or keyword to select alphabets. Giovanni Battista Porta (~ 1563): invented using mixed alphabets. Blaise de Vigenère (~ 1586): combined table or Trithemius, keyword of Belaso, and mixed alphabets of Porta into an autokey cipher.
12 Johannes Trithemius ( ) Abbot, occultist. First printed book crypto book. Most famous for Steganagraphia (banned book). Believed to be about occult. Decrypted in 1998.
13 Trithemius Cipher The Trithemius Cipher cycles through each row of the table. Encryption: Meetusatthebridge ABCDEFGHIJKLMNOPQ MFEWYXGABQOMDVRVG
14 So-called Chiffre Indéchiffrable The Bellaso Cipher uses a keyword to select alphabets. Encryption: ZEBRASZEBRASZEBRAS therearesomethirty SLFIESQITFMWSLJRTQ ** ** Decryption: ZEBRASZEBRASZEBRAS slfiesqitfmwsljrtq THEREARESOMETHIRTY
15 Vigenère's Autokey Cipher Uses mixed alphabets and the text itself as the key. Encryption: Therearesomethirty (MSG=col) Xtherearesomethirt (KEY=row) OZGUUAOUVIZNWZMYDP (Crypto) Decryption: OZGUUAOUVIZNWZMYDP(MSG=ltr) XthereareS.. (KEY=row) O in row X gives column T... V in row E gives column S 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 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 Z E B R A F I S H C D G J K L M N O P Q T U V W X Y E B R A F I S H C D G J K L M N O P Q T U V W X Y Z B R A F I S H C D G J K L M N O P Q T U V W X Y Z E R A F I S H C D G J K L M N O P Q T U V W X Y Z E B A F I S H C D G J K L M N O P Q T U V W X Y Z E B R F I S H C D G J K L M N O P Q T U V W X Y Z E B R A I S H C D G J K L M N O P Q T U V W X Y Z E B R A F S H C D G J K L M N O P Q T U V W X Y Z E B R A F I H C D G J K L M N O P Q T U V W X Y Z E B R A F I S C D G J K L M N O P Q T U V W X Y Z E B R A F I S H D G J K L M N O P Q T U V W X Y Z E B R A F I S H C G J K L M N O P Q T U V W X Y Z E B R A F I S H C D J K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y
16 Jefferson's Wheel Cipher Invented in wheels with random 26- letter alphabets. Reinvented by Etienne Bazeries in 1890s with wheels. Rearrange the wheels (key) and write message in one row and transmit any other row. U.S. Army M-94,
17 Our Polyalphabetic Cipher Disk Outer disk stationary with regular alphabet. Inner disk moveable with permuted alphabet. Keyword = zebrafish A B C D E F G H I/ J K L M N O P Q R S T U/ V X W Y X Z z e b r a f i/j s h c d g k l m n p q t u/v w o x y
18 Cipher Disk Exercise 1. Pick a keyword and write it in lower case letters, L to R, on the inner disk. 2. Fill in the rest of the alphabet on the inner disk (i/j and u/v go in one cell each). 3. Pick a key (e.g., A = k) and align the disks. 4. Encrypt: For each plaintext letter, find it on the outer disk and substitute the lower case letter on the inner disk. 5. Decrypt: For each ciphertext letter, find it on the inner disk and substitute the upper case letter on the outer disk.
19 Breaking the Unbreakable Cipher
20 Breaking the Vigenère Cipher Vigenère cipher a keyword of length n is used to select from among 26 Caesar-shifted alphabets. Thought to be unbreakable for ~ 300 years. 1863: Friederich Kasiski, a Prussian major, developed a method to break it. 1846: Charles Babbage, a British mathematician, philosopher, and inventor, discovered the same method. Basic approach: Find the length of the keyword, n, and use frequency analysis on the n columns, each of which is a Caesar shifted alphabet.
21 Kasiski Method Location: Keyword: RELAT IONSR ELATI ONSRE LATIO NSREL... Plaintext: TOBEO RNOTT OBETH ATIST HEQUE STION... Ciphertext: KSMEH ZBBLK SMEMP OGAJX SEJCS FLZSY... Repeated Bigram Location Distance Factors KS 9 9 9, 3 SM , 3 ME , Find the distances between repeated bigrams, some of which are due to repeated bigrams in the plaintext. Factor the distances the keyword should have length equal to one factor. Break the text into columns and use frequency analysis on each column to identify the shifted alphabet used to encrypt that column.
22 Automating Kasiski's Method
23 Index of Coincidence Index of coincidence the number of times two identical letters occur in the same position in two adjacent texts. William F. Friedman (Father of American cryptography). Language Normalized IC (1/26) Plain English German Caesar English Simple English Substitution Uniform distribution
24 Plain IC Example Caesar Simple Polyalphabetic 0.040
25 The Chi-square Test Used for comparing and observed frequency distribution with an expected distribution. Goodness-of-fit statistic the smaller the better.
26 Automated Algorithm Assumes: long enough polyalphabetic cipher text For each possible keyword length, 2, 3, 4,..., k Divide the text into k columns. Compute the average the IC for the columns. Select the IC that is closest to For each of the k columns For each possible shift, Compute the Chi-square value. Select the minimum as the correct Caesar alphabet. Demo:
27 Rotor Machines
28 The Enigma Machine
29 The Enigma Rotor
30 Rotor Details
31 Wiring Diagram Cool Simulation:
32 Enigma Cryptanalysis: Poles 1931: Poles deduced the wirings of rotors from betrayed documents and made a replica. Code book with daily keys Plugboard settings: A/K, B/G, M/S, Rotor order: Rotor setting: Q-C-W Message key transmitted twice: RAMRAM LVGHIB Polish cryptanalysis cracked the day keys: L and H encrypt R, V and I encrypt A, G and B encrypt M. Letter chains (A F W A) led to deduction of daily key. Marian Rejewski: Number of links independent of plugboard so daily keys reduced to 6 x 26 3 = 105,456.
33 Breaking Enigma Marian Rejewski Polish Biuro Syzfrow Alan Turing Government Code and Cypher School Hut 6, Bletchley Park
34 Enigma Cryptanalysis: Brits Alan Turing, GC&CS, Bletchley Park 159,000,000,000,000,000,000 daily keys. Exploited cycles within cribs of probable words. f u h r e r f--r--r--e--e--f R J T E F H Turing bombes 16 in all, each with 12 sets of Enigma rotors for loops of up to 12 links. Given a crib, the bombes would work out the rotor settings (independent of plugboard).
35 Bletchley Park Bombe Replica used in Enigma movie. Bletchley Park Model
36 Principles and Observations Kerckhoff's principle the cipher requires a key and should work even if the cipher is known. Simplicity More secure ciphers went unused because they were thought to be too difficult. Cryptanalysts were ahead of cryptographers. Mary Queen of Scots' problem: Implementation, implementation, implementation.
Cristina Nita-Rotaru. CS355: Cryptography. Lecture 4: Enigma.
CS355: Cryptography Lecture 4: Enigma. Towards cryptographic engines } How to move from pencil and paper to more automatic ways of encrypting and decrypting? } How to design more secure ciphers } Alberti
Lecture (04) Classical Encryption Techniques (III)
Lecture (04) Classical Encryption Techniques (III) Dr. Ahmed M. ElShafee ١ Playfair Cipher one approach to improve security was to encrypt multiple letters the Playfair Cipher is an example invented by
one approach to improve security was to encrypt multiple letters invented by Charles Wheatstone in 1854, but named after his
Lecture (04) Classical Encryption Techniques (III) Dr. Ahmed M. ElShafee ١ The rules for filling in this 5x5 matrix are: L to R, top to bottom, first with keyword after duplicate letters have been removed,
Cryptography. The Making and Breaking of Secret Codes. 5/29/2009 John C. Polking, Rice University 1
Cryptography The Making and Breaking of Secret Codes. 5/29/2009 John C. Polking, Rice University 1 Need for Cryptography Many areas of human endeavor require secret communication. Modern methods of communication
Cryptography CS 555. Topic 2: Evolution of Classical Cryptography CS555. Topic 2 1
Cryptography CS 555 Topic 2: Evolution of Classical Cryptography Topic 2 1 Lecture Outline Basics of probability Vigenere cipher. Attacks on Vigenere: Kasisky Test and Index of Coincidence Cipher machines:
Historical cryptography
Historical cryptography CSCI 470: Web Science Keith Vertanen Copyright 2013 Overview Historical cryptography Monoalphabetic substitution ciphers Breaking them Some improvements The cipher of Mary Queen
CSCI3381-Cryptography
CSCI3381-Cryptography Lecture 2: Classical Cryptosystems September 3, 2014 This describes some cryptographic systems in use before the advent of computers. All of these methods are quite insecure, from
1999 version 2001 simplified version
香港中文大學讀書會 1999 version 2001 simplified version Author Simon Singh http://simonsingh.net/ 1. Fermat s Last Theorem the epic quest to Solve the World's Greatest Mathematical Problem(2007) 2. The Code Book(1999)
Polyalphabetic Substitutions
Polyalphabetic Substitutions Klaus Pommerening Fachbereich Physik, Mathematik, Informatik der Johannes-Gutenberg-Universität Saarstraße 21 D-55099 Mainz October 25, 1999 English version October 13, 2013
Algebra for Cryptology
Algebra for Cryptology Arkadii Slinko Department of Mathematics The University of Auckland Auckland, 6 April, 2013 What is cryptology? Cryptology is about communication in the presence of adversaries or
Cryptanalysis. A walk through time. Arka Rai Choudhuri
Cryptanalysis A walk through time Arka Rai Choudhuri arkarai.choudhuri@gmail.com How many can you identify? History (or how I will give you hope of becoming world famous and earning $70 million along
Introduction to Cryptography
T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography EECE 412 1 Module Outline Historical background Classic ciphers One-time pad The Random Oracle model Random functions:
Classical Cryptography
Classical Cryptography CSG 252 Fall 2006 Riccardo Pucella Goals of Cryptography Alice wants to send message X to Bob Oscar is on the wire, listening to communications Alice and Bob share a key K Alice
I.T.I.S. E. DIVINI SAN SEVERINO MARCHE. CRIPTOGRAPHY Monday 9th January 2006
I.T.I.S. E. DIVINI SAN SEVERINO MARCHE CRIPTOGRAPHY Monday 9th January 2006 History of cryptography The history of cryptography dates back thousands of years. Until recent decades, it has been a history
... Assignment 3 - Cryptography. Information & Communication Security (WS 2018/19) Abtin Shahkarami, M.Sc.
Assignment 3 - Cryptography Information & Communication Security (WS 2018/19) Abtin Shahkarami, M.Sc. Deutsche Telekom Chair of Mobile Business & Multilateral Security Goethe-University Frankfurt a. M.
COS433/Math 473: Cryptography. Mark Zhandry Princeton University Spring 2017
COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Previously on COS 433 Pre- modern Cryptography 1900 B.C. mid 1900 s A.D With few exceptions, synonymous with encryption c = Enc(k,m)
Unveiling the Chaocipher. Born in Dublin, Ireland on February 11, 1880, John F. Byrne created a cipher called the
Strickland 1 Tanner Strickland Dr. Bruff Math 115F 2 November 2010 Unveiling the Chaocipher Born in Dublin, Ireland on February 11, 1880, John F. Byrne created a cipher called the Chaocipher that has long
Chapter 2 Classical Cryptosystems
Chapter 2 Classical Cryptosystems Note We will use the convention that plaintext will be lowercase and ciphertext will be in all capitals. 2.1 Shift Ciphers The idea of the Caesar cipher: To encrypt, shift
About Vigenere cipher modifications
Proceedings of the Workshop on Foundations of Informatics FOI-2015, August 24-29, 2015, Chisinau, Republic of Moldova About Vigenere cipher modifications Eugene Kuznetsov Abstract TheaimofthisworkisamodificationoftheclassicalVigenere
Final Exam Math 105: Topics in Mathematics Cryptology, the Science of Secret Writing Rhodes College Tuesday, 30 April :30 11:00 a.m.
Final Exam Math 10: Topics in Mathematics Cryptology, the Science of Secret Writing Rhodes College Tuesday, 0 April 2002 :0 11:00 a.m. Instructions: Please be as neat as possible (use a pencil), and show
monoalphabetic cryptanalysis Character Frequencies (English) Security in Computing Common English Digrams and Trigrams Chapter 2
Common English Digrams and Trigrams Digrams EN RE ER NT TH ON IN TF AN OR Trigrams ENT ION AND ING IVE TIO FOR OUR THI ONE monoalphabetic cryptanalysis See class example Pfleeger, Security in Computing,
AN ENHANCED CRYPTOGRAPHIC SUBSTITUTION METHOD FOR INFORMATION SECURITY
! """#$# AN ENHANCED CRYPTOGRAPHIC SUBSTITUTION METHOD FOR INFORMATION SECURITY *Kallam Ravindra Babu 1, Dr. S. Udaya Kumar 2, Dr. A. Vinaya Babu 3 and Dr. M. Thirupathi Reddy 4 1 Research Scholar (JNTUH),
Number Theory in Cryptography
Number Theory in Cryptography Introduction September 20, 2006 Universidad de los Andes 1 Guessing Numbers 2 Guessing Numbers (person x) (last 6 digits of phone number of x) 3 Guessing Numbers (person x)
The Web Cryptology Game CODEBREAKERS.EU edition 2015
Lecture 5 in which we return to the dream about le chiffre indechiffrable. We will see this dream come true and next we will try, step by step, to break this unbreakable cipher. As you might remember,
Polyalphabetic Ciphers
Polyalphabetic Ciphers 1 Basic Idea: The substitution alphabet used for enciphering successive letters of plaintext changes. The selection of alphabets may depend on a keyword, a key stream, or electromechanical
Introduction to Cryptographic Engineering. Steven M. Bellovin
Introduction to Cryptographic Engineering Steven M. Bellovin https://www.cs.columbia.edu/~smb 1 Cryptographic Engineering? There are lots of introductions to encryption But using encryption in the real
Efficient Cryptanalysis of Homophonic Substitution Ciphers
Efficient Cryptanalysis of Homophonic Substitution Ciphers Amrapali Dhavare Richard M. Low Mark Stamp Abstract Substitution ciphers are among the earliest methods of encryption. Examples of classic substitution
CPSC 467b: Cryptography and Computer Security
CPSC 467b: Cryptography and Computer Security Michael J. Fischer Lecture 3 January 22, 2013 CPSC 467b, Lecture 3 1/35 Perfect secrecy Caesar cipher Loss of perfection Classical ciphers One-time pad Affine
Introduction to Cryptology. Lecture 2
Introduction to Cryptology Lecture 2 Announcements 2 nd vs. 1 st edition of textbook HW1 due Tuesday 2/9 Readings/quizzes (on Canvas) due Friday 2/12 Agenda Last time Historical ciphers and their cryptanalysis
The Turing Bombe and its Role in Breaking Enigma
he uring Bombe and its Role in Breaking Enigma Neil igmon npsigmon@radford.edu Department of Mathematics and tatistics Radford University U..A. Rick Klima klimare@appstate.edu Department of Mathematical
Historical cryptography
Historical cryptography Alice Bob Eve CSCI 470: Web Science Keith Vertanen Overview Historical cryptography Monoalphabetic substitution ciphers Breaking them Some improvements The cipher of Mary Queen
Facts & Myths of Enigma
Facts & Myths of Enigma Breaking Stereotypes Arkadiusz Orłowski & Kris Gaj How should we begin? Begin at the beginning, and go on till you come to the end: then stop. The King to the White Rabbit Lewis
secretsaremadetobefoundoutwithtime UGETGVUCTGOCFGVQDGHQWPFQWVYKVJVKOG Breaking the Code
Breaking the Code To keep your secret is wisdom; but to expect others to keep it is folly. Samuel Johnson Secrets are made to be found out with time Charles Sanford Codes have been used by the military
Lecture Notes. Advanced Discrete Structures COT S
Lecture Notes Advanced Discrete Structures COT 4115.001 S15 2015-01-22 Recap Two methods for attacking the Vigenère cipher Frequency analysis Dot Product Playfair Cipher Classical Cryptosystems - Section
1/18 2/16 3/20 4/17 5/6 6/9 7/14 % Please do not write in the spaces above.
1/18 2/16 3/20 4/17 5/6 6/9 7/14 % Please do not write in the spaces above. Directions: You have 50 minutes in which to complete this exam. Please make sure that you read through this entire exam before
Data and information security: 2. Classical cryptography
ICS 423: s Data and information security: 2. Classical cryptography UHM ICS 423 Fall 2014 Outline ICS 423: s s and crypto systems ciphers ciphers Breaking ciphers What did we learn? Outline ICS 423: s
Classical Cryptography
JASS 05 Seminar: Algorithms for IT Security Classical Cryptography Ilya Saverchenko June 6, 2005 Abstract Cryptography is a study of secret writing. It allows two people, usually referred to as Alice and
Computer Security. 07. Cryptography. Paul Krzyzanowski. Rutgers University. Spring 2018
Computer Security 07. Cryptography Paul Krzyzanowski Rutgers University Spring 2018 March 20, 2018 CS 419 2018 Paul Krzyzanowski 1 cryptography κρυπός γραφία hidden writing A secret manner of writing,
The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and )
A Better Cipher The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and ) To the first letter, add 1 To the second letter, add 14 To the third
The CRYPTOGRAPHY. Classical cryptography. 1. History of cryptography
The CRYPTOGRAPHY 1. History of cryptography The history of cryptography dates back thousands of years. Until recent decades, it has been a history of classic cryptography of methods of encryption that
CHAPTER 4 REDUCTION OF VARIABLE LENGTH KEY SEARCH TIME OF VIGENERE CIPHER USING FIREFLY ALGORITHM
64 CHAPTER 4 REDUCTION OF VARIABLE LENGTH KEY SEARCH TIME OF VIGENERE CIPHER USING FIREFLY ALGORITHM 4.1 INTRODUCTION Any Cryptanalyst should focus on the two basic needs of cryptanalysis such as 1. To
Specialized Cryptanalytic Machines: Two examples, 60 years apart. Patrick Schaumont ECE Department Virginia Tech
Specialized Cryptanalytic Machines: Two examples, 60 years apart Patrick Schaumont ECE Department Virginia Tech What is cryptanalysis? Cryptography aims to defeat cryptanalysis Cryptanalysis aims to defeat
5. Classical Cryptographic Techniques from modular arithmetic perspective
. Classical Cryptographic Techniques from modular arithmetic perspective By classical cryptography we mean methods of encipherment that have been used from antiquity through the middle of the twentieth
Historical Ciphers. Required Reading. W. Stallings, Cryptography and Network Security, Chapter 2, Classical Encryption Techniques
ECE 646 - Lecture 6 Historical Ciphers Required Reading W tallings, Cryptography and Network ecurity, Chapter, Classical Encryption Techniques A Menezes et al, Handbook of Applied Cryptography, Chapter
Historical Ciphers. ECE Lecture 6. Why (not) to study historical ciphers? Required Reading. Secret Writing. Mary, Queen of Scots
ECE - Lecture Required Reading W tallings, Cryptography and Network ecurity, Historical Ciphers Chapter, Classical Encryption Techniques A Menezes et al, Handbook of Applied Cryptography, Chapter 73 Classical
Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering. Apr Cryptography Slide 1
Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering Apr. 2016 Cryptography Slide 1 About This Presentation This presentation belongs to the lecture series
Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering. Apr Cryptography Slide 1
Cryptography A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering Apr. 2007 Cryptography Slide 1 About This Presentation This presentation belongs to the lecture series
Clock Arithmetic and Euclid s Algorithm
Clock Arithmetic and Euclid s Algorithm Lecture notes for Access 2008 by Erin Chamberlain. Earlier we discussed Caesar Shifts and other substitution ciphers, and we saw how easy it was to break these ciphers
Historical cryptography. cryptography encryption main applications: military and diplomacy
Historical cryptography cryptography encryption main applications: military and diplomacy ancient times world war II Historical cryptography All historical cryptosystems badly broken! No clear understanding
UNIVERSITY OF CALIFORNIA Santa Barbara. Cryptanalysis of the SIGABA
UNIVERSITY OF CALIFORNIA Santa Barbara Cryptanalysis of the SIGABA A Thesis submitted in partial satisfaction of the requirements for the degree Master of Science in Computer Science by Michael Lee Committee
last name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK
last name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK 8 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 1 b c d e f g h i j k l m n o p q
Shift Cipher. For 0 i 25, the ith plaintext character is. E.g. k = 3
Shift Cipher For 0 i 25, the ith plaintext character is shifted by some value 0 k 25 (mod 26). E.g. k = 3 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 D E F G H I J K L M N O P Q R S T U V W X Y
Secrecy and the Quantum
Secrecy and the Quantum Benjamin Schumacher Department of Physics Kenyon College Bright Horizons 35 (July, 2018) Keeping secrets Communication Alice sound waves, photons, electrical signals, paper and
Theory of Computation CS3102 Spring 2014 A tale of computers, math, problem solving, life, love and tragic death
Theory of Computation CS3102 Spring 2014 A tale of computers, math, problem solving, life, love and tragic death Nathan Brunelle Department of Computer Science University of Virginia www.cs.virginia.edu/~njb2b/theory
Cryptography: A Fairy Tale for Mathematicians and Starring Mathematicians!
Cryptography: A Fairy Tale for Mathematicians and Starring Mathematicians! University of California, Berkeley Mathematics Undergraduate Student Association October 27, 2014 Why Crypto? So why on earth
Sound approaches to cryptography
CHAPTER 4: CLASSICAL (SECRET-KEY) CRYPTOSYSTEMS Part IV Secret-key cryptosystems In this chapter we deal with some of the very old, or quite old, classical (secret-key or symmetric) cryptosystems that
Innovation and Cryptoventures. Cryptology. Campbell R. Harvey. Duke University, NBER and Investment Strategy Advisor, Man Group, plc.
Innovation and Cryptoventures Cryptology Campbell R. Harvey Duke University, NBER and Investment Strategy Advisor, Man Group, plc January 20, 2017 Overview Cryptology Cryptography Cryptanalysis Symmetric
1/16 2/17 3/17 4/7 5/10 6/14 7/19 % Please do not write in the spaces above.
1/16 2/17 3/17 4/7 5/10 6/14 7/19 % Please do not write in the spaces above. Directions: You have 75 minutes in which to complete this exam. Please make sure that you read through this entire exam before
Simple Codes MTH 440
Simple Codes MTH 440 Not all codes are for the purpose of secrecy Morse Code ASCII Zip codes Area codes Library book codes Credit Cards ASCII Code Steganography: Hidden in plain sight (example from http://www.bbc.co.uk/news/10
Hidden Markov Models for Vigenère Cryptanalysis
Hidden Markov Models for Vigenère Cryptanalysis Mark Stamp Fabio Di Troia Department of Computer Science San Jose State University San Jose, California mark.stamp@sjsu.edu fabioditroia@msn.com Miles Stamp
The Evolution of Cryptology
California State University, San Bernardino CSUSB ScholarWorks Electronic Theses, Projects, and Dissertations Office of Graduate Studies 6-2016 The Evolution of Cryptology Gwendolyn Rae Souza California
Introduction to Information Security
Introuction to Inforation Security Lecture : Classical Ciphers 007. 6. Prof. Byoungcheon Lee sultan (at) joongbu. ac. kr Inforation an Counications University Contents 1. History of cryptographic research.
Cryptography. Lecture 2: Perfect Secrecy and its Limitations. Gil Segev
Cryptography Lecture 2: Perfect Secrecy and its Limitations Gil Segev Last Week Symmetric-key encryption (KeyGen, Enc, Dec) Historical ciphers that are completely broken The basic principles of modern
Cook-Levin Theorem. SAT is NP-complete
Cook-Levin Theorem SAT is NP-complete In other words SAT NP A NP A P SAT 1 Consider any A NP NTM N that decides A in polytime n k For any input w Σ * valid tableau of configurations 2 Properties of an
Computer Security. 07. Cryptography. Paul Krzyzanowski. Rutgers University. Spring 2017
Computer Security 07. Cryptography Paul Krzyzanowski Rutgers University Spring 2017 March 26, 2017 CS 419 2017 Paul Krzyzanowski 1 cryptography κρυπός γραφία hidden writing A secret manner of writing,
Video intypedia001en EXERCISES
Video intypedia001en LESSON 1: HISTORY OF CRYPTOGRAPHY AND ITS EARLY STAGES IN EUROPE EXERCISES Dr. Arturo Ribagorda Garnacho, Carlos III University of Madrid, Spain. EXERCISE 1 The discovery that in each
Dr Richard Clayton. 8 October 2009
Introducing Cryptanalysis Dr Richard Clayton richard.clayton@cl.cam.ac.ukclayton@cl cam ac Hills Road Sixth Form College 8 October 2009 It s all Greek to me! ΡΙΧΑΡ Secret communication Steganography: hiding
Cryptography. P. Danziger. Transmit...Bob...
10.4 Cryptography P. Danziger 1 Cipher Schemes A cryptographic scheme is an example of a code. The special requirement is that the encoded message be difficult to retrieve without some special piece of
NOI 2009 Solutions to Contest Tasks
NOI 2009 Solutions to Contest Tasks Martin Henz March 14, 2009 Martin Henz NOI 2009 Solutions to Contest Tasks 1 The Scientific Committee of NOI 2009 Ben Leong Chang Ee-Chien Colin Tan Frank Stephan Martin
Jay Daigle Occidental College Math 401: Cryptology
3 Block Ciphers Every encryption method we ve studied so far has been a substitution cipher: that is, each letter is replaced by exactly one other letter. In fact, we ve studied stream ciphers, which produce
Real scripts backgrounder 3 - Polyalphabetic encipherment - XOR as a cipher - RSA algorithm. David Morgan
Real scripts backgrounder 3 - Polyalphabetic encipherment - XOR as a cipher - RSA algorithm David Morgan XOR as a cipher Bit element encipherment elements are 0 and 1 use modulo-2 arithmetic Example: 1
An Introduction to Cryptography
An Introduction to Cryptography Spotlight on Science J. Robert Buchanan Department of Mathematics Spring 2008 What is Cryptography? cryptography: study of methods for sending messages in a form that only
1.5 Rise of the West Rise of the West 47
1.5. Rise of the West 47 1.5 Rise of the West Oh, East is East, and West is West, and never the twain shall meet, Till Earth and Sky stand presently at God s great Judgement Seat... Rudyard (Joseph) Kipling,
Introduction to Cryptography
slides available for download at: www.math.cm.is.nagoya-u.ac.jp/~buscemi/crypto.pdf Introduction to Cryptography from ancient ciphers to quantum cryptography ブシェーミ F( 計算機数理科学専攻 )buscemi@is.nagoya-u.ac.jp
The Hill Cipher A Linear Algebra Perspective
The Hill Cipher A Linear Algebra Perspective Contents 1 Introduction to Classical Cryptography 3 1.1 Alice, Bob & Eve................................. 3 1.2 Types of Attacks.................................
Security of Networks (12) Exercises
(12) Exercises 1.1 Below are given four examples of ciphertext, one obtained from a Substitution Cipher, one from a Vigenere Cipher, one from an Affine Cipher, and one unspecified. In each case, the task
17.1 Binary Codes Normal numbers we use are in base 10, which are called decimal numbers. Each digit can be 10 possible numbers: 0, 1, 2, 9.
( c ) E p s t e i n, C a r t e r, B o l l i n g e r, A u r i s p a C h a p t e r 17: I n f o r m a t i o n S c i e n c e P a g e 1 CHAPTER 17: Information Science 17.1 Binary Codes Normal numbers we use
Powers in Modular Arithmetic, and RSA Public Key Cryptography
1 Powers in Modular Arithmetic, and RSA Public Key Cryptography Lecture notes for Access 2006, by Nick Korevaar. It was a long time from Mary Queen of Scotts and substitution ciphers until the end of the
ADVANCED CRYPTOLOGY (COD2) CTY COURSE SYLLABUS. Week 1. Info sheet, pre-test, Sunday survey, honor codes, computer lab forms, check roster.
ADVANCED CRYPTOLOGY (COD2) CTY COURSE SYLLABUS Week 1 Info sheet, pre-test, Sunday survey, honor codes, computer lab forms, check roster Day 1 Previously in Cryptology : skit Introductions Icebreaker involving
Systems of Equations and Inequalities
7 Systems of Equations and Inequalities CHAPTER OUTLINE Introduction Figure 1 Enigma machines like this one, once owned by Italian dictator Benito Mussolini, were used by government and military officials
CODING AND CRYPTOLOGY III CRYPTOLOGY EXERCISES. The questions with a * are extension questions, and will not be included in the assignment.
CODING AND CRYPTOLOGY III CRYPTOLOGY EXERCISES A selection of the following questions will be chosen by the lecturer to form the Cryptology Assignment. The Cryptology Assignment is due by 5pm Sunday 1
CPE 776:DATA SECURITY & CRYPTOGRAPHY. Some Number Theory and Classical Crypto Systems
CPE 776:DATA SECURITY & CRYPTOGRAPHY Some Number Theory and Classical Crypto Systems Dr. Lo ai Tawalbeh Computer Engineering Department Jordan University of Science and Technology Jordan Some Number Theory
Block Ciphers and Feistel cipher
introduction Lecture (07) Block Ciphers and cipher Dr. Ahmed M. ElShafee Modern block ciphers are widely used to provide encryption of quantities of information, and/or a cryptographic checksum to ensure
Public Key Cryptography
Public Key Cryptography Spotlight on Science J. Robert Buchanan Department of Mathematics 2011 What is Cryptography? cryptography: study of methods for sending messages in a form that only be understood
26 HIDDEN MARKOV MODELS
26 HIDDEN MARKOV MODELS techniques to HMMs. Consequently, a clear understanding of the material in this chapter is crucial before proceeding with the remainder of the book. The homework problem will help
2.4 The Autokey cipher and cribs
2.4 The Autokey cipher and cribs 2.4.1 Using a crib One common tool in cryptanalysis is a crib, which is a known or guessed bit of plaintext corresponding to a ciphertext. (The term comes from the phrase
Linear Ciphers. Klaus Pommerening Fachbereich Physik, Mathematik, Informatik der Johannes-Gutenberg-Universität Saarstraße 21 D Mainz
Linear Ciphers Klaus Pommerening Fachbereich Physik, Mathematik, Informatik der Johannes-Gutenberg-Universität Saarstraße 21 D-55099 Mainz January 16, 2000 English version July 28, 2014 last change August
Cryptography and Secure Communication Protocols
Cryptography and Secure Communication Protocols Jayadev Misra The University of Texas at Austin October 1, 2003 Contents 1 Introduction 1 2 Early Encryption Schemes 2 2.1 Substitution cyphers.........................
CODING, CRYPTOGRAPHY and CRYPTOGRAPHIC PROTOCOLS
CODING, CRYPTOGRAPHY and CRYPTOGRAPHIC PROTOCOLS prof. RNDr. Jozef Gruska, DrSc. Faculty of Informatics Masaryk University October 17, 2016 Part I Secret-key cryptosystems basics PROLOGUE - I. Decrypt
Lecture 8 - Cryptography and Information Theory
Lecture 8 - Cryptography and Information Theory Jan Bouda FI MU April 22, 2010 Jan Bouda (FI MU) Lecture 8 - Cryptography and Information Theory April 22, 2010 1 / 25 Part I Cryptosystem Jan Bouda (FI
Great Theoretical Ideas in Computer Science
15-251 Great Theoretical Ideas in Computer Science Lecture 22: Cryptography November 12th, 2015 What is cryptography about? Adversary Eavesdropper I will cut your throat I will cut your throat What is
A block cipher enciphers each block with the same key.
Ciphers are classified as block or stream ciphers. All ciphers split long messages into blocks and encipher each block separately. Block sizes range from one bit to thousands of bits per block. A block
University of Regina Department of Mathematics & Statistics Final Examination (April 21, 2009)
Make sure that this examination has 10 numbered pages University of Regina Department of Mathematics & Statistics Final Examination 200910 (April 21, 2009) Mathematics 124 The Art and Science of Secret
Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 08 Shannon s Theory (Contd.)
CRYPTOGRAPHY AND NUMBER THEORY
CRYPTOGRAPHY AND NUMBER THEORY XINYU SHI Abstract. In this paper, we will discuss a few examples of cryptographic systems, categorized into two different types: symmetric and asymmetric cryptography. We
7 Cryptanalysis. 7.1 Structural Attacks CA642: CRYPTOGRAPHY AND NUMBER THEORY 1
CA642: CRYPTOGRAPHY AND NUMBER THEORY 1 7 Cryptanalysis Cryptanalysis Attacks such as exhaustive key-search do not exploit any properties of the encryption algorithm or implementation. Structural attacks
10 Modular Arithmetic and Cryptography
10 Modular Arithmetic and Cryptography 10.1 Encryption and Decryption Encryption is used to send messages secretly. The sender has a message or plaintext. Encryption by the sender takes the plaintext and
CSA E0 235: Cryptography March 16, (Extra) Lecture 3
CSA E0 235: Cryptography March 16, 2015 Instructor: Arpita Patra (Extra) Lecture 3 Submitted by: Ajith S 1 Chosen Plaintext Attack A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which
A Block Cipher using an Iterative Method involving a Permutation
Journal of Discrete Mathematical Sciences & Cryptography Vol. 18 (015), No. 3, pp. 75 9 DOI : 10.1080/097059.014.96853 A Block Cipher using an Iterative Method involving a Permutation Lakshmi Bhavani Madhuri
Cryptography. pieces from work by Gordon Royle
Cryptography pieces from work by Gordon Royle The set-up Cryptography is the mathematics of devising secure communication systems, whereas cryptanalysis is the mathematics of breaking such systems. We