Solving Cipher Secrets
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Simple Substitution Cipher Evelyn Guo
Simple Substitution Cipher Evelyn Guo Topic: Data Frequency Analysis, Logic Curriculum Competencies: • Develop thinking strategies to solve puzzles and play games • Think creatively and with curiosity and wonder when exploring problems • Apply flexible and strategic approaches to solve problems • Solve problems with persistence and a positive disposition Grade Levels: G3 - G12 Resource: University of Cambridge Millennium Mathematics Project - NRICH https://nrich.maths.org/4957 Cipher Challenge Toolkit https://nrich.maths.org/7983 Practical Cryptography website http://practicalcryptography.com/ciphers/classical-era/simple- substitution/ Materials: Ipad and Laptop which could run excel spreadsheet. Flip Chart with tips and hints for different levels of players Booklet flyers for anyone taking home. Printed coded message and work sheet (help sheet) with plain alphabet and cipher alphabet (leave blank) Pencils Extension: • Depends on individual player’s interest and math abilities, introduce easier (Atbash Cipher, Caesar Cipher) or harder ways ( AutoKey Cipher) to encrypt messages. • Introduce students how to use the practical cryptography website to create their own encrypted message instantly. • Allow players create their own cipher method. • Understand in any language some letters tend to appear more often than other letters Activity Sheet for Substitution Cipher Opening Question: Which Letters do you think are the most common in English? Start by performing a frequency analysis on some selected text to see which letters appear most often. It is better to use longer texts, as a short text might have an unusual distribution of letters, like the "quick brown fox jumps over the lazy dog" Introduce the Problem: In the coded text attached, every letter in the original message was switched with another letter. -
The Mathemathics of Secrets.Pdf
THE MATHEMATICS OF SECRETS THE MATHEMATICS OF SECRETS CRYPTOGRAPHY FROM CAESAR CIPHERS TO DIGITAL ENCRYPTION JOSHUA HOLDEN PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock; design by Lorraine Betz Doneker All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Holden, Joshua, 1970– author. Title: The mathematics of secrets : cryptography from Caesar ciphers to digital encryption / Joshua Holden. Description: Princeton : Princeton University Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2016014840 | ISBN 9780691141756 (hardcover : alk. paper) Subjects: LCSH: Cryptography—Mathematics. | Ciphers. | Computer security. Classification: LCC Z103 .H664 2017 | DDC 005.8/2—dc23 LC record available at https://lccn.loc.gov/2016014840 British Library Cataloging-in-Publication Data is available This book has been composed in Linux Libertine Printed on acid-free paper. ∞ Printed in the United States of America 13579108642 To Lana and Richard for their love and support CONTENTS Preface xi Acknowledgments xiii Introduction to Ciphers and Substitution 1 1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher 1 1.2 The Key to the Matter: Generalizing the Caesar Cipher 4 1.3 Multiplicative Ciphers 6 -
Recommendation for Block Cipher Modes of Operation Methods
NIST Special Publication 800-38A Recommendation for Block 2001 Edition Cipher Modes of Operation Methods and Techniques Morris Dworkin C O M P U T E R S E C U R I T Y ii C O M P U T E R S E C U R I T Y Computer Security Division Information Technology Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899-8930 December 2001 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary of Commerce for Technology National Institute of Standards and Technology Arden L. Bement, Jr., Director iii Reports on Information Security Technology The Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation’s measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analyses to advance the development and productive use of information technology. ITL’s responsibilities include the development of technical, physical, administrative, and management standards and guidelines for the cost-effective security and privacy of sensitive unclassified information in Federal computer systems. This Special Publication 800-series reports on ITL’s research, guidance, and outreach efforts in computer security, and its collaborative activities with industry, government, and academic organizations. Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. -
Polish Mathematicians Finding Patterns in Enigma Messages
Fall 2006 Chris Christensen MAT/CSC 483 Machine Ciphers Polyalphabetic ciphers are good ways to destroy the usefulness of frequency analysis. Implementation can be a problem, however. The key to a polyalphabetic cipher specifies the order of the ciphers that will be used during encryption. Ideally there would be as many ciphers as there are letters in the plaintext message and the ordering of the ciphers would be random – an one-time pad. More commonly, some rotation among a small number of ciphers is prescribed. But, rotating among a small number of ciphers leads to a period, which a cryptanalyst can exploit. Rotating among a “large” number of ciphers might work, but that is hard to do by hand – there is a high probability of encryption errors. Maybe, a machine. During World War II, all the Allied and Axis countries used machine ciphers. The United States had SIGABA, Britain had TypeX, Japan had “Purple,” and Germany (and Italy) had Enigma. SIGABA http://en.wikipedia.org/wiki/SIGABA 1 A TypeX machine at Bletchley Park. 2 From the 1920s until the 1970s, cryptology was dominated by machine ciphers. What the machine ciphers typically did was provide a mechanical way to rotate among a large number of ciphers. The rotation was not random, but the large number of ciphers that were available could prevent depth from occurring within messages and (if the machines were used properly) among messages. We will examine Enigma, which was broken by Polish mathematicians in the 1930s and by the British during World War II. The Japanese Purple machine, which was used to transmit diplomatic messages, was broken by William Friedman’s cryptanalysts. -
Index-Of-Coincidence.Pdf
The Index of Coincidence William F. Friedman in the 1930s developed the index of coincidence. For a given text X, where X is the sequence of letters x1x2…xn, the index of coincidence IC(X) is defined to be the probability that two randomly selected letters in the ciphertext represent, the same plaintext symbol. For a given ciphertext of length n, let n0, n1, …, n25 be the respective letter counts of A, B, C, . , Z in the ciphertext. Then, the index of coincidence can be computed as 25 ni (ni −1) IC = ∑ i=0 n(n −1) We can also calculate this index for any language source. For some source of letters, let p be the probability of occurrence of the letter a, p be the probability of occurrence of a € b the letter b, and so on. Then the index of coincidence for this source is 25 2 Isource = pa pa + pb pb +…+ pz pz = ∑ pi i=0 We can interpret the index of coincidence as the probability of randomly selecting two identical letters from the source. To see why the index of coincidence gives us useful information, first€ note that the empirical probability of randomly selecting two identical letters from a large English plaintext is approximately 0.065. This implies that an (English) ciphertext having an index of coincidence I of approximately 0.065 is probably associated with a mono-alphabetic substitution cipher, since this statistic will not change if the letters are simply relabeled (which is the effect of encrypting with a simple substitution). The longer and more random a Vigenere cipher keyword is, the more evenly the letters are distributed throughout the ciphertext. -
Secure Communications One Time Pad Cipher
Cipher Machines & Cryptology © 2010 – D. Rijmenants http://users.telenet.be/d.rijmenants THE COMPLETE GUIDE TO SECURE COMMUNICATIONS WITH THE ONE TIME PAD CIPHER DIRK RIJMENANTS Abstract : This paper provides standard instructions on how to protect short text messages with one-time pad encryption. The encryption is performed with nothing more than a pencil and paper, but provides absolute message security. If properly applied, it is mathematically impossible for any eavesdropper to decrypt or break the message without the proper key. Keywords : cryptography, one-time pad, encryption, message security, conversion table, steganography, codebook, message verification code, covert communications, Jargon code, Morse cut numbers. version 012-2011 1 Contents Section Page I. Introduction 2 II. The One-time Pad 3 III. Message Preparation 4 IV. Encryption 5 V. Decryption 6 VI. The Optional Codebook 7 VII. Security Rules and Advice 8 VIII. Appendices 17 I. Introduction One-time pad encryption is a basic yet solid method to protect short text messages. This paper explains how to use one-time pads, how to set up secure one-time pad communications and how to deal with its various security issues. It is easy to learn to work with one-time pads, the system is transparent, and you do not need special equipment or any knowledge about cryptographic techniques or math. If properly used, the system provides truly unbreakable encryption and it will be impossible for any eavesdropper to decrypt or break one-time pad encrypted message by any type of cryptanalytic attack without the proper key, even with infinite computational power (see section VII.b) However, to ensure the security of the message, it is of paramount importance to carefully read and strictly follow the security rules and advice (see section VII). -
John F. Byrne's Chaocipher Revealed
John F. Byrne’s Chaocipher Revealed John F. Byrne’s Chaocipher Revealed: An Historical and Technical Appraisal MOSHE RUBIN1 Abstract Chaocipher is a method of encryption invented by John F. Byrne in 1918, who tried unsuccessfully to interest the US Signal Corp and Navy in his system. In 1953, Byrne presented Chaocipher-encrypted messages as a challenge in his autobiography Silent Years. Although numerous students of cryptanalysis attempted to solve the challenge messages over the years, none succeeded. For ninety years the Chaocipher algorithm was a closely guarded secret known only to a handful of persons. Following fruitful negotiations with the Byrne family during the period 2009-2010, the Chaocipher papers and materials have been donated to the National Cryptologic Museum in Ft. Meade, MD. This paper presents a comprehensive historical and technical evaluation of John F. Byrne and his Chaocipher system. Keywords ACA, American Cryptogram Association, block cipher encryption modes, Chaocipher, dynamic substitution, Greg Mellen, Herbert O. Yardley, John F. Byrne, National Cryptologic Museum, Parker Hitt, Silent Years, William F. Friedman 1 Introduction John Francis Byrne was born on 11 February 1880 in Dublin, Ireland. He was an intimate friend of James Joyce, the famous Irish writer and poet, studying together in Belvedere College and University College in Dublin. Joyce based the character named Cranly in Joyce’s A Portrait of the Artist as a Young Man on Byrne, used Byrne’s Dublin residence of 7 Eccles Street as the home of Leopold and Molly Bloom, the main characters in Joyce’s Ulysses, and made use of real-life anecdotes of himself and Byrne as the basis of stories in Ulysses. -
Shift Cipher Substitution Cipher Vigenère Cipher Hill Cipher
Lecture 2 Classical Cryptosystems Shift cipher Substitution cipher Vigenère cipher Hill cipher 1 Shift Cipher • A Substitution Cipher • The Key Space: – [0 … 25] • Encryption given a key K: – each letter in the plaintext P is replaced with the K’th letter following the corresponding number ( shift right ) • Decryption given K: – shift left • History: K = 3, Caesar’s cipher 2 Shift Cipher • Formally: • Let P=C= K=Z 26 For 0≤K≤25 ek(x) = x+K mod 26 and dk(y) = y-K mod 26 ʚͬ, ͭ ∈ ͔ͦͪ ʛ 3 Shift Cipher: An Example ABCDEFGHIJKLMNOPQRSTUVWXYZ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 • P = CRYPTOGRAPHYISFUN Note that punctuation is often • K = 11 eliminated • C = NCJAVZRCLASJTDQFY • C → 2; 2+11 mod 26 = 13 → N • R → 17; 17+11 mod 26 = 2 → C • … • N → 13; 13+11 mod 26 = 24 → Y 4 Shift Cipher: Cryptanalysis • Can an attacker find K? – YES: exhaustive search, key space is small (<= 26 possible keys). – Once K is found, very easy to decrypt Exercise 1: decrypt the following ciphertext hphtwwxppelextoytrse Exercise 2: decrypt the following ciphertext jbcrclqrwcrvnbjenbwrwn VERY useful MATLAB functions can be found here: http://www2.math.umd.edu/~lcw/MatlabCode/ 5 General Mono-alphabetical Substitution Cipher • The key space: all possible permutations of Σ = {A, B, C, …, Z} • Encryption, given a key (permutation) π: – each letter X in the plaintext P is replaced with π(X) • Decryption, given a key π: – each letter Y in the ciphertext C is replaced with π-1(Y) • Example ABCDEFGHIJKLMNOPQRSTUVWXYZ πBADCZHWYGOQXSVTRNMSKJI PEFU • BECAUSE AZDBJSZ 6 Strength of the General Substitution Cipher • Exhaustive search is now infeasible – key space size is 26! ≈ 4*10 26 • Dominates the art of secret writing throughout the first millennium A.D. -
Applications of Search Techniques to Cryptanalysis and the Construction of Cipher Components. James David Mclaughlin Submitted F
Applications of search techniques to cryptanalysis and the construction of cipher components. James David McLaughlin Submitted for the degree of Doctor of Philosophy (PhD) University of York Department of Computer Science September 2012 2 Abstract In this dissertation, we investigate the ways in which search techniques, and in particular metaheuristic search techniques, can be used in cryptology. We address the design of simple cryptographic components (Boolean functions), before moving on to more complex entities (S-boxes). The emphasis then shifts from the construction of cryptographic arte- facts to the related area of cryptanalysis, in which we first derive non-linear approximations to S-boxes more powerful than the existing linear approximations, and then exploit these in cryptanalytic attacks against the ciphers DES and Serpent. Contents 1 Introduction. 11 1.1 The Structure of this Thesis . 12 2 A brief history of cryptography and cryptanalysis. 14 3 Literature review 20 3.1 Information on various types of block cipher, and a brief description of the Data Encryption Standard. 20 3.1.1 Feistel ciphers . 21 3.1.2 Other types of block cipher . 23 3.1.3 Confusion and diffusion . 24 3.2 Linear cryptanalysis. 26 3.2.1 The attack. 27 3.3 Differential cryptanalysis. 35 3.3.1 The attack. 39 3.3.2 Variants of the differential cryptanalytic attack . 44 3.4 Stream ciphers based on linear feedback shift registers . 48 3.5 A brief introduction to metaheuristics . 52 3.5.1 Hill-climbing . 55 3.5.2 Simulated annealing . 57 3.5.3 Memetic algorithms . 58 3.5.4 Ant algorithms . -
Decrypt Cryptotexts: GBLVMUB JOGPSNBUJLZ VMNIR RPNBMZ EBMFLP OFABKEFT Decrypt: VHFUHW GH GHXA VHFUHW GH GLHX, VHFUHW GH WURLV VH
PROLOGUE - I. Decrypt cryptotexts: Part IV GBLVMUB JOGPSNBUJLZ Secret-key cryptosystems VMNIR RPNBMZ EBMFLP OFABKEFT prof. Jozef Gruska IV054 4. Secret-key cryptosystems 2/99 PROLOGUE - II. CHAPTER 4: SECRET-KEY (SYMMETRIC) CRYPTOGRAPHY Decrypt: In this chapter we deal with some of the very old, or quite old, classical (secret-key or symmetric) cryptosystems and their cryptanalysis that were primarily used in the pre-computer era. VHFUHW GH GHXA These cryptosystems are too weak nowadays, too easy to break, especially VHFUHW GH GLHX, with computers. However, these simple cryptosystems give a good illustration of several of the VHFUHW GH WURLV important ideas of the cryptography and cryptanalysis. Moreover, most of them can be very useful in combination with more modern VHFUHW GH WRXV. cryptosystem - to add a new level of security. prof. Jozef Gruska IV054 4. Secret-key cryptosystems 3/99 prof. Jozef Gruska IV054 4. Secret-key cryptosystems 4/99 BASICS CRYPTOLOGY - HISTORY + APPLICATIONS Cryptology (= cryptography + cryptanalysis) has more than four thousand years long history. Some historical observation People have always had fascination with keeping information away from others. Some people – rulers, diplomats, military people, businessmen – have always had needs to keep some information away from others. BASICS Importance of cryptography nowadays Applications: cryptography is the key tool to make modern information transmission secure, and to create secure information society. Foundations: cryptography gave rise to several new key concepts of the foundation of informatics: one-way functions, computationally perfect pseudorandom generators, zero-knowledge proofs, holographic proofs, program self-testing and self-correcting, . prof. Jozef Gruska IV054 4. Secret-key cryptosystems 5/99 prof. -
Substitution Ciphers
Foundations of Computer Security Lecture 40: Substitution Ciphers Dr. Bill Young Department of Computer Sciences University of Texas at Austin Lecture 40: 1 Substitution Ciphers Substitution Ciphers A substitution cipher is one in which each symbol of the plaintext is exchanged for another symbol. If this is done uniformly this is called a monoalphabetic cipher or simple substitution cipher. If different substitutions are made depending on where in the plaintext the symbol occurs, this is called a polyalphabetic substitution. Lecture 40: 2 Substitution Ciphers Simple Substitution A simple substitution cipher is an injection (1-1 mapping) of the alphabet into itself or another alphabet. What is the key? A simple substitution is breakable; we could try all k! mappings from the plaintext to ciphertext alphabets. That’s usually not necessary. Redundancies in the plaintext (letter frequencies, digrams, etc.) are reflected in the ciphertext. Not all substitution ciphers are simple substitution ciphers. Lecture 40: 3 Substitution Ciphers Caesar Cipher The Caesar Cipher is a monoalphabetic cipher in which each letter is replaced in the encryption by another letter a fixed “distance” away in the alphabet. For example, A is replaced by C, B by D, ..., Y by A, Z by B, etc. What is the key? What is the size of the keyspace? Is the algorithm strong? Lecture 40: 4 Substitution Ciphers Vigen`ere Cipher The Vigen`ere Cipher is an example of a polyalphabetic cipher, sometimes called a running key cipher because the key is another text. Start with a key string: “monitors to go to the bathroom” and a plaintext to encrypt: “four score and seven years ago.” Align the two texts, possibly removing spaces: plaintext: fours corea ndsev enyea rsago key: monit orsto gotot hebat hroom ciphertext: rcizl qfkxo trlso lrzet yjoua Then use the letter pairs to look up an encryption in a table (called a Vigen`ere Tableau or tabula recta). -
Algorithms and Mechanisms Historical Ciphers
Algorithms and Mechanisms Cryptography is nothing more than a mathematical framework for discussing the implications of various paranoid delusions — Don Alvarez Historical Ciphers Non-standard hieroglyphics, 1900BC Atbash cipher (Old Testament, reversed Hebrew alphabet, 600BC) Caesar cipher: letter = letter + 3 ‘fish’ ‘ilvk’ rot13: Add 13/swap alphabet halves •Usenet convention used to hide possibly offensive jokes •Applying it twice restores the original text Substitution Ciphers Simple substitution cipher: a=p,b=m,c=f,... •Break via letter frequency analysis Polyalphabetic substitution cipher 1. a = p, b = m, c = f, ... 2. a = l, b = t, c = a, ... 3. a = f, b = x, c = p, ... •Break by decomposing into individual alphabets, then solve as simple substitution One-time Pad (1917) Message s e c r e t 18 5 3 17 5 19 OTP +15 8 1 12 19 5 7 13 4 3 24 24 g m d c x x OTP is unbreakable provided •Pad is never reused (VENONA) •Unpredictable random numbers are used (physical sources, e.g. radioactive decay) One-time Pad (ctd) Used by •Russian spies •The Washington-Moscow “hot line” •CIA covert operations Many snake oil algorithms claim unbreakability by claiming to be a OTP •Pseudo-OTPs give pseudo-security Cipher machines attempted to create approximations to OTPs, first mechanically, then electronically Cipher Machines (~1920) 1. Basic component = wired rotor •Simple substitution 2. Step the rotor after each letter •Polyalphabetic substitution, period = 26 Cipher Machines (ctd) 3. Chain multiple rotors Each rotor steps the next one when a full