An Extended Hybridization of Vigenere and Caesar Cipher Techniques for Secure Communication
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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. -
Codebusters Coaches Institute Notes
BEING COVER AGENT FIXED DELAY, PILOT RIGHT PLANE, CATCH SMALL RADIO (CODEBUSTERS) This is the first year CodeBusters will be a National event. A few changes have been made since the North Carolina trial event last year. 1. The Atbash Cipher has been added. 2. The running key cipher has been removed. 3. K2 alphabets have been added in addition to K1 alphabets 4. Hill Cipher decryption has been added with a given decryption matrix. 5. The points scale has been doubled, but the timing bonus has been increased by only 50% in order to further balance the test. 1 TYPES OF PROBLEMS 1.1 ARISTOCRAT (EASY TO HARD DIFFICULTY) http://www.cryptograms.org/tutorial.php An Aristocrat is the typical Crypto-quote you see in the newspaper. Word spaces are preserved. No letter will stand for itself and the replacement table is given as a guide (but doesn’t need to be filled in by the team to get credit). FXP PGYAPYF FIKP ME JAKXPT AY FXP GTAYFMJTGF THE EASIEST TYPE OF CIPHER IS THE ARISTOCRAT 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 Frequency 4 1 6 3 1 2 2 2 6 3 3 4 Replacement I F T A Y C P O E R H S 1.2 ARISTOCRATS WITH SPELLING AND/OR GRAMMAR ERRORS (MEDIUM TO VERY HARD DIFFICULTY) For these, either words will be misspelled or grammatical errors introduced. From a student perspective, it is what they might expect when someone finger fumbles a text message or has a bad voice transcription. -
A Cipher Based on the Random Sequence of Digits in Irrational Numbers
https://doi.org/10.48009/1_iis_2016_14-25 Issues in Information Systems Volume 17, Issue I, pp. 14-25, 2016 A CIPHER BASED ON THE RANDOM SEQUENCE OF DIGITS IN IRRATIONAL NUMBERS J. L. González-Santander, [email protected], Universidad Católica de Valencia “san Vicente mártir” G. Martín González. [email protected], Universidad Católica de Valencia “san Vicente mártir” ABSTRACT An encryption method combining a transposition cipher with one-time pad cipher is proposed. The transposition cipher prevents the malleability of the messages and the randomness of one-time pad cipher is based on the normality of "almost" all irrational numbers. Further, authentication and perfect forward secrecy are implemented. This method is quite suitable for communication within groups of people who know one each other in advance, such as mobile chat groups. Keywords: One-time Pad Cipher, Transposition Ciphers, Chat Mobile Groups Privacy, Forward Secrecy INTRODUCTION In cryptography, a cipher is a procedure for encoding and decoding a message in such a way that only authorized parties can write and read information about the message. Generally speaking, there are two main different cipher methods, transposition, and substitution ciphers, both methods being known from Antiquity. For instance, Caesar cipher consists in substitute each letter of the plaintext some fixed number of positions further down the alphabet. The name of this cipher came from Julius Caesar because he used this method taking a shift of three to communicate to his generals (Suetonius, c. 69-122 AD). In ancient Sparta, the transposition cipher entailed the use of a simple device, the scytale (skytálē) to encrypt and decrypt messages (Plutarch, c. -
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 -
A Hybrid Cryptosystem Based on Vigenère Cipher and Columnar Transposition Cipher
International Journal of Advanced Technology & Engineering Research (IJATER) www.ijater.com A HYBRID CRYPTOSYSTEM BASED ON VIGENÈRE CIPHER AND COLUMNAR TRANSPOSITION CIPHER Quist-Aphetsi Kester, MIEEE, Lecturer Faculty of Informatics, Ghana Technology University College, PMB 100 Accra North, Ghana Phone Contact +233 209822141 Email: [email protected] / [email protected] graphy that use the same cryptographic keys for both en- Abstract cryption of plaintext and decryption of cipher text. The keys may be identical or there may be a simple transformation to Privacy is one of the key issues addressed by information go between the two keys. The keys, in practice, represent a Security. Through cryptographic encryption methods, one shared secret between two or more parties that can be used can prevent a third party from understanding transmitted raw to maintain a private information link [5]. This requirement data over unsecured channel during signal transmission. The that both parties have access to the secret key is one of the cryptographic methods for enhancing the security of digital main drawbacks of symmetric key encryption, in compari- contents have gained high significance in the current era. son to public-key encryption. Typical examples symmetric Breach of security and misuse of confidential information algorithms are Advanced Encryption Standard (AES), Blow- that has been intercepted by unauthorized parties are key fish, Tripple Data Encryption Standard (3DES) and Serpent problems that information security tries to solve. [6]. This paper sets out to contribute to the general body of Asymmetric or Public key encryption on the other hand is an knowledge in the area of classical cryptography by develop- encryption method where a message encrypted with a reci- ing a new hybrid way of encryption of plaintext. -
Grade 6 Math Circles Cryptography Solutions Atbash Cipher Caesar Cipher
Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 6 Math Circles November 5/6 2019 Cryptography Solutions Hello World Khoor Zruog Hello Zruog Khoor Khoor Zruog World 1. Person A encrypts plaintext 2. Person B receives ciphertext 3. Person B decrypts ciphertext back into ciphertext into plaintext Atbash Cipher Examples 1. Encrypt \Math Circles" using the Atbash cipher. Nzgs Xrixovh 2. Decrypt \ORLM PRMT" using the Atbash cipher. LION KING Caesar Cipher Examples: Encrypt or decrypt the following messages using the shift number given in parentheses: a) Welcome to Math Circles! (5) Bjqhtrj yt Rfym Hnwhqjx! plaintext 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 ciphertext 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 1 b) Ljw hxd anjm cqrb? (9) Can you read this? plaintext 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 ciphertext 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 c) What if I did a Caesar Shift of 26 units on \Welcome to Math Circles!"? A Caesar shift of 26 would be shifting by the length of the alphabet. For example I would be shifting A 26 letters to the right. -
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). -
Breaking Transposition Cipher with Genetic Algorithm
Breaking Transposition Cipher with Genetic Algorithm C.Obi Reddy, National University of Singapore(NUS), ECE Department, [email protected] Abstract: In recent years a number of example total number of letters is 20 optimisation algorithms have emerged which is regular case with the key order of which have proven to be effective in 5. If the plain text is irregular then solving a variety of NP-complete padding of X is done at the tail of the text problems. In this paper an example the to make it regular. kind in cryptanalysis, breaking of Encryption of plain text is done as follows transposition cipher using a heuristic genetic algorithm is presented. Regular: Plain 1 2 3 4 5 Introduction: Text In the Brute Force attack the attacker Key 1 4 2 5 3 tries every possible (k! Keys) key on a T H I S I piece of cipher text until an intelligible S A S I M translation into plaintext is obtained. P L E M E Many types of classical ciphers exist, S S A G E although most fall into one of two broad categories: substitution ciphers and Cipher Text: TSPS ISEA IMEE HALS SIMG transposition ciphers. In the former one, every plaintext character is substituted by Irregular: a cipher character, using a substitution Plain 1 2 3 4 5 alphabet, and in the latter one, plaintext Text characters are permuted using a Key 1 4 2 5 3 predetermined permutation. T H I S I S A S I M Transposition cipher works by breaking P L E M E the plain text in to fixed number of blocks S S A G E and then shuffling the characters in each block according to the agreed key K. -
ISA 562 Information Security Theory & Practice
ISA 562 Information Security Theory & Practice Introduction to Cryptography Agenda • Basics & Definitions • Classical Cryptography • Symmetric (Secret Key) Cryptography • DES (Data Encryption Standard) • Multiple Encryptions • Modes of Block Cipher Operations • Math Essential • Asymmetric (Public Key) Cryptography 2 1 Basics & Definitions Security Concepts (I) • Confidentiality – Prevent information from being exposed to unintended party – Ex: An employee should not come to know the salary of his manager • Integrity – Assure that the information has not been tempered – Ex: An employee should not be able to modify the employee's own salary • Identity – Assure that the party of concern is authentic - it is what it claims to be – Ex: An employee should be able to uniquely identify and authenticate himself/herself 4 2 Security Concepts (II) • Availability – Assure that unused service or resource is available to legitimate users – Ex: Paychecks should be printed on time as stipulated by law • Anonymity – Assure that the identity of some party is remain anonymous – Ex: The manager should not know who had a critical review of him • Non-Repudiation – Assure that authenticated party has indeed done something that cannot be denied – Ex: Once the employee has cashed his paycheck, he can’t deny it. 5 Cryptography • Crypt = secret • Graph = writing • Cryptography is the science / art of transforming meaningful information into unintelligible text Becoming a science that relies on mathematics (number theory, algebra) • Cryptanalysis is the science / art of breaking cryptographic codes • Cryptology is the science / art / study of both cryptography and cryptanalysis 6 3 Applications of Cryptography • Assuring document integrity • Assuring document confidentiality • Authenticating parties • Document signature • Non-repudiation • Secure transactions • Exchanging keys • Sharing Secrets • Digital cash • Preserving anonymity • Copyright protection • More . -
Lecture 2: Classical Cryptography
Lecture 2: Classical Cryptography Data and Information Management: ELEN 3015 School of Electrical and Information Engineering, University of the Witwatersrand Introduction Monoalphabetic Cipher - Frequency analysis Classical Ciphers Other Substitution Ciphers Transposition ciphers Stream vs Block Enciphering 1. Homework hqfubswlrq lv d phdqv ri dwwdlqlqj vhfxuh frpsxwdwlrq ryhu lqvhfxuh fkdqqhov eb xvlqj hqfubswlrq zh glvjxlvh wkh phvvdjh vr wkdw hyhq li wkh wudqvplvvlrq lv glyhuwhg wkh phvvdjh zloo qrw eh uhyhdohg 1. Monoalphabetic Cipher - Frequency analysis Do a frequency analysis Letter distribution of English language is fixed (for a large body of text) Tables of letter distribution For instance, most commonly used letter is \e" 1. Monoalphabetic Cipher - Frequency analysis 1. Monoalphabetic Cipher - Answer ENCRYPTION IS A MEANS OF ATTAINING SECURE COMMUNICATION OVER INSECURE CHANNELS BY USING ENCRYPTION WE DISGUISE THE MESSAGE SO THAT EVEN IF THE TRANSMISSION IS DIVERTED THE MESSAGE WILL NOT BE REVEALED 2. Classical Ciphers How do we increase security of the monoalphabetic cipher? 3. Polyalphabetic ciphers Use more than one alphabetic substitution to flatten the frequency distribution Combine substitutions that are high with those that are low Eg use: • P1(a) = (a*3)mod26 • P2(a) = ((5*a)+13)mod26 3. Polyalphabetic ciphers Cipher I: ABCDEFG ::: STUVWXYZ a d g j m p s ::: c f i l o r u x Cipher II: ABCDEFG ::: STUVWXYZ n s x c h m r ::: z e j o t y d i 3. Polyalphabetic ciphers - Frequency distribution 3. Vigenere tables a b c d e f ::: t u v w x y z π A a b c d e f ::: t u v w x y z 0 B b c d e f g ::: u v w x y z a 1 C c d e f g h ::: v w x y z a b 2 . -
Cryptology: an Historical Introduction DRAFT
Cryptology: An Historical Introduction DRAFT Jim Sauerberg February 5, 2013 2 Copyright 2013 All rights reserved Jim Sauerberg Saint Mary's College Contents List of Figures 8 1 Caesar Ciphers 9 1.1 Saint Cyr Slide . 12 1.2 Running Down the Alphabet . 14 1.3 Frequency Analysis . 15 1.4 Linquist's Method . 20 1.5 Summary . 22 1.6 Topics and Techniques . 22 1.7 Exercises . 23 2 Cryptologic Terms 29 3 The Introduction of Numbers 31 3.1 The Remainder Operator . 33 3.2 Modular Arithmetic . 38 3.3 Decimation Ciphers . 40 3.4 Deciphering Decimation Ciphers . 42 3.5 Multiplication vs. Addition . 44 3.6 Koblitz's Kid-RSA and Public Key Codes . 44 3.7 Summary . 48 3.8 Topics and Techniques . 48 3.9 Exercises . 49 4 The Euclidean Algorithm 55 4.1 Linear Ciphers . 55 4.2 GCD's and the Euclidean Algorithm . 56 4.3 Multiplicative Inverses . 59 4.4 Deciphering Decimation and Linear Ciphers . 63 4.5 Breaking Decimation and Linear Ciphers . 65 4.6 Summary . 67 4.7 Topics and Techniques . 67 4.8 Exercises . 68 3 4 CONTENTS 5 Monoalphabetic Ciphers 71 5.1 Keyword Ciphers . 72 5.2 Keyword Mixed Ciphers . 73 5.3 Keyword Transposed Ciphers . 74 5.4 Interrupted Keyword Ciphers . 75 5.5 Frequency Counts and Exhaustion . 76 5.6 Basic Letter Characteristics . 77 5.7 Aristocrats . 78 5.8 Summary . 80 5.9 Topics and Techniques . 81 5.10 Exercises . 81 6 Decrypting Monoalphabetic Ciphers 89 6.1 Letter Interactions . 90 6.2 Decrypting Monoalphabetic Ciphers .