Midterm Project - the Trithemius Cipher Spring 2017

Total Page:16

File Type:pdf, Size:1020Kb

Midterm Project - the Trithemius Cipher Spring 2017 Midterm Project - The Trithemius Cipher Spring 2017 This project should consist of a short written report which includes your responses for the questions and exercises below. Include a bibliography of sources you used. 1. Who was Johannes Trithemius and when did he live? Was his cipher created before or after the Alberti Cipher? Was it a monoalphabetic or polyalphabetic cipher? Why? Why is it important? 2. Describe how the Trithemius cipher was used. Compare it to the Alberti cipher. Explain what a \progressive key cipher" is. Write out a tabula recta and explain how it was used in the encoding process. How is it different from the Vigenere cipher? 3. Now encrypt the message Cryptography is fun using the Trithemius cipher where you start with the first column of the tabula recta. Do not encrypt spaces. Explain your steps. What key, if any, does the receiver need to decrypt the message? 4. Now decrypt the message JPJDRSKZBASETRAXKJ using the Trithemius cipher where it was encrypted by starting with the first column of the tabula recta. Explain your steps. 5. This cipher is not very secure. One option to improve it, would be start with a column other than the first in the tabula recta. This would be the key that the decoder needs. (a) Encrypt the message Cryptography is fun using the Trithemius cipher and a key of 20 (the starting column number). (b) Now decrypt the message SUSMB where it was encrypted by starting with a random column. Explain your reasoning to decrypt it. How does the decryption process compare with a shifted Caesar cipher? Is it more secure? Why? 6. Another approach to making this more secure is to basically have two (or more) alphabets which are indicated by the starting column; e.g., 10 and 20 or the starting letters \J' and \T". The first letter of the message (assume it is HELP) is encrypted in the usual manner using alphabet 1; for example if we start with the column where\J" is at the top we encrypt \H" as \Q". The second letter of the message is \E" and we use the second alphabet, i.e., we look at the column with \T" at the top and see that we encrypt \E" as \X". To encrypt the \L" we return to the first alphabet which started at column 10 and so now we progress to column 11 and see that it is encrypted as \V'. Lastly we encrypt \P" using the second alphabet so we use column 21 to get \J". Of course we can use more than two alphabets. (a) Encrypt the message \Cryptography is fun" using a key of columns 5 and 12. (b) Encrypt the message \Cryptography is fun" using a key word (which indicates the column numbers) \FSU". 1.
Recommended publications
  • Download Download
    International Journal of Integrated Engineering: Special Issue 2018: Data Information Engineering, Vol. 10 No. 6 (2018) p. 183-192. © Penerbit UTHM DOI: https://doi.org/10.30880/ijie.2018.10.06.026 Analysis of Four Historical Ciphers Against Known Plaintext Frequency Statistical Attack Chuah Chai Wen1*, Vivegan A/L Samylingam2, Irfan Darmawan3, P.Siva Shamala A/P Palaniappan4, Cik Feresa Mohd. Foozy5, Sofia Najwa Ramli6, Janaka Alawatugoda7 1,2,4,5,6Information Security Interest Group (ISIG), Faculty Computer Science and Information Technology University Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia E-mail: [email protected], [email protected], {shamala, feresa, sofianajwa}@uthm.edu.my 3School of Industrial Engineering, Telkom University, 40257 Bandung, West Java, Indonesia 7Department of Computer Engineering, University of Peradeniya, Sri Lanka E-mail: [email protected] Received 28 June 2018; accepted 5August 2018, available online 24 August 2018 Abstract: The need of keeping information securely began thousands of years. The practice to keep the information securely is by scrambling the message into unreadable form namely ciphertext. This process is called encryption. Decryption is the reverse process of encryption. For the past, historical ciphers are used to perform encryption and decryption process. For example, the common historical ciphers are Hill cipher, Playfair cipher, Random Substitution cipher and Vigenère cipher. This research is carried out to examine and to analyse the security level of these four historical ciphers by using known plaintext frequency statistical attack. The result had shown that Playfair cipher and Hill cipher have better security compare with Vigenère cipher and Random Substitution cipher.
    [Show full text]
  • COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Cryptography Is Everywhere a Long & Rich History
    COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Cryptography Is Everywhere A Long & Rich History Examples: • ~50 B.C. – Caesar Cipher • 1587 – Babington Plot • WWI – Zimmermann Telegram • WWII – Enigma • 1976/77 – Public Key Cryptography • 1990’s – Widespread adoption on the Internet Increasingly Important COS 433 Practice Theory Inherent to the study of crypto • Working knowledge of fundamentals is crucial • Cannot discern security by experimentation • Proofs, reductions, probability are necessary COS 433 What you should expect to learn: • Foundations and principles of modern cryptography • Core building blocks • Applications Bonus: • Debunking some Hollywood crypto • Better understanding of crypto news COS 433 What you will not learn: • Hacking • Crypto implementations • How to design secure systems • Viruses, worms, buffer overflows, etc Administrivia Course Information Instructor: Mark Zhandry (mzhandry@p) TA: Fermi Ma (fermima1@g) Lectures: MW 1:30-2:50pm Webpage: cs.princeton.edu/~mzhandry/2017-Spring-COS433/ Office Hours: please fill out Doodle poll Piazza piaZZa.com/princeton/spring2017/cos433mat473_s2017 Main channel of communication • Course announcements • Discuss homework problems with other students • Find study groups • Ask content questions to instructors, other students Prerequisites • Ability to read and write mathematical proofs • Familiarity with algorithms, analyZing running time, proving correctness, O notation • Basic probability (random variables, expectation) Helpful: • Familiarity with NP-Completeness, reductions • Basic number theory (modular arithmetic, etc) Reading No required text Computer Science/Mathematics Chapman & Hall/CRC If you want a text to follow along with: Second CRYPTOGRAPHY AND NETWORK SECURITY Cryptography is ubiquitous and plays a key role in ensuring data secrecy and Edition integrity as well as in securing computer systems more broadly.
    [Show full text]
  • "Cyber Security" Activity
    Cyber Security Keeping your information safe Standards: (Core ideas related to the activity) NGSS: ETS1.B – A solution needs to be tested and them modified on the basis of the test results in order to improve it MS-PS4.C – Digitized signals sent as wave pulses are a more reliable way to encode and transmit information CC Math: 5.OA-3 – Analyze patterns and relationships K12CS: 3-5 CS-Devices – Computing devices may be connected to other devices or components to extend their capabilities. Connections can take many forms such as physical or wireless. 3-5 N&I-Cybersecurity – Information can be protected using various security measures. These measures can be physical or digital 3-5 IoC-Culture – The development and modification of computing technology is driven by people’s needs and wants and can affect different groups differently 6-8 CS-Devices – The interaction between humans and computing devices presents advantages, disadvantages, and unintended consequences. The study of human-computer interaction can improve the design of devices and extend the abilities of humans. 6-8 N&I-Cybersecurity – The information sent and received across networks can be protected from unauthorized access and modification in a variety of ways, such as encryption to maintain its confidentiality and restricted access to maintain its integrity. Security measures to safeguard online information proactively address the threat of breaches to personal and private data 6-8 A&P-Algorithms – Algorithms affect how people interact with computers and the way computers respond. People design algorithms that are generalizable to many situations 6-8 IoC-Culture – Advancements in computing technology change people’s everyday activities.
    [Show full text]
  • 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
    [Show full text]
  • Can You Keep a Secret?
    Codes and Ciphers 20 Can You Keep a Secret? Codes and ciphers have been around just about as long as there has been written language. The ability to communicate in secret – as well as the ability to peer into the secret communications of others – has been central to a surprising number of major world events throughout history, often with nations as well as lives hanging in the balance. A word first about the difference between a code and a cipher: • A code is a secret language used to disguise the meaning of a message. The simplest form is a “jargon code,” where a particular phrase corresponds to a previously defined message. “The milkman comes in the morning,” for example, could mean “the invasion begins at dawn.” • A cipher conceals what is referred to as a “plaintext” message by substituting (a “substitu- tion cipher”) and/or scrambling (a “transposition cipher”) the letters. As we shall see later, a simple substitution cipher may encrypt the message “Call me tomorrow morning” as “FDO OPH WRP RUU RZP RUQ LQJ.” For our purposes, we will use such general terms as “code,” Cryptography, sometimes called “cryptology,” is “code breaker,” “encryp- tion” and “decryption” to from the Greek, meaning “hidden writing,” and its refer both to codes and ci- use has been documented for over 2,000 years. phers, rather than repeatedly drawing the distinction between the two. Hidden Writing Cryptography, sometimes called “cryptology,” is from the Greek, meaning “hidden writing” and its use has been documented for over 2,000 years. From the beginning, codes have always been of greatest use in matters of war and diplomacy.
    [Show full text]
  • 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).
    [Show full text]
  • Vigenere Cryptography
    Fall 2006 Chris Christensen MAT/CSC 483 Cryptography of the Vigenère Cipher Cryptanalysis is based upon finding the ghosts of patterns of the plaintext. We have seen that an important technique of doing this is frequency analysis. So, cryptographers try to develop ciphers that are not easily attacked by frequency analysis. There are two basic ways to do this: use more than one ciphertext alphabet or encrypt more than one letter in a block. First, we will consider using more than one cipher text alphabet. Simple substitution ciphers, Caesar ciphers, multiplicative ciphers, and affine ciphers are all examples of monoalphabetic ciphers – only one ciphertext alphabet is used. Even if the original word lengths are concealed and the substitution alphabet is random, it is possible to find a solution by using frequency data, repetition patterns and information about the way letters combine with one another. What makes the solution possible is the fact that a given plain language letter is always represented by the same cipher letter. As a consequence, all the properties of plain language such as frequencies and combinations are carried over into the cipher and may be utilized for solution. In effect we could say that all such properties are invariant except that the names of the letters have been changed. It would seem then that one way to obtain greater security would be to use more than one alphabet in enciphering a message. The general system could be one that uses a number of different alphabets for encipherment, with an understanding between correspondents of the order in which the alphabets are to be used.
    [Show full text]
  • Midterm Project - the Alberti Cipher Wheel Spring 2017
    Midterm Project - The Alberti Cipher Wheel Spring 2017 This project should consist of a short written report (about 5 pages) which includes your responses for (1)-(4), (6), (7) plus the physical Alberti wheel and video/photos illustrating its use as described in (6). Include a bibliography of sources you used. The Alberti wheel you will use is illustrated in the figure below and was used with Latin so certain letters are missing. 1. Who was Leon Battista Alberti and when did he live? Why was it so important at the time? Was it used as a monoalphabetic or polyalphabetic cipher? Why? Could it be used as the other type of cipher? (i.e., if you answer monoalphabetic, then could it be used as a polyalphabetic cipher or vis versa) 2. Describe how the Alberti cipher was used. Describe how a pointer character was used, how a key word was used and how the numbers were used to encrypt a shift.. Explain what constitutes a key for the Alberti cipher. How many different starting positions are there? 3. The Alberti cipher disk was made to be used in Latin so certain letters (like \H") are missing. In this case you have to make a decision on how these are going to be encrypted. For example, \H" is often encrypted as \FF". I believe there are six of these letters missing on the outer disk. State how you are going to encrypt them. 4. The Alberti cipher contains four numbers (1,2,3,4) on the outer wheel. If you use the \O" to encrypt zero, then we could encrypt a number using base 5 (recall that for binary numbers we used base 2, i.e., 0 and 1.) What is the number 15 (in our decimal system) in base 5 and how would you encrypt it assuming the wheel is set as in the figure.
    [Show full text]
  • Plaintext, Encryption, Ciphertext: a History of Cryptography and Its Influence on Contemporary Society
    TOC PLAINTEXT, ENCRYPTION, CIPHERTEXT: A HISTORY OF CRYPTOGRAPHY AND ITS INFLUENCE ON CONTEMPORARY SOCIETY QUINN DUPONT PHD DISSERTATION UNIVERSITY OF TORONTO, FACULTY OF INFORMATION CHAPTER 1 “REPRESENTATION” – SUBMISSION TO SIGCIS 2015 DRAFT (PLEASE DO NOT DISTRIBUTE) 1 TOC TABLE OF CONTENTS 1.! Introduction i.! Philological complexity ii.! What do we know of cryptography? iii.! Rewriting three schemata iv.! Chapter summaries Part One: Plaintext 2.! Representation i.! Alberti’s notation ii.! Mimesis and media iii.! Ancient theories of mimesis i.! Plato’s theory of mimesis ii.! Aristotle’s theory of mimesis iv.! Late medieval and renaissance web of resemblances v.! Conventia in memory techniques from Lull to Alberti’s cipher wheel vi.! Aemulatio, analogy, and sympathy in Trithemius’ magical cryptography 3.! Media and notation i.! Francis Bacon’s artifcial languages (1605-1623) i.! Francis Bacon’s bi-literal cipher ii.! Te development of notational schemes (1605-1686) iii.! Notational discourse networks i.! Identity and the alphabet ii.! A theory of notation 4.! Codes and codeworks i.! Agrippa (a book of the dead) i.! Forensic description of Agrippa ii.! Te compiled binary iii.! Te cryptographic algorithm 1.! Encryption efect 2.! Te “self-destruct” mechanism ii.! Bitcoin iii.! Executable software Part Two: Encryption 5.! Media of perception 6.! Communication and transmission 7.! Translation and Transcription 2 TOC Part Tree: Ciphertext 8.! Otherness and order, revealed 9.! Silence 10.! Epilogue i.! Politics: Homogeneity and visibility ii.! Rise of mnenotechnologies iii.! Ubiquitous cryptography 3 PART 1 – PLAINTEXT CHAPTER 2 – REPRESENTATION PLAINTEXT In his seminal work on cryptography De componendis cifris,1 Leon Battista Alberti (1404-1472) diverts from his task of exploring and inventing cryptography systems to recall a time strolling through a garden with his friend Dati.
    [Show full text]
  • CS1132 Fall 2013 Assignment 2 Due 11/21 11:59Pm 1 Cryptography Fun!
    CS1132 Fall 2013 Assignment 2 due 11/21 11:59pm Adhere to the Code of Academic Integrity. You may discuss background issues and general strategies with others and seek help from course staff, but the implementations that you submit must be your own. In particular, you may discuss general ideas with others but you may not work out the detailed solutions with others. It is never OK for you to see or hear another student's code and it is never OK to copy code from published/Internet sources. If you feel that you cannot complete the assignment on you own, seek help from the course staff. When submitting your assignment, follow the instructions summarized in Section 4 of this document. Do not use the break or continue statement in any homework or test in CS1132. 1 Cryptography Fun! Just several decades ago, cryptography existed solely in the domain of national governments and large corporations. However, the advent of the Internet and the wide availability of computers have now made cryptography an indispensable part of everyday digital communications. In this part of the assignment, you will implement one well-known classical ciphers: the Vigenere cipher. This ci- phers predates modern cryptography but nonetheless provide a relevant and insightful look at some commonly used cryptography techniques. You will implement it as MATLAB functions that can be used to encrypt and subsequently decrypt messages. The Vigenre cipher is one of the most well-known ciphers of all time. It is a method of encrypting plaintext using a series of different Caesar ciphers based on the letters of the keyword.
    [Show full text]
  • Nomenclators Nomenclator Example Alberti's Cipher Disk
    Nomenclators Early code/cipher combination, popular form 1400s-1800s. Philip of Spain (1589, see Kahn): LO = Spain POM = King of Spain 64 = confederation overlined two-digit groups = null + substitution cipher with homophones Nomenclator Example Nomenclator used by Mary, Queen of Scots . in 1586 in the plot against Elizabeth I Taken from Simon Singh. The Code Book. Alberti’s Cipher Disk Invented by Leon Battista Alberti in 1460s. outer disk (fixed) plaintext inner disk (moving) ciphertext Agree on index letter on inner disk. Key: letter corresponding to index letter on outer disk. Key can change during encryption 1 Cipher Disk Examples Let’s choose “K” as index letter. Examples: rRVTZOK aKVtTRCK HKmZMEP Since the key can change, this cipher is no longer monoalphabetic, but polyalphabetic. Are there other ways to use the cipher disk? Johannes Trithemius 1462-1516, Germany Polygraphiae, 1518 First printed book on cryptography. • Ave Maria Cipher • Polyalphabetic substitution • Progressive key Steganographia, 1606 • hidden writing http://diglib.hab.de/drucke/12-3-rhet-2f/start.htm Polygraphiae I The Polygraphiae contains many pages of code. 2 Polygraphiae II: Ave Maria 1st and 2nd page Steganographia http://books.google.com/books?id=bQdC AAAAcAAJ&dq=Trithemius%20Stegano graphia&pg=PR6#v=onepage&q&f=false Polygraphiae III Tabula recta, from the 6th book of the Polygraphiae. • Polyalphabetic substitution • Progressive key The history of information security: a comprehensive handbook, de Leeuw, Bergstra 3 Polygraphiae IV Examples (starting with first alphabet) • Johannes • SUGKESUOWSUN The history of information security: a comprehensive handbook, de Leeuw, Bergstra Modern Tabula Recta More Examples (not from beginning) • XNNN • NUGUV http://commons.wikimedia.org/wiki/File:Vigenere-square.png Giovan Batista Belaso La cifra del.
    [Show full text]
  • Decoding Running Key Ciphers
    Decoding Running Key Ciphers Sravana Reddy∗ Kevin Knight Department of Computer Science Information Sciences Institute The University of Chicago University of Southern California 1100 E. 58th Street 4676 Admiralty Way Chicago, IL 60637, USA Marina del Rey, CA 90292, USA [email protected] [email protected] Abstract Since we know that the plaintext and running key are both drawn from natural language, our objective There has been recent interest in the problem function for the solution plaintext under some lan- of decoding letter substitution ciphers using techniques inspired by natural language pro- guage model is: cessing. We consider a different type of classi- ˆ cal encoding scheme known as the running key P = arg max log Pr(P ) Pr(RP,C ) (1) cipher, and propose a search solution using P Gibbs sampling with a word language model. where the running key RP,C is the key that corre- We evaluate our method on synthetic cipher- sponds to plaintext P and ciphertext C. texts of different lengths, and find that it out- Note that if RP,C is a perfectly random sequence performs previous work that employs Viterbi of letters, this scheme is effectively a ‘one-time pad’, decoding with character-based models. which is provably unbreakable (Shannon, 1949). The knowledge that both the plaintext and the key 1 Introduction are natural language strings is important in breaking The running key cipher is an encoding scheme that a running key cipher. uses a secret key R that is typically a string of words, The letter-frequency distribution of running key usually taken from a book or other text that is agreed ciphertexts is notably flatter than than the plaintext upon by the sender and receiver.
    [Show full text]