H12 Cryptography
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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. -
Simple Substitution and Caesar Ciphers
Spring 2015 Chris Christensen MAT/CSC 483 Simple Substitution Ciphers The art of writing secret messages – intelligible to those who are in possession of the key and unintelligible to all others – has been studied for centuries. The usefulness of such messages, especially in time of war, is obvious; on the other hand, their solution may be a matter of great importance to those from whom the key is concealed. But the romance connected with the subject, the not uncommon desire to discover a secret, and the implied challenge to the ingenuity of all from who it is hidden have attracted to the subject the attention of many to whom its utility is a matter of indifference. Abraham Sinkov In Mathematical Recreations & Essays By W.W. Rouse Ball and H.S.M. Coxeter, c. 1938 We begin our study of cryptology from the romantic point of view – the point of view of someone who has the “not uncommon desire to discover a secret” and someone who takes up the “implied challenged to the ingenuity” that is tossed down by secret writing. We begin with one of the most common classical ciphers: simple substitution. A simple substitution cipher is a method of concealment that replaces each letter of a plaintext message with another letter. Here is the key to a simple substitution cipher: Plaintext letters: abcdefghijklmnopqrstuvwxyz Ciphertext letters: EKMFLGDQVZNTOWYHXUSPAIBRCJ The key gives the correspondence between a plaintext letter and its replacement ciphertext letter. (It is traditional to use small letters for plaintext and capital letters, or small capital letters, for ciphertext. We will not use small capital letters for ciphertext so that plaintext and ciphertext letters will line up vertically.) Using this key, every plaintext letter a would be replaced by ciphertext E, every plaintext letter e by L, etc. -
Cryptography in Modern World
Cryptography in Modern World Julius O. Olwenyi, Aby Tino Thomas, Ayad Barsoum* St. Mary’s University, San Antonio, TX (USA) Emails: [email protected], [email protected], [email protected] Abstract — Cryptography and Encryption have been where a letter in plaintext is simply shifted 3 places down used for secure communication. In the modern world, the alphabet [4,5]. cryptography is a very important tool for protecting information in computer systems. With the invention ABCDEFGHIJKLMNOPQRSTUVWXYZ of the World Wide Web or Internet, computer systems are highly interconnected and accessible from DEFGHIJKLMNOPQRSTUVWXYZABC any part of the world. As more systems get interconnected, more threat actors try to gain access The ciphertext of the plaintext “CRYPTOGRAPHY” will to critical information stored on the network. It is the be “FUBSWRJUASLB” in a Caesar cipher. responsibility of data owners or organizations to keep More recent derivative of Caesar cipher is Rot13 this data securely and encryption is the main tool used which shifts 13 places down the alphabet instead of 3. to secure information. In this paper, we will focus on Rot13 was not all about data protection but it was used on different techniques and its modern application of online forums where members could share inappropriate cryptography. language or nasty jokes without necessarily being Keywords: Cryptography, Encryption, Decryption, Data offensive as it will take those interested in those “jokes’ security, Hybrid Encryption to shift characters 13 spaces to read the message and if not interested you do not need to go through the hassle of converting the cipher. I. INTRODUCTION In the 16th century, the French cryptographer Back in the days, cryptography was not all about Blaise de Vigenere [4,5], developed the first hiding messages or secret communication, but in ancient polyalphabetic substitution basically based on Caesar Egypt, where it began; it was carved into the walls of cipher, but more difficult to crack the cipher text. -
Battle Management Language: History, Employment and NATO Technical Activities
Battle Management Language: History, Employment and NATO Technical Activities Mr. Kevin Galvin Quintec Mountbatten House, Basing View, Basingstoke Hampshire, RG21 4HJ UNITED KINGDOM [email protected] ABSTRACT This paper is one of a coordinated set prepared for a NATO Modelling and Simulation Group Lecture Series in Command and Control – Simulation Interoperability (C2SIM). This paper provides an introduction to the concept and historical use and employment of Battle Management Language as they have developed, and the technical activities that were started to achieve interoperability between digitised command and control and simulation systems. 1.0 INTRODUCTION This paper provides a background to the historical employment and implementation of Battle Management Languages (BML) and the challenges that face the military forces today as they deploy digitised C2 systems and have increasingly used simulation tools to both stimulate the training of commanders and their staffs at all echelons of command. The specific areas covered within this section include the following: • The current problem space. • Historical background to the development and employment of Battle Management Languages (BML) as technology evolved to communicate within military organisations. • The challenges that NATO and nations face in C2SIM interoperation. • Strategy and Policy Statements on interoperability between C2 and simulation systems. • NATO technical activities that have been instigated to examine C2Sim interoperation. 2.0 CURRENT PROBLEM SPACE “Linking sensors, decision makers and weapon systems so that information can be translated into synchronised and overwhelming military effect at optimum tempo” (Lt Gen Sir Robert Fulton, Deputy Chief of Defence Staff, 29th May 2002) Although General Fulton made that statement in 2002 at a time when the concept of network enabled operations was being formulated by the UK and within other nations, the requirement remains extant. -
Elements of Cryptography
Elements Of Cryptography The discussion of computer security issues and threats in the previous chap- ters makes it clear that cryptography provides a solution to many security problems. Without cryptography, the main task of a hacker would be to break into a computer, locate sensitive data, and copy it. Alternatively, the hacker may intercept data sent between computers, analyze it, and help himself to any important or useful “nuggets.” Encrypting sensitive data com- plicates these tasks, because in addition to obtaining the data, the wrongdoer also has to decrypt it. Cryptography is therefore a very useful tool in the hands of security workers, but is not a panacea. Even the strongest cryp- tographic methods cannot prevent a virus from damaging data or deleting files. Similarly, DoS attacks are possible even in environments where all data is encrypted. Because of the importance of cryptography, this chapter provides an introduction to the principles and concepts behind the many encryption al- gorithms used by modern cryptography. More historical and background ma- terial, descriptions of algorithms, and examples, can be found in [Salomon 03] and in the many other texts on cryptography, code breaking, and data hiding that are currently available in libraries, bookstores, and the Internet. Cryptography is the art and science of making data impossible to read. The task of the various encryption methods is to start with plain, readable data (the plaintext) and scramble it so it becomes an unreadable ciphertext. Each encryption method must also specify how the ciphertext can be de- crypted back into the plaintext it came from, and Figure 1 illustrates the relation between plaintext, ciphertext, encryption, and decryption. -
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IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 4, No 2, July 2013 ISSN (Print): 1694-0814 | ISSN (Online): 1694-0784 www.IJCSI.org 89 An Eccentric Scheme for Oblivious Communication Khan Farhan Rafat and Muhammad Sher Department of Computer Science, International Islamic University Islamabad, 44000, Pakistan alphabets and then threading the yarn through these holes Abstract in an order which when detached spelt out letters of hidden Trust is the foremost requirement in any form of communication. message in its correct sequence [3]: Building trust through physical contact, gesture etc. is easy but hard to establish in electronic data communication as one can’t “padielaporsymesarponomeuaspeludynmalpreaxo” be sure of the presence of the intended recipient at the other end. “Ave Maria” is yet another smart method for encoding This necessitated the need to devise and suggest covert schemes secret message where list of distinct words for each unique for oblivious communication that only the intended recipient may alphabet are grouped in a series of Tables. For every unveil. Steganography is one such technique where information alphabet constituting the message, word corresponding to to be sent is seamlessly superimposed on the carrier such that it that letter from the set of Tables gets substituted and easily crosses the information confronting barriers without appeared as innocent rhyme whenever the Tables are used detection. This paper endeavors at evolving a data hiding scheme in sequence. envisaged by Shannon and in adherence to Kerchoff’s principle that hides secret information inside statistically random English Cardano introduced the “Grille System” [4] where every alphabets appearing as cryptogram. -
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 -
Short History Polybius's Square History – Ancient Greece
CRYPTOLOGY : CRYPTOGRAPHY + CRYPTANALYSIS Polybius’s square Polybius, Ancient Greece : communication with torches Cryptology = science of secrecy. How : 12345 encipher a plaintext into a ciphertext to protect its secrecy. 1 abcde The recipient deciphers the ciphertext to recover the plaintext. 2 f g h ij k A cryptanalyst shouldn’t complete a successful cryptanalysis. 3 lmnop 4 qrstu Attacks [6] : 5 vwxyz known ciphertext : access only to the ciphertext • known plaintexts/ciphertexts : known pairs TEXT changed in 44,15,53,44. Characteristics • (plaintext,ciphertext) ; search for the key encoding letters by numbers chosen plaintext : known cipher, chosen cleartexts ; • shorten the alphabet’s size • search for the key encode• a character x over alphabet A in y finite word over B. Polybius square : a,...,z 1,...,5 2. { } ! { } Short history History – ancient Greece J. Stern [8] : 3 ages : 500 BC : scytale of Sparta’s generals craft age : hieroglyph, bible, ..., renaissance, WW2 ! • technical age : complex cipher machines • paradoxical age : PKC • Evolves through maths’ history, computing and cryptanalysis : manual • electro-mechanical • by computer Secret key : diameter of the stick • History – Caesar Goals of cryptology Increasing number of goals : secrecy : an enemy shouldn’t gain access to information • authentication : provides evidence that the message • comes from its claimed sender signature : same as auth but for a third party • minimality : encipher only what is needed. • Change each char by a char 3 positions farther A becomes d, B becomes e... The plaintext TOUTE LA GAULE becomes wrxwh od jdxoh. Why enciphering ? The tools Yesterday : • I for strategic purposes (the enemy shouldn’t be able to read messages) Information Theory : perfect cipher I by the church • Complexity : most of the ciphers just ensure computational I diplomacy • security Computer science : all make use of algorithms • Mathematics : number theory, probability, statistics, Today, with our numerical environment • algebra, algebraic geometry,.. -
Tap Code 1 2 3 4 5 1 a B C D E 2 F G H I J 3 L M N O P 4 Q R S T U 5
Solution to Kryptos 2: Challenge 1 The audio files indicate that the prisoners are communicating with each other by “tapping”. There are two distinct tapping sounds which indicate the two prisoners are exchanging some sort of information back and forth. Furthermore, unlike Morse Code, each audio file is made up of pairs of taps which leads one to believe that each pair of taps corresponds to a word or letter. The longest tapping sequence is five, so if one assumes that each tap-pair corresponds to a pair of integers between 1 and 5, then this code could encipher 25 items – most likely letters. At this point, one could try a frequency analysis to help identify which pairs of integers correspond to which letters. Alternatively, a little research might yield the “tap code” (see e.g. Wikipedia) which has been used by prisoners of war in various conflicts throughout history, most recently Vietnam. It is based on the Polybius square, some of which have slightly different arrangements of the 26 letters placed into 25 cells. Challenge 1 was based on the following key found on Wikipedia: Tap code 1 2 3 4 5 1 A B C D E 2 F G H I J 3 L M N O P 4 Q R S T U 5 V W X Y Z The tap code table This has all letters except “K”, so “C” is used instead. The letter “X” is used to separate sentences. The first audio file begins with the following tap-pairs: (2,4), (4,3), (1,3), (3,4), (5,1), (1,5), (4,2),… which yields the following plaintext: i, s, c, o, v, e, r, … By adding in the likely punctuation, the complete conversation can be decoded: PLAINTEXT Prisoner 1: Is cover intact? Prisoner 2: Yes. -
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. -
Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford ([email protected])
Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford ([email protected]) Smithsonian Institute October 31, 2009 © 2009 Ralph Morelli You are free to reuse and remix this presentation under a creative commons license provided you give credit to the author. http://creativecommons.org/licenses/by/3.0/us/ This presentation was created using Open Office 3.0, free and open source software. http://www.openoffice.org/ Today's Themes • Crypto Cat vs. Mouse: Cryptographer vs. Cryptanalyst • Theoretical security vs. practical security • Implementation, implementation, implementation • The key is security. Part I: Classical Cryptology Basic Terminology Secret Writing Cryptography – making secret messages. Cryptanalysis – breaking secret messages. Cryptology – cryptography and cryptanalysis. Steganography – concealing messages. Cipher Cipher – a method for transforming a message. encipher meet me at six Cipher mmseeieaxtt plaintext ciphertext decipher Code Code – a system in which codewords replace plaintext words or symbols using a codebook. Codebook meet ... 149 me at at 15 146 15 652 six … … me 146 meet 149 … six 652 Types of Cipher Transposition hello Cipher ELOLH (rearrange) 23541 Substitution KHOOR hello Cipher (replace) Plaintext alphabet: 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 Cipher alphabet: 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 Earliest Ciphers Herodotus (484-425 B.C.) Persian War (~480 BC), Demaratus' secret message to the Spartans was hidden under the wax on a wooden tablet (steganography). -
1. History of Cryptography Cryptography (From Greek , Hidden
1. History of cryptography Cryptography (from Greek , hidden, and , writing), is the practice and study of secret writing(or hidden information). Before the modern era, cryptography was concerned solely with message confidentiality (i.e., encryption) — conversion of messages from a comprehensible form into an incomprehensible one and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely the key needed for decryption of that message). History is filled with examples where people tried to keep information secret from adversaries. Kings and generals communicated with their troops using basic cryptographic methods to prevent the enemy from learning sensitive military information. In fact, Julius Caesar reportedly used a simple cipher, which has been named after him. As society has evolved, the need for more sophisticated methods of protecting data has increased. As the word becomes more connected, the demand for information and electronic services is growing, and with the increased demand comes increased dependency on electronic systems. Already the exchange of sensitive information, such as credit card numbers, over the internet is common practice. Protecting data and electronic system is crucial to our way of living. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs and secure computation, among others. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering. It is necessary to distinct cryptography, crypto analysis and cryptology. Cryptography is a branch of cryptology dealing with the design of system for encryption and decryption intended to ensure confidentiality, integrity and authenticity of message.