Principle and Computer Simulation Model of Variation of Delastell's
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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. -
What Is a Cryptosystem?
Cryptography What is a Cryptosystem? • K = {0, 1}l • P = {0, 1}m • C′ = {0, 1}n,C ⊆ C′ • E : P × K → C • D : C × K → P • ∀p ∈ P, k ∈ K : D(E(p, k), k) = p • It is infeasible to find F : P × C → K Let’s start again, in English. Steven M. Bellovin September 13, 2006 1 Cryptography What is a Cryptosystem? A cryptosystem is pair of algorithms that take a key and convert plaintext to ciphertext and back. Plaintext is what you want to protect; ciphertext should appear to be random gibberish. The design and analysis of today’s cryptographic algorithms is highly mathematical. Do not try to design your own algorithms. Steven M. Bellovin September 13, 2006 2 Cryptography A Tiny Bit of History • Encryption goes back thousands of years • Classical ciphers encrypted letters (and perhaps digits), and yielded all sorts of bizarre outputs. • The advent of military telegraphy led to ciphers that produced only letters. Steven M. Bellovin September 13, 2006 3 Cryptography Codes vs. Ciphers • Ciphers operate syntactically, on letters or groups of letters: A → D, B → E, etc. • Codes operate semantically, on words, phrases, or sentences, per this 1910 codebook Steven M. Bellovin September 13, 2006 4 Cryptography A 1910 Commercial Codebook Steven M. Bellovin September 13, 2006 5 Cryptography Commercial Telegraph Codes • Most were aimed at economy • Secrecy from casual snoopers was a useful side-effect, but not the primary motivation • That said, a few such codes were intended for secrecy; I have some in my collection, including one intended for union use Steven M. -
A Covert Encryption Method for Applications in Electronic Data Interchange
Technological University Dublin ARROW@TU Dublin Articles School of Electrical and Electronic Engineering 2009-01-01 A Covert Encryption Method for Applications in Electronic Data Interchange Jonathan Blackledge Technological University Dublin, [email protected] Dmitry Dubovitskiy Oxford Recognition Limited, [email protected] Follow this and additional works at: https://arrow.tudublin.ie/engscheleart2 Part of the Digital Communications and Networking Commons, Numerical Analysis and Computation Commons, and the Software Engineering Commons Recommended Citation Blackledge, J., Dubovitskiy, D.: A Covert Encryption Method for Applications in Electronic Data Interchange. ISAST Journal on Electronics and Signal Processing, vol: 4, issue: 1, pages: 107 -128, 2009. doi:10.21427/D7RS67 This Article is brought to you for free and open access by the School of Electrical and Electronic Engineering at ARROW@TU Dublin. It has been accepted for inclusion in Articles by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License A Covert Encryption Method for Applications in Electronic Data Interchange Jonathan M Blackledge, Fellow, IET, Fellow, BCS and Dmitry A Dubovitskiy, Member IET Abstract— A principal weakness of all encryption systems is to make sure that the ciphertext is relatively strong (but not that the output data can be ‘seen’ to be encrypted. In other too strong!) and that the information extracted is of good words, encrypted data provides a ‘flag’ on the potential value quality in terms of providing the attacker with ‘intelligence’ of the information that has been encrypted. -
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. -
A New Cryptosystem for Ciphers Using Transposition Techniques
Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 8 Issue 04, April-2019 A New Cryptosystem for Ciphers using Transposition Techniques U. Thirupalu Dr. E. Kesavulu Reddy FCSRC (USA) Research Scholar Assistant Professor, Dept. of Computer Science Dept. of Computer Science S V U CM&CS – Tirupati S V U CM&CS - Tirupati India – 517502 India – 517502 Abstract:- Data Encryption techniques is used to avoid the performs the decryption. Cryptographic algorithms are unauthorized access original content of a data in broadly classified as Symmetric key cryptography and communication between two parties, but the data can be Asymmetric key cryptography. recovered only through using a key known as decryption process. The objective of the encryption is to secure or save data from unauthorized access in term of inspecting or A. Symmetric Cryptography adapting the data. Encryption can be implemented occurs by In the symmetric key encryption, same key is used for both using some substitute technique, shifting technique, or encryption and decryption process. Symmetric algorithms mathematical operations. By adapting these techniques we more advantageous with low consuming with more can generate a different form of that data which can be computing power and it works with high speed in encrypt difficult to understand by any person. The original data is them. The symmetric key encryption takes place in two referred to as the plaintext and the encrypted data as the modes either as the block ciphers or as the stream ciphers. cipher text. Several symmetric key base algorithms have been The block cipher mode provides, whole data is divided into developed in the past year. -
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. -
Caesar's Cipher Is a Monoalphabetic
Mathematical summer in Paris - Cryptography Exercise 1 (Caesar’s cipher ?) Caesar’s cipher is a monoalphabetic encryption method where all letters in the alphabet are shifted by a certain constant d. For example, with d = 3, we obtain A ! D; B ! E;:::; Y ! B; Z ! C: 1. Translate the encryption function f in algebraic terms. What is the decryption function g? 2. What is the key in Caesar’s cipher? How many keys are possible? 3. Decrypt the ciphertext LIPPSASVPH. Exercise 2 (Affine encryption ?) We now want to study a more general kind of encryption method, called affine encryption. We represent each letter in the latin alphabet by its position in the alphabet, starting with 0, i.e. A ! 0; B ! 1; C ! 2;:::; Z ! 25; and we consider the map f : x ! ax + b mod 26; where a and b are fixed integers between 0 and 25. We want to use the map f to encrypt each letter in the plaintext. 1. What happens if we choose a = 1? We now choose a = 10 and b = 3. def 2. Let 0 ≤ y ≤ 25 such that y = f(x) = 10x + 3 mod 26. Prove that there exists k 2 Z such that y = 10x + 26k + 3. 3. Prove that y is always odd. 4. What can we say about this encryption method? We now choose a = 9 and b = 4. 5. Find an integer u 2 Z such that 9u = 1 mod 26. 6. Explain why the equation y = 9x + 4 mod 26, with 0 ≤ y ≤ 25, always has a solution. -
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,.. -
A Secure Variant of the Hill Cipher
† A Secure Variant of the Hill Cipher Mohsen Toorani ‡ Abolfazl Falahati Abstract the corresponding key of each block but it has several security problems [7]. The Hill cipher is a classical symmetric encryption In this paper, a secure cryptosystem is introduced that algorithm that succumbs to the know-plaintext attack. overcomes all the security drawbacks of the Hill cipher. Although its vulnerability to cryptanalysis has rendered it The proposed scheme includes an encryption algorithm unusable in practice, it still serves an important that is a variant of the Affine Hill cipher for which a pedagogical role in cryptology and linear algebra. In this secure cryptographic protocol is introduced. The paper, a variant of the Hill cipher is introduced that encryption core of the proposed scheme has the same makes the Hill cipher secure while it retains the structure of the Affine Hill cipher but its internal efficiency. The proposed scheme includes a ciphering manipulations are different from the previously proposed core for which a cryptographic protocol is introduced. cryptosystems. The rest of this paper is organized as follows. Section 2 briefly introduces the Hill cipher. Our 1. Introduction proposed scheme is introduced and its computational costs are evaluated in Section 3, and Section 4 concludes The Hill cipher was invented by L.S. Hill in 1929 [1]. It is the paper. a famous polygram and a classical symmetric cipher based on matrix transformation but it succumbs to the 2. The Hill Cipher known-plaintext attack [2]. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still In the Hill cipher, the ciphertext is obtained from the serves an important pedagogical role in both cryptology plaintext by means of a linear transformation. -
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.