DOCSLIB.ORG

ECE 646 – Fall 2010 Multiple-Choice Test

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

ECE 646 – Fall 2010 Multiple-choice test 1. (0.5 pt) Arrange the following ciphers in the order of the increasing measure of roughness for the ciphertext obtained by encrypting 1000-letter message with a given cipher (start from the cipher giving the smallest value of the measure of roughness; group together, using an “=” sign, ciphers for which the measure of roughness is the same or very close to each other, e.g. A=B=C, D, E=F, G) A. running key cipher B. transposition cipher C. general monoalphabetic cipher D. shift cipher E. Enigma F. Vigenère cipher with the period d=5 G. general polyalphabetic cipher with the period d=3 H. letter-based Vernam cipher with the encryption described by the equation ci = mi + ki mod 26, where mi is a code of the plaintext letter, ci is a code of the ciphertext letter, and ki is a code of the keystream letter; the keystream is generated at random and can be used only once. 2. (0.5 pt) In the ciphertext obtained using the Vigenère cipher, a four-character sequence RFW appears at positions 31, 136, and 283. Additionally, the index of coincidence for this ciphertext is equal to 0.044. Based on this information, the most likely period of the Vigenère cipher is: A. 2 B. 3 C. 4 D. 6 E. 7 F. 9 G. 21 3. (0.5 pt) Select an attack type which is the most efficient against a Playfair cipher A. Kasiski’s method B. linear cryptanalysis C. frequency analysis of single ciphertext characters D. method of index of coincidence E. frequency analysis of ciphertext digrams F. exhaustive key search 4. (0.5 pt) The major weaknesses of the inverse CBC mode of DES, for which encryption transformation is given below are that (more than one answer may be correct): A. decryption is not possible B. IV must be kept secret C. encryption is more time consuming than decryption D. encryption cannot be parallelized E. the same plaintext block is always encrypted to the same ciphertext block F. the mode is not suitable for a fast random read access to the block mj G. exhaustive key search is easier to mount than in the ECB mode H. analysis of the ciphertext may reveal patterns (e.g., repeating blocks) in the plaintext I. decryption circuit takes more area than the encryption circuit 5. (0.5 pt) Match the following ciphers with the number of different round keys they use during encryption A. DESX B. Triple DES with two keys K1 and K2 C. IDEA D. RC5 32/12/16 E. RC5 64/26/32 a. 52 b. 26 c. 16 d. 54 e. 32 6. (0.5 pt) Divide the following transformations performed when exchanging a signed only message using PGP, into those A. performed only on the sender’s side B. performed only on the receiver’s side C. performed on both sides D. not performed at either side Transformations: a. generating a random session key b. accessing a private key ring c. decompression using ZIP algorithm d. generating hash value of a message e. accessing a public key ring f. public key transformation determined by a private key of the receiver g. public key transformation determined by a private key of the sender h. verifying certificate of the sender Short problems 1. (3 pts) Break the affine cipher (i.e., find the key (k1, k2)) based on the knowledge that the cipher encrypts “R” to “I”, and “H” to “C”. Using the obtained key, decrypt the ciphertext: “RFP”. 2. (3 pts) Encrypt the message "BIRDS OF A FEATHER FLOCK TOGETHER" using the Vigenère cipher with the key "ORNITHOLOGIST". Compute the index of coincidence of the obtained ciphertext (you do not have to reduce it to a single number, but you need to replace variables in the I.C. equation with actual numbers). Can the period of this cipher be determined using the Kasiski’s method based on the obtained ciphertext? If so, how? 3. (3 pts) What is the output from the first subround of IDEA (half of the first round) for the following values of inputs and internal keys. X1 = 0010, K1 = 1234 X2 = ABCD, K2 = 5433 X3 = 1234, K3 = 5678 X4 = FFFE, K4 = 0000 Hint: Note that all values can be computed without using a calculator by using the following formula: ab mod (216+1) = ab mod 216 – ab div 216 (mod 216+1) 4. (3 pts) Suppose the DES Mangler function F mapped every 32-bit input R, regardless of the value of the 48-bit input K, to a) 32-bit string of ones, b) bitwise complement of R. What would be the expression for R16L16 as a function of L0R0 during encryption? What would be the expression for L0R0 as a function of R16L16 during decryption? Hint: You can use the following properties of the xor operation: (A xor B) xor C = A xor (B xor C) A xor A = 0 A xor 0 = A A xor 1 = bitwise complement of A where A, B, C are n-bit strings of bits 0 is an n-bit string of zeros 1 is an n-bit string of ones 5. (3 pt) What is a result of decryption using RC5-16/1/8 (ONE round, word size w=16) for the ciphertext C=AB (where A, B are 16-bit words) assuming the following contents of the internal key array (all in hexadecimal notation): S[0]=0012, S[1]=0123, S[2]=1234, S[3]=2345, A=9ABC, B=ABCD. .
Recommended publications
  • Amy Bell Abilene, TX December 2005

    Amy Bell Abilene, TX December 2005

    Compositional Cryptology Thesis Presented to the Honors Committee of McMurry University In partial fulfillment of the requirements for Undergraduate Honors in Math By Amy Bell Abilene, TX December 2005 i ii Acknowledgements I could not have completed this thesis without all the support of my professors, family, and friends. Dr. McCoun especially deserves many thanks for helping me to develop the idea of compositional cryptology and for all the countless hours spent discussing new ideas and ways to expand my thesis. Because of his persistence and dedication, I was able to learn and go deeper into the subject matter than I ever expected. My committee members, Dr. Rittenhouse and Dr. Thornburg were also extremely helpful in giving me great advice for presenting my thesis. I also want to thank my family for always supporting me through everything. Without their love and encouragement I would never have been able to complete my thesis. Thanks also should go to my wonderful roommates who helped to keep me motivated during the final stressful months of my thesis. I especially want to thank my fiancé, Gian Falco, who has always believed in me and given me so much love and support throughout my college career. There are many more professors, coaches, and friends that I want to thank not only for encouraging me with my thesis, but also for helping me through all my pursuits at school. Thank you to all of my McMurry family! iii Preface The goal of this research was to gain a deeper understanding of some existing cryptosystems, to implement these cryptosystems in a computer programming language of my choice, and to discover whether the composition of cryptosystems leads to greater security.
  • Codebusters Coaches Institute Notes

    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.
  • Historical Ciphers • A

    Historical Ciphers • A

    ECE 646 - Lecture 6 Required Reading • W. Stallings, Cryptography and Network Security, Chapter 2, Classical Encryption Techniques Historical Ciphers • A. Menezes et al., Handbook of Applied Cryptography, Chapter 7.3 Classical ciphers and historical development Why (not) to study historical ciphers? Secret Writing AGAINST FOR Steganography Cryptography (hidden messages) (encrypted messages) Not similar to Basic components became modern ciphers a part of modern ciphers Under special circumstances modern ciphers can be Substitution Transposition Long abandoned Ciphers reduced to historical ciphers Transformations (change the order Influence on world events of letters) Codes Substitution The only ciphers you Ciphers can break! (replace words) (replace letters) Selected world events affected by cryptology Mary, Queen of Scots 1586 - trial of Mary Queen of Scots - substitution cipher • Scottish Queen, a cousin of Elisabeth I of England • Forced to flee Scotland by uprising against 1917 - Zimmermann telegram, America enters World War I her and her husband • Treated as a candidate to the throne of England by many British Catholics unhappy about 1939-1945 Battle of England, Battle of Atlantic, D-day - a reign of Elisabeth I, a Protestant ENIGMA machine cipher • Imprisoned by Elisabeth for 19 years • Involved in several plots to assassinate Elisabeth 1944 – world’s first computer, Colossus - • Put on trial for treason by a court of about German Lorenz machine cipher 40 noblemen, including Catholics, after being implicated in the Babington Plot by her own 1950s – operation Venona – breaking ciphers of soviet spies letters sent from prison to her co-conspirators stealing secrets of the U.S. atomic bomb in the encrypted form – one-time pad 1 Mary, Queen of Scots – cont.
  • The Mathemathics of Secrets.Pdf

    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
  • Index-Of-Coincidence.Pdf

    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.
  • A Hybrid Cryptosystem Based on Vigenère Cipher and Columnar Transposition Cipher

    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.
  • Shift Cipher Substitution Cipher Vigenère Cipher Hill Cipher

    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.
  • Classic Crypto

    Classic Crypto

    Classic Crypto Classic Crypto 1 Overview We briefly consider the following classic (pen and paper) ciphers o Transposition ciphers o Substitution ciphers o One-time pad o Codebook These were all chosen for a reason o We see same principles in modern ciphers Classic Crypto 2 Transposition Ciphers In transposition ciphers, we transpose (scramble) the plaintext letters o The scrambled text is the ciphertext o The transposition is the key Corresponds to Shannon’s principle of diffusion (more about this later) o This idea is widely used in modern ciphers Classic Crypto 3 Scytale Spartans, circa 500 BC Wind strip of leather around a rod Write message across the rod T H E T I M E H A S C O M E T H E W A L R U S S A I D T O T A L K O F M A N Y T H I N G S When unwrapped, letters are scrambled TSATAHCLONEORTYTMUATIESLHMTS… Classic Crypto 4 Scytale Suppose Alice and Bob use Scytale to encrypt a message o What is the key? o How hard is it for Trudy to break without key? Suppose many different rod diameters are available to Alice and Bob… o How hard is it for Trudy to break a message? o Can Trudy attack messages automatically—without manually examining each putative decrypt? Classic Crypto 5 Columnar Transposition Put plaintext into rows of matrix then read ciphertext out of columns For example, suppose matrix is 3 x 4 o Plaintext: SEETHELIGHT o Ciphertext: SHGEEHELTTIX Same effect as Scytale o What is the key? Classic Crypto 6 Keyword Columnar Transposition For example o Plaintext: CRYPTOISFUN o Matrix 3 x 4 and keyword MATH o Ciphertext:
  • Decrypt Cryptotexts: GBLVMUB JOGPSNBUJLZ VMNIR RPNBMZ EBMFLP OFABKEFT Decrypt: VHFUHW GH GHXA VHFUHW GH GLHX, VHFUHW GH WURLV VH

    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

    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).
  • ISA 562 Information Security Theory & Practice

    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 .

  • Cryptanalysis of a Vigenère

    Security of Networks 2011- 2012 (10) Cryptanalysis of a Vigenère: A Vigenère cipher can be broken using the techniques of breaking a shift cipher as soon as the length of the keyword is known. This is because each repeat of a letter in the keyword corresponds to a single shift cipher. There are two ways to determine the keylength. Kasiski Test (1863 - Major F.W. Kasiski, German cryptologist): Length of keyword is a divisor of the gcd of the distances between identical strings of length at least 3. Friedman Test (1925, Colonel William Frederick Friedman (1891-1969)) also called the Kappa Test: The index of coincidence of a message is the probability that a randomly chosen pair of letters in the message are equal. If the message has length th n and ni denotes the number of occurrences of the i letter then the index, denoted by I, is given by: Now we can also calculate this index for any language source if we know the probabilities of occurrence of each of the letters. Thus, if pa is the probability of occurrence of the letter a, for example, then we get: Using our knowledge of these probabilities we can easily calculate that IEnglish ~ 0.065 and if we had a random source of English letters then IRandom ~ 0.038 (= 1/26). This index can give information about a message. For instance, if a ciphered message was either a transposition or a monoalphabetic substitution then one would expect to have IMessage ~ IEnglish , but if a polyalphabetic substitution was used then this value should decrease (but Dr.