Introduction to Cryptography - 1 CSC4601 F04 Overviewoverview
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Simple Substitution Cipher Evelyn Guo
Simple Substitution Cipher Evelyn Guo Topic: Data Frequency Analysis, Logic Curriculum Competencies: • Develop thinking strategies to solve puzzles and play games • Think creatively and with curiosity and wonder when exploring problems • Apply flexible and strategic approaches to solve problems • Solve problems with persistence and a positive disposition Grade Levels: G3 - G12 Resource: University of Cambridge Millennium Mathematics Project - NRICH https://nrich.maths.org/4957 Cipher Challenge Toolkit https://nrich.maths.org/7983 Practical Cryptography website http://practicalcryptography.com/ciphers/classical-era/simple- substitution/ Materials: Ipad and Laptop which could run excel spreadsheet. Flip Chart with tips and hints for different levels of players Booklet flyers for anyone taking home. Printed coded message and work sheet (help sheet) with plain alphabet and cipher alphabet (leave blank) Pencils Extension: • Depends on individual player’s interest and math abilities, introduce easier (Atbash Cipher, Caesar Cipher) or harder ways ( AutoKey Cipher) to encrypt messages. • Introduce students how to use the practical cryptography website to create their own encrypted message instantly. • Allow players create their own cipher method. • Understand in any language some letters tend to appear more often than other letters Activity Sheet for Substitution Cipher Opening Question: Which Letters do you think are the most common in English? Start by performing a frequency analysis on some selected text to see which letters appear most often. It is better to use longer texts, as a short text might have an unusual distribution of letters, like the "quick brown fox jumps over the lazy dog" Introduce the Problem: In the coded text attached, every letter in the original message was switched with another letter. -
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 -
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. -
DOCUMENT RESUME ED 071 911 SE 015 548 TITLE Project Physics
DOCUMENT RESUME ED 071 911 SE 015 548 TITLE Project Physics Teacher Guide 6, The Nucleus. INSTITUTION Harvard Univ., Cambridge, Mass. Harvard Project Physics. SPONS AGENCY Office of Education (DHEW) Washington, D.C. Bureau of Research. BUREAU NO BR-5-1038 PUB DATE 68 CONTRACT OEC-5-10-058 NOTE 235p.; Authorized Interim Version EDRS PRICE MF-$0.65 HC-S9.87 DESCRIPTORS Instructional Materials; *Multimedia Instruction; *Nuclear Physics; Physics; *Radiation; Science Activities; Secondary Grades; *Secondary School Science; *Teaching Glides; Teaching Procedures IDENTIFIERS Harvard Project Physics ABSTRACT Teaching procedures of Project Physics Unit 6are presented to help teachers make effectiveuse of learning materials. Unit contents are discussed in connection withteaching aid lists, multi-media schedules, schedule blocks, andresource charts. Brief summaries are made for transparencies, 16mm films, and reader articles. Included is information about the backgroundand development of each unit chapter, procedures in demonstrations, apparatus operations, notes on the student handbook, andan explanation of film loops. Additional articlesare concerned with objects dated by radiocarbon, radiation safety, propertiesof radiations, radioactive sources, radioactivity determinationby electroscopes, and radiation detecting devices.Scalers, counters, Geiger tubes, and cadmium selenide photocellsare analyzed; and a bibliography of references is given, Solutionsto the study guide are provided in detail, and answers to test itemsare suggested. The sixth unit of the text, with marginal commentson each section, is also compiled in the manual. The work of Harvard ProjectPhysics has . been financially supported by: the Carnegie Corporation ofNew York, the Ford Foundation, the National Science Foundation,the Alfred P. Sloan Foundation, the United States office of Education,and Harvard University. -
A Complete Bibliography of Publications in Cryptologia
A Complete Bibliography of Publications in Cryptologia Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 04 September 2021 Version 3.64 Title word cross-reference 10016-8810 [?, ?]. 1221 [?]. 125 [?]. 15.00/$23.60.0 [?]. 15th [?, ?]. 16th [?]. 17-18 [?]. 18 [?]. 180-4 [?]. 1812 [?]. 18th (t; m)[?]. (t; n)[?, ?]. $10.00 [?]. $12.00 [?, ?, ?, ?, ?]. 18th-Century [?]. 1930s [?]. [?]. 128 [?]. $139.99 [?]. $15.00 [?]. $16.95 1939 [?]. 1940 [?, ?]. 1940s [?]. 1941 [?]. [?]. $16.96 [?]. $18.95 [?]. $24.00 [?]. 1942 [?]. 1943 [?]. 1945 [?, ?, ?, ?, ?]. $24.00/$34 [?]. $24.95 [?, ?]. $26.95 [?]. 1946 [?, ?]. 1950s [?]. 1970s [?]. 1980s [?]. $29.95 [?]. $30.95 [?]. $39 [?]. $43.39 [?]. 1989 [?]. 19th [?, ?]. $45.00 [?]. $5.95 [?]. $54.00 [?]. $54.95 [?]. $54.99 [?]. $6.50 [?]. $6.95 [?]. $69.00 2 [?, ?]. 200/220 [?]. 2000 [?]. 2004 [?, ?]. [?]. $69.95 [?]. $75.00 [?]. $89.95 [?]. th 2008 [?]. 2009 [?]. 2011 [?]. 2013 [?, ?]. [?]. A [?]. A3 [?, ?]. χ [?]. H [?]. k [?, ?]. M 2014 [?]. 2017 [?]. 2019 [?]. 20755-6886 [?, ?]. M 3 [?]. n [?, ?, ?]. [?]. 209 [?, ?, ?, ?, ?, ?]. 20th [?]. 21 [?]. 22 [?]. 220 [?]. 24-Hour [?, ?, ?]. 25 [?, ?]. -Bit [?]. -out-of- [?, ?]. -tests [?]. 25.00/$39.30 [?]. 25.00/839.30 [?]. 25A1 [?]. 25B [?]. 26 [?, ?]. 28147 [?]. 28147-89 000 [?]. 01Q [?, ?]. [?]. 285 [?]. 294 [?]. 2in [?, ?]. 2nd [?, ?, ?, ?]. 1 [?, ?, ?, ?]. 1-4398-1763-4 [?]. 1/2in [?, ?]. 10 [?]. 100 [?]. 10011-4211 [?]. 3 [?, ?, ?, ?]. 3/4in [?, ?]. 30 [?]. 310 1 2 [?, ?, ?, ?, ?, ?, ?]. 312 [?]. 325 [?]. 3336 [?, ?, ?, ?, ?, ?]. affine [?]. [?]. 35 [?]. 36 [?]. 3rd [?]. Afluisterstation [?, ?]. After [?]. Aftermath [?]. Again [?, ?]. Against 4 [?]. 40 [?]. 44 [?]. 45 [?]. 45th [?]. 47 [?]. [?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?]. Age 4in [?, ?]. [?, ?]. Agencies [?]. Agency [?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?]. -
Traditional Symmetric-Key Ciphers
Traditional Symmetric-Key Ciphers A Biswas, IT, BESU Shibpur General idea of symmetric-key cipher The original message from Alice to Bob is called plaintext; the message that is sent through the channel is called the ciphertext. To create the ciphertext from the plaintext, Alice uses an encryption algorithm and a shared secret key. To create the plaintext from ciphertext, Bob uses a decryption algorithm and the same secret key. If P is the plaintext, C is the ciphertext, and K is the key, We assume that Bob creates P1; we prove that P1 = P: Locking and unlocking with the same key Kerckhoff’s Principle Based on Kerckhoff’s principle, one should always assume that the adversary, Eve, knows the encryption/decryption algorithm. The resistance of the cipher to attack must be based only on the secrecy of the key. Cryptanalysis As cryptography is the science and art of creating secret codes, cryptanalysis is the science and art of breaking those codes. Cryptanalysis attacks Ciphertext-Only Attack Ciphertext-only attack Known-Plaintext Attack Known-plaintext attack Chosen-Plaintext Attack Chosen-plaintext attack Chosen-Ciphertext Attack Chosen-ciphertext attack SUBSTITUTION CIPHERS A substitution cipher replaces one symbol with another. Substitution ciphers can be categorized as either monoalphabetic ciphers or polyalphabetic ciphers. Note A substitution cipher replaces one symbol with another. 1 Monoalphabetic Ciphres 2 Polyalphabetic Ciphers Monoalphabetic Ciphers Note In monoalphabetic substitution, the relationship between a symbol in the plaintext to a symbol in the ciphertext is always one-to-one. Example The following shows a plaintext and its corresponding ciphertext. -
Kryptos: a 29 Year Old Mystery Alfie Baines* — 170180540 [email protected] School of Mathematics, Statistics and Physics Supervisor: Dr Stuart Hall
Kryptos: A 29 year old mystery Alfie Baines* | 170180540 [email protected] School of Mathematics, Statistics and Physics Supervisor: Dr Stuart Hall 1. Aims 3. Frequency analysis 5. Index of coincidence 6. Transposition Cipher H I To automate a majority of the cryptanalysis that has already The index of coincidence (IC) is the I A transposition cipher takes the original been carried out on Kryptos probability that two randomly chosen letters text and creates an anagram of it based on a I To use computing to decipher the final section of Kryptos, known in a block of text are identical. We know regular system or algorithm. as K4 IC ≈ 0:067, and IC ≈ 0:0385 I By taking the text in the green section and english random reversing the order, you can use the following n 1 X key, 1526374, based on the word KRYPTOS, 2. Transcript of Kryptos ciphertext IC = F (F − 1) (3) N(N − 1) i i to decipher the message. i=1 EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJ I The key is obtained as follows: YQTQUXQBQVYUVLLTREVJYQTMKYRDMFD I N is the length of the text K T 1 5 R O 2 6 VFPJUDEEHZWETZYVGWHKKQETGFQJNCE I n is the length of the alphabet = = 1526374 Y S 3 7 I Fi is the frequency of the ith letter in the alphabet GGWHKK?DQMCPFQZDQMMIAGPFXHQRLG P 4 TIMVMZJANQLVKQEDAGDVFRPJUNGEUNA (When read horizontally) QZGZLECGYUXUEENJTBJLBQCRTBJDFHRR I The same method of using columns YIZETKZEMVDUFKSJHKFWHKUWQLSZFTI containing 4 letters and 3 letters is used in HHDDDUVH?DWKBFUFPWNTDFIYCUQZERE the rearrangement of the green section EVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDX during decryption. FLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKF I The similarity between generating a key, and FHQNTGPUAECNUVPDJMQCLQUMUNEDFQ deciphering the text leads to the belief that this may be the intended method of ELZZVRRGKFFVOEEXBDMVPNFQXEZLGRE decryption by the author. -
2.4 the Autokey Cipher and Cribs
Jay Daigle Occidental College Math 400: Cryptology 2.4 The Autokey cipher and cribs 2.4.1 Using a crib One common tool in cryptanalysis is a crib, which is a known or guessed bit of plaintext corresponding to a ciphertext. (The term comes from the phrase \to crib notes" or \to crib an answer", meaning to copy or cheat on an assignment). Often a crib can be used to dramatically simplify cryptanalysis. (In fact, frequency analysis is essentially an attempt to imitate a crib). Cribs were famously used in Bletchley Park during World War II (where the term was coined). Many German Enigma operators used standardized terminology, including the reg- ular use of the word Wetter (\weather") in weather reports, and one operator who repeatedly transmitted the message \Nothing to report". Enigma operators were required to spell out all numbers, so Turing determined that the single most common word in messages was eins, meaning \one". Turing precomputed a catalog of what eins would look like encrypted in every possible position with various keys, which dramatically sped up decryption processes by seeing which of those were possible and judging them most likely. You will notice that this is basically the same idea as frequency analysis: instead of taking common letters, we instead look for common words. eins was not enough to break messages on its own, but it could give substantial speedups and hints for other encryption messages. 2.4.2 Breaking the Autokey cipher Cribs are an especially powerful tool in breaking the Autokey cipher, since the plaintext is also most of the keystream. -
Finishing Polyalphabetics & Demonstrating Transpositions
Finishing polyalphabetics & demonstrating transpositions Recorded lecture for 4/6/20 CS 330 Polyalphabetics & Transpositions HW is out • Due Wednesday night • Write C program to count letter frequencies in English text (ciphertext or plaintext) CS 330 Polyalphabetics & Transpositions Recall: Vigenère Cipher • write the keyword repeatedly (identifies column) • write the plaintext out (identifies row) • Encrypt each letter by writing the value at that row and column key: deceptivedeceptivedeceptive plaintext: wearediscoveredsaveyourself ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ CS 330 Polyalphabetics & Transpositions Recall: Finding the key length using sorted frequencies CS 330 Polyalphabetics & Transpositions 51 CS 330 Polyalphabetics & Transpositions 52 Finding the key length, Part two • we can quantify this by noticing that the best coset signature curves are generally those that are as low as possible on the left and as high as possible on the right. • we can measure this tendency by finding the difference between the area under the curve for the top half (from 14 to 26), minus the area of the curve for the bottom half (from 1 to 13), called Vj CS 330 Polyalphabetics & Transpositions 53 Finding the key length, Part two • The average (Ai) of these differences for all the cosets for a suggested key length L, gives us a value which measures how close we are to the signature of English. • The local maximum of these values for all numbers of coset values is the likely key length. CS 330 Polyalphabetics & Transpositions 54 Algorithm for finding key length: 1. read in the text and the maximum key length to try 2. for every L from 1 to the max key length do 3. -
Substitution Cipher in Cryptography, a Substitution Cipher Is a Method Of
Substitution cipher In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing an inverse substitution. Substitution ciphers can be compared with transposition ciphers. In a transposition cipher, the units of the plaintext are rearranged in a different and usually quite complex order, but the units themselves are left unchanged. By contrast, in a substitution cipher, the units of the plaintext are retained in the same sequence in the ciphertext, but the units themselves are altered. There are a number of different types of substitution cipher. If the cipher operates on single letters, it is termed a simple substitution cipher; a cipher that operates on larger groups of letters is termed polygraphic. A monoalphabetic cipher uses fixed substitution over the entire message, whereas a polyalphabetic cipher uses a number of substitutions at different times in the message, where a unit from the plaintext is mapped to one of several possibilities in the ciphertext and vice-versa. Contents • 1 Simple substitution o 1.1 Examples o 1.2 Security for simple substitution ciphers • 2 Homophonic substitution • 3 Polyalphabetic substitution • 4 Polygraphic substitution • 5 Mechanical substitution ciphers • 6 The one-time pad • 7 Substitution in modern cryptography • 8 Substitution ciphers in popular culture Simple substitution 1 ROT13 is a Caesar cipher, a type of substitution cipher. In ROT13, the alphabet is rotated 13 steps. -
THE CIA KRYPTOS SCULPTURE: a Summary of Previous Work and New Revelations in Working Toward Its Complete Solution By
DOCID: 4145037 CONFIDENTIALHREL TO USA, FVEYH20320108 (U) THE CIA KRYPTOS SCULPTURE: A summary of previous work and new revelations in working toward its complete solution by PL 86-36/50 USC 3605 pprnved or Release v ~-~SA on 9-16-2014. OIA Case .. 65414 CO~:FUltJ;NTIALh'IU;L TO USA, FYEY//20320108 1 DOCID: 4145037 CONFIBENTIALHREL T0 USA, FYEYH26326168 (U//FOUO) Back in 1990, the Central Intelligence Agency's Fine Arts Commission canvassed Washington, DC, area artists, asking for proposals for costs and designs for a sculpture which would be erected in the CIA's new Courtyard outside its cafeteria. The winning sculptor was James Sanborn, and he created a nice little puzzle. It stands about 3 metres (10 feet) tall, and con sists of two curved copper plates standing side-by-side, forming an "S" shape if viewed from above. (U/IFOUC>) Before we look at the cipher on the sculpture, here's what James Sanborn had to say about his creation on November 3, 1990, the day it was dedicated: "The stonework at the entrance and in the courtyard served two functions. First, it creates a natural framework for the project as a whole, and is part of a landscaping scheme designed to recall the natural stone outcropping that existed on the site before the Agency, and that will endure, as do mountains. "Second, the tilted strata tell a story like pages of a document. Inserted between these stone pages is a flat copper sheet through which letters and symbols have been cut. This code, which includes certain ancient ciphers, begins as international morse, and increases in complexity as you move through the piece at the entrance and into the courtyard. -
Raw Notes from Elonka Dunin and John Wilson
Raw notes from Elonka Dunin and John Wilson: X & Q in K3 are/could be quote marks Miniature was missing the extra L, and Sanborn asked about an M when looking at it 2 people have the key to K4 - Jae (S.O.) and Muffin (friend) in Tucson, AZ Muffin has one of the COF's Sanborn says there are about 14 COF's Duck pond slabs were supposed to have Morse also, but he ran out of time The Morse code slabs continue under the rock, so the "T is your position" is actually "What is your position" Scheidt gave a talk to the Kryptos society @ NSA, and went over the math behind the codes of Kryptos Arabic COF was originally translated at an Arabic Language Facility in Falls Church, VA, but Sanborn later found out that they gave him some Islamic propaganda in the mix, so he had the translations checked by people he personally knew. PT on the Arabic was from CIA tradecraft Ed Scheidt already knew Whitfield Diffie Ed Scheidt is the ISO person doing the standardization of various crypto techniques for XML formats Sanborn expressed surprise that we didn't include the rotation of the pool in the 3D modeling Sanborn was harassed by CIA personnel during the CIA installation, saying his work was a "waste of money" Christie'isms: errors in various pulped art pieces Errors in CP were Sanborn'isms Christie was suspended above the pulped pieces in a sling in order to be able to reach the inner letters Gilbert Kinney (original purchaser of Untitled Kryptos Piece) currently lives in NY Sanborn has bunches of docs from the Library of Congress Current location of the large COF-english is in his studio.