Week 3: Block ciphers
|
|
- Amberlynn Oliver
- 5 years ago
- Views:
Transcription
1 Week 3: Block ciphers Jay Daigle Occidental College September 13, 2018 Jay Daigle (Occidental College) Week 3: September 13, / 12
2 Jay Daigle (Occidental College) Week 3: September 13, / 12
3 Definition A block cipher encrypts fixed-sized blocks of ciphertext, rather than single letters at a time. Jay Daigle (Occidental College) Week 3: September 13, / 12
4 Permutation ciphers Jay Daigle (Occidental College) Week 3: September 13, / 12
5 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. Jay Daigle (Occidental College) Week 3: September 13, / 12
6 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. To encrypt, we break our plaintext into blocks of size n, padding the final block with nonsense characters if necessary. Then we permute each block according to the key k. Jay Daigle (Occidental College) Week 3: September 13, / 12
7 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. To encrypt, we break our plaintext into blocks of size n, padding the final block with nonsense characters if necessary. Then we permute each block according to the key k. To decrypt, we take the inverse permutation k 1 and apply this to each ciphertext block. Jay Daigle (Occidental College) Week 3: September 13, / 12
8 Permutation ciphers Jay Daigle (Occidental College) Week 3: September 13, / 12
9 Permutation ciphers Fourscore and seven years ago Jay Daigle (Occidental College) Week 3: September 13, / 12
10 Permutation ciphers Fourscore and seven years ago Block size five Jay Daigle (Occidental College) Week 3: September 13, / 12
11 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). Jay Daigle (Occidental College) Week 3: September 13, / 12
12 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago Jay Daigle (Occidental College) Week 3: September 13, / 12
13 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
14 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
15 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
16 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
17 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
18 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
19 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU ECOAR ENDVS EENAY GRSOA. Jay Daigle (Occidental College) Week 3: September 13, / 12
20 Modular Arithmetic and Matrices Jay Daigle (Occidental College) Week 3: September 13, / 12
21 Modular Arithmetic and Matrices [ ] 1 ( [ ]) 1 [ ] a b a b d b = det = c d c d c a 1 ad bc [ d b c a ]. Jay Daigle (Occidental College) Week 3: September 13, / 12
22 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
23 The Hill Cipher Lester Hill s patented cipher machine Jay Daigle (Occidental College) Week 3: September 13, / 12
24 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
25 The Hill Cipher Hill Cipher We first choose a block size n. We choose a key, which is a n n matrix K with entries in Z/26Z (that is, integers modulo 26). We require that gcd(26, det K) = 1. We divide our message into blocks of length n. We write each plaintext block as a column vector B (Z/26Z) n. The corresponding ciphertext block is given by KB. To decrypt, we compute K 1 in Z/26Z. Given a ciphertext block C, the corresponding plaintext block is K 1 C. Jay Daigle (Occidental College) Week 3: September 13, / 12
26 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
27 The Hill Cipher It was a dark and stormy night. Jay Daigle (Occidental College) Week 3: September 13, / 12
28 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT Jay Daigle (Occidental College) Week 3: September 13, / 12
29 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT Jay Daigle (Occidental College) Week 3: September 13, / 12
30 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT K [ ] 8 = 19 [ ] [ ] 17 0 Jay Daigle (Occidental College) Week 3: September 13, / 12
31 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT K [ ] 8 = 19 [ ] [ ] 17 0 K [ ] [ ] = [ ] 14 6 Jay Daigle (Occidental College) Week 3: September 13, / 12
32 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = K [ ] [ ] = [ ] 14 6 Jay Daigle (Occidental College) Week 3: September 13, / 12
33 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = Jay Daigle (Occidental College) Week 3: September 13, / 12
34 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = Jay Daigle (Occidental College) Week 3: September 13, / 12
35 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = RA OG CM JP JA NA BZ TT LF HQ EA OV Jay Daigle (Occidental College) Week 3: September 13, / 12
36 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
37 The Hill Cipher how are you today Jay Daigle (Occidental College) Week 3: September 13, / 12
38 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
39 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
40 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
41 Diffusion and Confusion Jay Daigle (Occidental College) Week 3: September 13, / 12
42 Diffusion and Confusion Claude Shannon Picture CC BY-SA 2.0 de by Konrad Jacobs Jay Daigle (Occidental College) Week 3: September 13, / 12
43 Diffusion and Confusion Jay Daigle (Occidental College) Week 3: September 13, / 12
44 Diffusion and Confusion Definition An encryption method has good diffusion if changing one character of the plaintext changes several characters of the ciphertext, and vice versa. Jay Daigle (Occidental College) Week 3: September 13, / 12
45 Diffusion and Confusion Definition An encryption method has good diffusion if changing one character of the plaintext changes several characters of the ciphertext, and vice versa. Definition An encryption method has good confusion if the key does not relate straightforwardly to the ciphertext, but each part of the ciphertext depends on many parts of the key. Jay Daigle (Occidental College) Week 3: September 13, / 12
Example Enemy agents are trying to invent a new type of cipher. They decide on the following encryption scheme: Plaintext converts to Ciphertext
Cryptography Codes Lecture 4: The Times Cipher, Factors, Zero Divisors, and Multiplicative Inverses Spring 2014 Morgan Schreffler Office: POT 902 http://www.ms.uky.edu/~mschreffler New Cipher Times Enemy
More informationExample Enemy agents are trying to invent a new type of cipher. They decide on the following encryption scheme: Plaintext converts to Ciphertext
Cryptography Codes Lecture 3: The Times Cipher, Factors, Zero Divisors, and Multiplicative Inverses Spring 2015 Morgan Schreffler Office: POT 902 http://www.ms.uky.edu/~mschreffler New Cipher Times Enemy
More informationDUBLIN CITY UNIVERSITY
DUBLIN CITY UNIVERSITY SEMESTER ONE EXAMINATIONS 2013 MODULE: (Title & Code) CA642 Cryptography and Number Theory COURSE: M.Sc. in Security and Forensic Computing YEAR: 1 EXAMINERS: (Including Telephone
More informationClassical Cryptography
Classical Cryptography CS 6750 Lecture 1 September 10, 2009 Riccardo Pucella Goals of Classical Cryptography Alice wants to send message X to Bob Oscar is on the wire, listening to all communications Alice
More informationB. Substitution Ciphers, continued. 3. Polyalphabetic: Use multiple maps from the plaintext alphabet to the ciphertext alphabet.
B. Substitution Ciphers, continued 3. Polyalphabetic: Use multiple maps from the plaintext alphabet to the ciphertext alphabet. Non-periodic case: Running key substitution ciphers use a known text (in
More informationCryptography. Module in Autumn Term 2016 University of Birmingham. Lecturers: Mark D. Ryan and David Galindo
Lecturers: Mark D. Ryan and David Galindo. Cryptography 2017. Slide: 1 Cryptography Module in Autumn Term 2016 University of Birmingham Lecturers: Mark D. Ryan and David Galindo Slides originally written
More informationPublic Key Cryptography Great Ideas in Theoretical Computer Science Saarland University, Summer 2014
7 Public Key Cryptography Great Ideas in Theoretical Computer Science Saarland University, Summer 2014 Cryptography studies techniques for secure communication in the presence of third parties. A typical
More informationChapter 4 The Data Encryption Standard
Chapter 4 The Data Encryption Standard History of DES Most widely used encryption scheme is based on DES adopted by National Bureau of Standards (now National Institute of Standards and Technology) in
More informationCPSC 467: Cryptography and Computer Security
CPSC 467: Cryptography and Computer Security Michael J. Fischer Lecture 5b September 11, 2013 CPSC 467, Lecture 5b 1/11 Stream ciphers CPSC 467, Lecture 5b 2/11 Manual stream ciphers Classical stream ciphers
More informationMath 1111 Math Exam Study Guide
Math 1111 Math Exam Study Guide The math exam will cover the mathematical concepts and techniques we ve explored this semester. The exam will not involve any codebreaking, although some questions on the
More informationNetwork Security: Secret Key Cryptography
1 Network Security: Secret Key Cryptography Henning Schulzrinne Columbia University, New York schulzrinne@cs.columbia.edu Columbia University, Fall 2000 cfl1999-2000, Henning Schulzrinne Last modified
More informationEE 418 Network Security and Cryptography Lecture #3
EE 418 Network Security and Cryptography Lecture #3 October 6, 2016 Classical cryptosystems. Lecture notes prepared by Professor Radha Poovendran. Tamara Bonaci Department of Electrical Engineering University
More informationSecret Key Systems (block encoding) Encrypting a small block of text (say 128 bits) General considerations for cipher design:
Secret Key Systems (block encoding) Encrypting a small block of text (say 128 bits) General considerations for cipher design: Secret Key Systems (block encoding) Encrypting a small block of text (say 128
More informationData security (Cryptography) exercise book
University of Debrecen Faculty of Informatics Data security (Cryptography) exercise book 1 Contents 1 RSA 4 1.1 RSA in general.................................. 4 1.2 RSA background.................................
More informationClassification of Ciphers
Classification of Ciphers A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Technology by Pooja Maheshwari to the Department of Computer Science & Engineering Indian
More informationDiscrete Mathematics & Mathematical Reasoning Multiplicative Inverses and Some Cryptography
Discrete Mathematics & Mathematical Reasoning Multiplicative Inverses and Some Cryptography Colin Stirling Informatics Some slides based on ones by Myrto Arapinis Colin Stirling (Informatics) Discrete
More informationTMA4155 Cryptography, Intro
Trondheim, December 12, 2006. TMA4155 Cryptography, Intro 2006-12-02 Problem 1 a. We need to find an inverse of 403 modulo (19 1)(31 1) = 540: 540 = 1 403 + 137 = 17 403 50 540 + 50 403 = 67 403 50 540
More informationDrill Time: Remainders from Long Division
Drill Time: Remainders from Long Division Example (Drill Time: Remainders from Long Division) Get some practice finding remainders. Use your calculator (if you want) then check your answers with a neighbor.
More informationLecture 32. Handout or Document Camera or Class Exercise. Which of the following is equal to [53] [5] 1 in Z 7? (Do not use a calculator.
Lecture 32 Instructor s Comments: This is a make up lecture. You can choose to cover many extra problems if you wish or head towards cryptography. I will probably include the square and multiply algorithm
More informationSuccessful Implementation of the Hill and Magic Square Ciphers: A New Direction
Successful Implementation of the Hill and Magic Square Ciphers: A New Direction ISSN:319-7900 Tomba I. : Dept. of Mathematics, Manipur University, Imphal, Manipur (INDIA) Shibiraj N, : Research Scholar
More informationBlock Ciphers Security of block ciphers. Symmetric Ciphers
Lecturers: Mark D. Ryan and David Galindo. Cryptography 2016. Slide: 26 Assume encryption and decryption use the same key. Will discuss how to distribute key to all parties later Symmetric ciphers unusable
More informationCRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK CIPHER
CRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK CIPHER P.Sundarayya 1, M.M.Sandeep Kumar 2, M.G.Vara Prasad 3 1,2 Department of Mathematics, GITAM, University, (India) 3 Department
More informationChallenge 2. uzs yfr uvjf kay btoh abkqhb khgb tv hbk lk t tv bg akwv obgr
Challenge 2 Solution uzs yfr uvjf kay btoh abkqhb khgb tv hbk lk t tv bg akwv obgr muc utb gkzt qn he hint "the cipher method used can be found by reading the first part of the ciphertext" suggests that
More informationDr. V.U.K.Sastry Professor (CSE Dept), Dean (R&D) SreeNidhi Institute of Science & Technology, SNIST Hyderabad, India. P = [ p
Vol., No., A Block Cipher Involving a Key Bunch Matrix and an Additional Key Matrix, Supplemented with XOR Operation and Supported by Key-Based Permutation and Substitution Dr. V.U.K.Sastry Professor (CSE
More informationLinear Congruences. The solutions to a linear congruence ax b (mod m) are all integers x that satisfy the congruence.
Section 4.4 Linear Congruences Definition: A congruence of the form ax b (mod m), where m is a positive integer, a and b are integers, and x is a variable, is called a linear congruence. The solutions
More informationFermat s little theorem. RSA.
.. Computing large numbers modulo n (a) In modulo arithmetic, you can always reduce a large number to its remainder a a rem n (mod n). (b) Addition, subtraction, and multiplication preserve congruence:
More informationCryptography CS 555. Topic 20: Other Public Key Encryption Schemes. CS555 Topic 20 1
Cryptography CS 555 Topic 20: Other Public Key Encryption Schemes Topic 20 1 Outline and Readings Outline Quadratic Residue Rabin encryption Goldwasser-Micali Commutative encryption Homomorphic encryption
More informationThe number theory behind cryptography
The University of Vermont May 16, 2017 What is cryptography? Cryptography is the practice and study of techniques for secure communication in the presence of adverse third parties. What is cryptography?
More informationA Secure Image Encryption Algorithm Based on Hill Cipher System
Buletin Teknik Elektro dan Informatika (Bulletin of Electrical Engineering and Informatics) Vol.1, No.1, March 212, pp. 51~6 ISSN: 289-3191 51 A Secure Image Encryption Algorithm Based on Hill Cipher System
More informationChapter 4 MASK Encryption: Results with Image Analysis
95 Chapter 4 MASK Encryption: Results with Image Analysis This chapter discusses the tests conducted and analysis made on MASK encryption, with gray scale and colour images. Statistical analysis including
More informationOverview. The Big Picture... CSC 580 Cryptography and Computer Security. January 25, Math Basics for Cryptography
CSC 580 Cryptography and Computer Security Math Basics for Cryptography January 25, 2018 Overview Today: Math basics (Sections 2.1-2.3) To do before Tuesday: Complete HW1 problems Read Sections 3.1, 3.2
More informationMA 111, Topic 2: Cryptography
MA 111, Topic 2: Cryptography Our next topic is something called Cryptography, the mathematics of making and breaking Codes! In the most general sense, Cryptography is the mathematical ideas behind changing
More informationMath 1111 Math Exam Study Guide
Math 1111 Math Exam Study Guide The math exam will cover the mathematical concepts and techniques we ve explored this semester. The exam will not involve any codebreaking, although some questions on the
More informationEE 418: Network Security and Cryptography
EE 418: Network Security and Cryptography Homework 3 Solutions Assigned: Wednesday, November 2, 2016, Due: Thursday, November 10, 2016 Instructor: Tamara Bonaci Department of Electrical Engineering University
More informationPublic-Key Cryptosystem Based on Composite Degree Residuosity Classes. Paillier Cryptosystem. Harmeet Singh
Public-Key Cryptosystem Based on Composite Degree Residuosity Classes aka Paillier Cryptosystem Harmeet Singh Harmeet Singh Winter 2018 1 / 26 Background s Background Foundation of public-key encryption
More informationPurple. Used by Japanese government. Not used for tactical military info. Used to send infamous 14-part message
Purple Purple 1 Purple Used by Japanese government o Diplomatic communications o Named for color of binder cryptanalysts used o Other Japanese ciphers: Red, Coral, Jade, etc. Not used for tactical military
More informationIntroduction to Modular Arithmetic
1 Integers modulo n 1.1 Preliminaries Introduction to Modular Arithmetic Definition 1.1.1 (Equivalence relation). Let R be a relation on the set A. Recall that a relation R is a subset of the cartesian
More informationCryptography Lecture 1: Remainders and Modular Arithmetic Spring 2014 Morgan Schreffler Office: POT 902
Cryptography Lecture 1: Remainders and Modular Arithmetic Spring 2014 Morgan Schreffler Office: POT 902 http://www.ms.uky.edu/~mschreffler Topic Idea: Cryptography Our next topic is something called Cryptography,
More information1 Introduction to Cryptology
U R a Scientist (CWSF-ESPC 2017) Mathematics and Cryptology Patrick Maidorn and Michael Kozdron (Department of Mathematics & Statistics) 1 Introduction to Cryptology While the phrase making and breaking
More informationCryptography, Number Theory, and RSA
Cryptography, Number Theory, and RSA Joan Boyar, IMADA, University of Southern Denmark November 2015 Outline Symmetric key cryptography Public key cryptography Introduction to number theory RSA Modular
More informationGeneration of AES Key Dependent S-Boxes using RC4 Algorithm
3 th International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 3, May 26 28, 29, E-Mail: asat@mtc.edu.eg Military Technical College, Kory Elkoah, Cairo, Egypt Tel : +(22) 2425292 243638,
More informationDUBLIN CITY UNIVERSITY
DUBLIN CITY UNIVERSITY SEMESTER ONE EXAMINATIONS 2013/2014 MODULE: CA642/A Cryptography and Number Theory PROGRAMME(S): MSSF MCM ECSA ECSAO MSc in Security & Forensic Computing M.Sc. in Computing Study
More informationJOINT BINARY CODE COMPRESSION AND ENCRYPTION
JOINT BINARY CODE COMPRESSION AND ENCRYPTION Prof. Atul S. Joshi 1, Dr. Prashant R. Deshmukh 2, Prof. Aditi Joshi 3 1 Associate Professor, Department of Electronics and Telecommunication Engineering,Sipna
More informationIntroduction to Cryptography
B504 / I538: Introduction to Cryptography Spring 2017 Lecture 10 Assignment 2 is due on Tuesday! 1 Recall: Pseudorandom generator (PRG) Defⁿ: A (fixed-length) pseudorandom generator (PRG) with expansion
More informationCS1800 Discrete Structures Fall 2016 Profs. Aslam, Gold, Ossowski, Pavlu, & Sprague 7 November, CS1800 Discrete Structures Midterm Version C
CS1800 Discrete Structures Fall 2016 Profs. Aslam, Gold, Ossowski, Pavlu, & Sprague 7 November, 2016 CS1800 Discrete Structures Midterm Version C Instructions: 1. The exam is closed book and closed notes.
More informationLecture 1: Introduction
Lecture 1: Introduction Instructor: Omkant Pandey Spring 2018 (CSE390) Instructor: Omkant Pandey Lecture 1: Introduction Spring 2018 (CSE390) 1 / 13 Cryptography Most of us rely on cryptography everyday
More informationOFDM Based Low Power Secured Communication using AES with Vedic Mathematics Technique for Military Applications
OFDM Based Low Power Secured Communication using AES with Vedic Mathematics Technique for Military Applications Elakkiya.V 1, Sharmila.S 2, Swathi Priya A.S 3, Vinodha.K 4 1,2,3,4 Department of Electronics
More informationStream Ciphers And Pseudorandomness Revisited. Table of contents
Stream Ciphers And Pseudorandomness Revisited Foundations of Cryptography Computer Science Department Wellesley College Fall 2016 Table of contents Introduction Stream Ciphers Stream ciphers & pseudorandom
More informationMath 412: Number Theory Lecture 6: congruence system and
Math 412: Number Theory Lecture 6: congruence system and classes Gexin Yu gyu@wm.edu College of William and Mary Chinese Remainder Theorem Chinese Remainder Theorem: let m 1, m 2,..., m k be pairwise coprimes.
More informationImage permutation scheme based on modified Logistic mapping
0 International Conference on Information Management and Engineering (ICIME 0) IPCSIT vol. 5 (0) (0) IACSIT Press, Singapore DOI: 0.7763/IPCSIT.0.V5.54 Image permutation scheme based on modified Logistic
More informationSheet 1: Introduction to prime numbers.
Option A Hand in at least one question from at least three sheets Sheet 1: Introduction to prime numbers. [provisional date for handing in: class 2.] 1. Use Sieve of Eratosthenes to find all prime numbers
More informationNew Linear Cryptanalytic Results of Reduced-Round of CAST-128 and CAST-256
New Linear Cryptanalytic Results of Reduced-Round of CAST-28 and CAST-256 Meiqin Wang, Xiaoyun Wang, and Changhui Hu Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education,
More informationProceedings of Meetings on Acoustics
Proceedings of Meetings on Acoustics Volume 19, 213 http://acousticalsociety.org/ ICA 213 Montreal Montreal, Canada 2-7 June 213 Signal Processing in Acoustics Session 2pSP: Acoustic Signal Processing
More informationCryptanalysis on short messages encrypted with M-138 cipher machine
Cryptanalysis on short messages encrypted with M-138 cipher machine Tsonka Baicheva Miroslav Dimitrov Institute of Mathematics and Informatics Bulgarian Academy of Sciences 10-14 July, 2017 Sofia Introduction
More informationElGamal Public-Key Encryption and Signature
ElGamal Public-Key Encryption and Signature Çetin Kaya Koç koc@cs.ucsb.edu Çetin Kaya Koç http://koclab.org Winter 2017 1 / 10 ElGamal Cryptosystem and Signature Scheme Taher ElGamal, originally from Egypt,
More informationTowards a Cryptanalysis of Scrambled Spectral-Phase Encoded OCDMA
Towards a Cryptanalysis of Scrambled Spectral-Phase Encoded OCDMA Sharon Goldberg* Ron Menendez **, Paul R. Prucnal* *, **Telcordia Technologies OFC 27, Anaheim, CA, March 29, 27 Secret key Security for
More informationV.Sorge/E.Ritter, Handout 2
06-20008 Cryptography The University of Birmingham Autumn Semester 2015 School of Computer Science V.Sorge/E.Ritter, 2015 Handout 2 Summary of this handout: Symmetric Ciphers Overview Block Ciphers Feistel
More informationA basic guitar is a musical string instrument with six strings. In standard tuning they have the notes E, A, D, G, B and E
A.Manimaran* et al. International Journal Of Pharmacy & Technology ISSN: 0975-766X CODEN: IJPTFI Available Online through Research Article www.ijptonline.com DATA ENCRYPTION AND DECRYPTION USING GUITAR
More informationDES Data Encryption standard
DES Data Encryption standard DES was developed by IBM as a modification of an earlier system Lucifer DES was adopted as a standard in 1977 Was replaced only in 2001 with AES (Advanced Encryption Standard)
More information1111: Linear Algebra I
1111: Linear Algebra I Dr. Vladimir Dotsenko (Vlad) Lecture 7 Dr. Vladimir Dotsenko (Vlad) 1111: Linear Algebra I Lecture 7 1 / 8 Invertible matrices Theorem. 1. An elementary matrix is invertible. 2.
More informationProposal of New Block Cipher Algorithm. Abstract
Proposal of New Block Cipher Algorithm Prof. Dr. Hilal Hadi Salih Dr. Ahmed Tariq Sadiq M.Sc.Alaa K.Frhan Abstract Speed and complexity are two important properties in the block cipher. The block length
More informationMathematics Explorers Club Fall 2012 Number Theory and Cryptography
Mathematics Explorers Club Fall 2012 Number Theory and Cryptography Chapter 0: Introduction Number Theory enjoys a very long history in short, number theory is a study of integers. Mathematicians over
More informationNumber Theory - Divisibility Number Theory - Congruences. Number Theory. June 23, Number Theory
- Divisibility - Congruences June 23, 2014 Primes - Divisibility - Congruences Definition A positive integer p is prime if p 2 and its only positive factors are itself and 1. Otherwise, if p 2, then p
More informationJournal of Discrete Mathematical Sciences & Cryptography Vol. ( ), No., pp. 1 10
Dynamic extended DES Yi-Shiung Yeh 1, I-Te Chen 2, Ting-Yu Huang 1, Chan-Chi Wang 1, 1 Department of Computer Science and Information Engineering National Chiao-Tung University 1001 Ta-Hsueh Road, HsinChu
More informationCryptography s Application in Numbers Station
Cryptography s Application in Numbers Station Jacqueline - 13512074 1 Program Studi Teknik Informatika Sekolah Teknik Elektro dan Informatika Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132, Indonesia
More informationGroups, Modular Arithmetic and Geometry
Groups, Modular Arithmetic and Geometry Pupil Booklet 2012 The Maths Zone www.themathszone.co.uk Modular Arithmetic Modular arithmetic was developed by Euler and then Gauss in the late 18th century and
More informationPixel Image Steganography Using EOF Method and Modular Multiplication Block Cipher Algorithm
Pixel Image Steganography Using EOF Method and Modular Multiplication Block Cipher Algorithm Robbi Rahim Abstract Purpose- This study aims to hide data or information on pixel image by using EOF method,
More informationSOLUTION OF POLYGRAPHIC SUBSTITUTION SYSTEMS. Analysis of Four-Square and Two-Square Ciphers
CHAPTER 7 SOLUTION OF POLYGRAPHIC SUBSTITUTION SYSTEMS Section I Analysis of Four-Square and Two-Square Ciphers 7-1. Identification of Plaintext Recovery of any digraphic system is largely dependent on
More informationKeywords: dynamic P-Box and S-box, modular calculations, prime numbers, key encryption, code breaking.
INTRODUCING DYNAMIC P-BOX AND S-BOX BASED ON MODULAR CALCULATION AND KEY ENCRYPTION FOR ADDING TO CURRENT CRYPTOGRAPHIC SYSTEMS AGAINST THE LINEAR AND DIFFERENTIAL CRYPTANALYSIS M. Zobeiri and B. Mazloom-Nezhad
More informationGrade 7 & 8 Math Circles October 12, 2011 Modular Arithmetic
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7 & 8 Math Circles October 12, 2011 Modular Arithmetic To begin: Before learning about modular arithmetic
More information4. Design Principles of Block Ciphers and Differential Attacks
4. Design Principles of Block Ciphers and Differential Attacks Nonli near 28-bits Trans forma tion 28-bits Model of Block Ciphers @G. Gong A. Introduction to Block Ciphers A Block Cipher Algorithm: E and
More informationSome Cryptanalysis of the Block Cipher BCMPQ
Some Cryptanalysis of the Block Cipher BCMPQ V. Dimitrova, M. Kostadinoski, Z. Trajcheska, M. Petkovska and D. Buhov Faculty of Computer Science and Engineering Ss. Cyril and Methodius University, Skopje,
More informationDistribution of Primes
Distribution of Primes Definition. For positive real numbers x, let π(x) be the number of prime numbers less than or equal to x. For example, π(1) = 0, π(10) = 4 and π(100) = 25. To use some ciphers, we
More informationSOME OBSERVATIONS ON AES AND MINI AES. Hüseyin Demirci TÜBİTAK UEKAE
SOME OBSERVTIONS ON ES ND MINI ES Hüseyin Demirci huseyind@uekae.tubitak.gov.tr TÜBİTK UEKE OVERVIEW OF THE PRESENTTION Overview of Rijndael and the Square ttack Half Square Property of Rijndael dvanced
More informationQuality of Encryption Measurement of Bitmap Images with RC6, MRC6, and Rijndael Block Cipher Algorithms
International Journal of Network Security, Vol.5, No.3, PP.241 251, Nov. 2007 241 Quality of Encryption Measurement of Bitmap Images with RC6, MRC6, and Rijndael Block Cipher Algorithms Nawal El-Fishawy
More informationCOS433/Math 473: Cryptography. Mark Zhandry Princeton University Spring 2017
COS433/Math 473: Cryptography Mar Zhandry Princeton University Spring 2017 Announcements Homewor 3 due tomorrow Homewor 4 up Tae- home midterm tentative dates: Posted 3pm am Monday 3/13 Due 1pm Wednesday
More informationMATH 433 Applied Algebra Lecture 12: Sign of a permutation (continued). Abstract groups.
MATH 433 Applied Algebra Lecture 12: Sign of a permutation (continued). Abstract groups. Permutations Let X be a finite set. A permutation of X is a bijection from X to itself. The set of all permutations
More informationp 1 MAX(a,b) + MIN(a,b) = a+b n m means that m is a an integer multiple of n. Greatest Common Divisor: We say that n divides m.
Great Theoretical Ideas In Computer Science Steven Rudich CS - Spring Lecture Feb, Carnegie Mellon University Modular Arithmetic and the RSA Cryptosystem p- p MAX(a,b) + MIN(a,b) = a+b n m means that m
More informationFPGA Implementation of Secured Image STEGNOGRAPHY based on VIGENERE CIPHER and X BOX Mapping Techniques
FPGA Implementation of Secured Image STEGNOGRAPHY based on VIGENERE CIPHER and X BOX Mapping Techniques Aniketkulkarni Sheela.c DhirajDeshpande M.Tech, TOCE Asst.Prof, TOCE Asst.prof,BKIT aniketoxc@gmail.com
More informationGrade 7 and 8 Math Circles March 19th/20th/21st. Cryptography
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7 and 8 Math Circles March 19th/20th/21st Cryptography Introduction Before we begin, it s important
More informationA Novel Image Steganography Based on Contourlet Transform and Hill Cipher
Journal of Information Hiding and Multimedia Signal Processing c 2015 ISSN 2073-4212 Ubiquitous International Volume 6, Number 5, September 2015 A Novel Image Steganography Based on Contourlet Transform
More informationCOS433/Math 473: Cryptography. Mark Zhandry Princeton University Spring 2017
COS433/Math 473: Cryptography Mark Zhandry Princeton University Spring 2017 Previously Pseudorandom Functions and Permutaitons Modes of Operation Pseudorandom Functions Functions that look like random
More informationSecure message transmission over wireless communication
Research Journal of Physical and Applied Sciences Vol. 2(3), pp. 030-035, June 2013 2013 Wudpecker Journals Secure message transmission over wireless communication Md. Mizanur Rahman and Farhana Enam Dept.
More informationProblem A. Ancient Keyboard
3th ACM International Collegiate Programming Contest, 5 6 Asia Region, Tehran Site Sharif University of Technology 1 Dec. 5 Sponsored by Problem A. Ancient Keyboard file: Program file: A.IN A.cpp/A.c/A.dpr/A.java
More informationTable 1: Vignere cipher with key MATH.
Score: Name: Project 3 - Cryptography Math 1030Q Fall 2014 Professor Hohn Show all of your work! Write neatly. No credit will be given to unsupported answers. Projects are due at the beginning of class.
More informationFREDRIK TUFVESSON ELECTRICAL AND INFORMATION TECHNOLOGY
1 Information Transmission Chapter 5, Block codes FREDRIK TUFVESSON ELECTRICAL AND INFORMATION TECHNOLOGY 2 Methods of channel coding For channel coding (error correction) we have two main classes of codes,
More informationSymmetric-key encryption scheme based on the strong generating sets of permutation groups
Symmetric-key encryption scheme based on the strong generating sets of permutation groups Ara Alexanyan Faculty of Informatics and Applied Mathematics Yerevan State University Yerevan, Armenia Hakob Aslanyan
More informationThe congruence relation has many similarities to equality. The following theorem says that congruence, like equality, is an equivalence relation.
Congruences A congruence is a statement about divisibility. It is a notation that simplifies reasoning about divisibility. It suggests proofs by its analogy to equations. Congruences are familiar to us
More informationGrade 7/8 Math Circles Winter March 24/25 Cryptography
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Winter 2015 - March 24/25 Cryptography What is Cryptography? Cryptography is the
More informationHigh Diffusion Cipher: Encryption and Error Correction in a Single Cryptographic Primitive
High Diffusion Cipher: Encryption and Error Correction in a Single Cryptographic Primitive Chetan Nanjunda Mathur, Karthik Narayan and K.P. Subbalakshmi Department of Electrical and Computer Engineering
More informationError-Correcting Codes
Error-Correcting Codes Information is stored and exchanged in the form of streams of characters from some alphabet. An alphabet is a finite set of symbols, such as the lower-case Roman alphabet {a,b,c,,z}.
More informationConnection between thermal printer DPU-414 and measuring equipment
Connection between thermal printer DPU- and measuring equipment When connecting the DPU- to various measuring instruments, function settings at the DPU- must be changed. The procedure for changing settings
More informationCryptography Math 1580 Silverman First Hour Exam Mon Oct 2, 2017
Name: Cryptography Math 1580 Silverman First Hour Exam Mon Oct 2, 2017 INSTRUCTIONS Read Carefully Time: 50 minutes There are 5 problems. Write your name legibly at the top of this page. No calculators
More informationDiffie-Hellman key-exchange protocol
Diffie-Hellman key-exchange protocol This protocol allows two users to choose a common secret key, for DES or AES, say, while communicating over an insecure channel (with eavesdroppers). The two users
More informationcode V(n,k) := words module
Basic Theory Distance Suppose that you knew that an English word was transmitted and you had received the word SHIP. If you suspected that some errors had occurred in transmission, it would be impossible
More informationConditional Cube Attack on Reduced-Round Keccak Sponge Function
Conditional Cube Attack on Reduced-Round Keccak Sponge Function Senyang Huang 1, Xiaoyun Wang 1,2,3, Guangwu Xu 4, Meiqin Wang 2,3, Jingyuan Zhao 5 1 Institute for Advanced Study, Tsinghua University,
More informationCounting in Algorithms
Counting Counting in Algorithms How many comparisons are needed to sort n numbers? How many steps to compute the GCD of two numbers? How many steps to factor an integer? Counting in Games How many different
More informationChapter 10 Error Detection and Correction
Chapter 10 Error Detection and Correction 10.1 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.2 Note Data can be corrupted during transmission. Some applications
More informationModular arithmetic Math 2320
Modular arithmetic Math 220 Fix an integer m 2, called the modulus. For any other integer a, we can use the division algorithm to write a = qm + r. The reduction of a modulo m is the remainder r resulting
More informationImage Encryption Based on New One-Dimensional Chaotic Map
Image Encryption Based on New One-Dimensional Chaotic Map N.F.Elabady #1, H.M.Abdalkader *2, M. I. Moussa #3,S. F. Sabbeh #4 # Computer Science Department, Faculty of Computer and Informatics, Benha University,
More information