Some Stuff About Crypto
|
|
- Gilbert Richard
- 6 years ago
- Views:
Transcription
1 Some Stuff About Crypto Adrian Frith Laboratory of Foundational Aspects of Computer Science Department of Mathematics and Applied Mathematics University of Cape Town This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 South Africa License. 6 October 2011 Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
2 What is cryptography? Literally hidden writing hiding information from an adversary The practice and study of techniques for secure communication in the presence of hostile third parties. Traditionally about encryption, i.e. confidentiality, now encompasses authentication and integrity. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
3 A note about names Cryptography versus cryptanalysis making versus breaking The distinction is not very useful Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
4 Some encryption terminology The plaintext is the message to be protected. Encryption converts the plaintext to a ciphertext, using a key. Decryption is the reverse. Encryption algorithm + decryption algorithm = cipher. (Don t say code!) A cryptosystem consists of a cipher plus keys, procedures, etc. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
5 Substitution ciphers Consistently map alphabet to alphabet Caesar cipher: alphabetic shift with rotation. E.g. attack at dawn, with a shift of 5, becomes fyyfhp fy ifbs Hebrew atbash: reverse the alphabet Generic substitution cipher: some permutation of the alphabet Vulnerable to frequency analysis: different characters appear with different frequencies In English: E T A O I N S H R D L U... Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
6 Variations on the theme Homophony: map smaller alphabet into larger alphabet to disguise frequency Nomenclator: combine a cipher with a codebook State of the art from 1400s to 1700s Great Cipher of France unbroken for 150 years Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
7 The Babington Plot Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
8 The Voynich Manuscript Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
9 Polyalphabetic substitution Many alphabets Cycle through different mappings from plaintext alphabet to ciphertext alphabet Le chiffre indéchiffrable - but it wasn t! Broken by Charles Babbage in the 1850s Use of repetions + frequency analysis Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
10 The Vigenère square Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
11 World War I the Zimmermann telegram Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
12 World War II Enigma A S D F 1 A 2 9 S D F 3 7 A S D F 8 Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
13 Modern cryptography Arises out of World War II work tied closely to development of the computer Claude Shannon information theory Cold War government secrecy DES 1977 first public crypto standard The problem of key distribution Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
14 Asymmetric encryption Diffie-Hellman key exchange (1976) see later Asymmetric cryptosystems RSA (1978) and others Crypto politics publication in the open literature Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
15 The structure of modern crypto Symmetric ciphers Block ciphers Stream ciphers Asymmetric ciphers Hash functions Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
16 Diffie-Hellmann key exchange The aim: Alice and Bob want to derive a shared secret key by exchanging information over a public channel (A diversion into modular arithmetic, if necessary.) 1 Alice chooses a prime p and a generator g and sends them to Bob. 2 Alice generates a random natural x a and Bob generates a random natural x b. 3 Alice calculates y a = g xa mod p and Bob calculates y b = g x b mod p. 4 Alice sends y a to Bob and Bob sends y b to Alice. 5 Alice calculates y xa 6 y xa b gx bx a g xax b y x b b mod p and Bob calculates y x b a mod p. a! Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
17 RSA encryption Rivest, Shamir, Adleman at MIT in 1978 Previously discovered by Cocks at GCHQ in 1973 One of the earliest, still the most used Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
18 RSA key generation 1 Choose two primes p and q. 2 Compute the modulus n = pq. 3 Compute ϕ(n) = (p 1)(q 1). (Size of the multiplicative group of integers mod n.) 4 Choose e such that 1 < e < ϕ(n) and e and ϕ(n) are relatively prime. 5 Calculate d = e 1 mod ϕ(n). (Extended Euclidean algorithm.) 6 The public key is (n, e) and the private key is (n, d). Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
19 RSA encryption and decryption Alice publishes her public key (n, e) and secures her private key (n, d). To encrypt a message m, Bob calculates c = m e mod n. To decrypt, Alice calculates c d mod n. Why does this work? c d m ed mod n. Remember ed 1 mod ϕ(n). Euler s theorem says a ϕ(n) 1 mod n. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
20 Some computation shortcuts Square-and-multiply for exponentiation a b mod n: 1 Let b t b t 1 b t 2...b 2 b 1 b 0 be the binary expansion of b. 2 Let z := 1. 3 Let y := a 4 For i in 0 to t: 1 If b i = 1 then let z := zy mod n. 2 Let y = yy mod n. 5 Return z. Optimize decryption with Chinese remainder theorem Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
21 Cryptographic Hash Functions A Very Brief Summary Definition A hash function maps bitstrings of arbitrary length ( messages ) to bitstrings of a fixed length n ( hashes ). A cryptographically secure hash function is: first-preimage resistant: given an n-bit string, it is infeasible to find a message that hashes to that string. second-preimage resistant: given a message, it is infeasible to find a different message with the same hash. collision resistant: it is infeasible to find a pair of messages which share a hash. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
22 Iterated Hash Functions a.k.a. the Merkle-Damgård Construction Definition A compression function maps bitstrings of length m to bitstrings of length n, where m > n. We construct a hash function F from a compression function f as follows: 1 Divide message M into l blocks of length m n. 2 Let h 0 be some fixed n-bit initialization vector. 3 For i in 1 to l: let h i = f(h i 1 m i ). 4 The final hash F(M) = h l. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
23 Iterated Hash Functions m 1 m 2 m l 1 m l h 0 f h 1 f h 2 h l 2 f h l 1 f h l With some caveats, this is the basis for MD5, SHA-1, SHA-2, etc. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
24 The Long Message Attack In hashing a 2 R -block message, 2 R intermediate hash values will be produced: h 1 through h 2 R. Find a message block m that hashes to one of these values, i.e. f(h 0 m ) = h i for some i in 1 through 2 R. Then F(M) = F(m m i+1 m i+2 m 2 R 1 m 2 R). m h 0 h i 1 m i h i m i+1 h i+1 h 2 R Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
25 The Long Message Attack Finding the Linking Block Calculate h = f(h 0 m ) for a random block m. h has 2 n possible values: therefore a 2R 2 n probability that it matches one of the intermediate values. Geometric distribution with p = 2 R n says we must test on average 2 n R random blocks before finding one that matches. Better than brute force 2 n. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
26 Merkle-Damgård Strengthening Avoiding the Long Message Attack Simple fix: append a final block to the message, containing a binary representation of the message s length. This can be worked around by using an expandable message. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
27 Expandable Messages Definition An expandable message is set of messages of different lengths, all of which have the same hash value when the Merkle-Damgård strengthening is not applied. Definition An (a, b)-expandable message is an expandable message containing messages of every length from a to b inclusive. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
28 Fixed-Point Expandable Messages A fixed point is a pair (h, m) such that f(h m) = h. To create an expandable message: 1 Generate 2 n/2 random fixed points: (h 1, m 1 ) through (h 2 n/2, m 2 n/2). 2 Generate 2 n/2 random blocks: m 1 through m. 2 n/2 3 Find a match where the hash of one of the random blocks is the same as the hash value in the fixed point: h i = f(h 0 m j ). Better than 1 2 probability that such a match exists. We can create a message of any length l by appending l 1 copies of m i after m j. This is a (1, )-expandable message. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
29 Generic Expandable Messages The Method of Kelsey and Schneier Method for constructing a (R, R + 2 R 1)-expandable message for any iterated hash function. Based on an method for creating a 1-block message and an k-block message that hash from the same intermediate value to the same intermediate value: 1 Generate 2 n/2 1-block messages. 2 Generate 2 n/2 k-block messages. 3 Check for a collision; one will exist with better than 1 2 probability. To create the expandable message, let i iterate from 1 to R and: 1 Find 1-block message m i and (2 i 1 + 1)-block message m i such that f(h i 1 m i ) = f(h i 1 m i ) 2 Let h i = f(h i 1 m i ). continues... Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
30 Generic Expandable Messages Constructing a k-block Message A k-block message (where R k R + 2 R 1) can be constructed as follows: 1 Let M be the empty message. 2 Let d = k R. Then 0 d 2 R 1. 3 Let s 1 s 2 s R be the binary representation of d with least significant bit first. 4 Let i iterate from 1 to R: If si = 0, append m i to M. If si = 1, append m i to M 5 Return M. The final hash value h R is always the same. This gives us an (R, R + 2 R 1)-expandable message. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
31 Using the Expandable Message Consider a message M of 2 R + R blocks. 1 Create an (R, R + 2 R 1)-expandable message. Let h e be the hash value shared by all the messages in the expandable message. 2 Use the basic long message attack to find a single block m link that hashes from h e to one of the intermediate values from h R+1 through h 2 R +R. Call this intermediate value h j. 3 Use the expandable message to create a (j 1)-block message m that hashes to h e. 4 Return the message M = m m link m j+1 m j+2 m 2 R +R. Bouillaguet and Fouque prove that this is the optimal generic second-preimage attack on an Merkle-Damgård hash function. Adrian Frith (University of Cape Town) Some Stuff About Crypto 6 October / 31
Public Key Cryptography
graphy CSS322: Security and Cryptography Sirindhorn International Institute of Technology Thammasat University Prepared by Steven Gordon on 29 December 2011 CSS322Y11S2L07, Steve/Courses/2011/S2/CSS322/Lectures/rsa.tex,
More informationDistributed Systems. 26. Cryptographic Systems: An Introduction. Paul Krzyzanowski. Rutgers University. Fall 2015
Distributed Systems 26. Cryptographic Systems: An Introduction Paul Krzyzanowski Rutgers University Fall 2015 1 Cryptography Security Cryptography may be a component of a secure system Adding cryptography
More informationCryptography MIS
Cryptography MIS-5903 http://community.mis.temple.edu/mis5903sec011s17/ Cryptography History Substitution Monoalphabetic Polyalphabetic (uses multiple alphabets) uses Vigenere Table Scytale cipher (message
More informationDr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010
CS 494/594 Computer and Network Security Dr. Jinyuan (Stella) Sun Dept. of Electrical Engineering and Computer Science University of Tennessee Fall 2010 1 Public Key Cryptography Modular Arithmetic RSA
More informationPublic-key encipherment concept
Date: onday, October 21, 2002 Prof.: Dr Jean-Yves Chouinard Design of Secure Computer Systems CSI4138/CEG4394 Notes on Public Key Cryptography Public-key encipherment concept Each user in a secure communication
More informationCryptography Symmetric Cryptography Asymmetric Cryptography Internet Communication. Telling Secrets. Secret Writing Through the Ages.
Telling Secrets Secret Writing Through the Ages William Turner Department of Mathematics & Computer Science Wabash College Crawfordsville, IN 47933 Tuesday 4 February 2014 W. J. Turner Telling Secrets
More informationChapter 3 Traditional Symmetric-Key Ciphers 3.1
Chapter 3 Traditional Symmetric-Key Ciphers 3.1 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 3 Objectives To define the terms and the concepts of symmetric
More informationGreat Theoretical Ideas in Computer Science. Lecture 27: Cryptography
15-251 Great Theoretical Ideas in Computer Science Lecture 27: Cryptography What is cryptography about? Adversary Eavesdropper I will cut his throat I will cut his throat What is cryptography about? loru23n8uladjkfb!#@
More informationCRYPTOLOGY KEY MANAGEMENT CRYPTOGRAPHY CRYPTANALYSIS. Cryptanalytic. Brute-Force. Ciphertext-only Known-plaintext Chosen-plaintext Chosen-ciphertext
CRYPTOLOGY CRYPTOGRAPHY KEY MANAGEMENT CRYPTANALYSIS Cryptanalytic Brute-Force Ciphertext-only Known-plaintext Chosen-plaintext Chosen-ciphertext 58 Types of Cryptographic Private key (Symmetric) Public
More informationPublic Key Cryptography and RSA
Public Key Cryptography and RSA Major topics Principles of public key cryptosystems The RSA algorithm The Security of RSA Motivations A public key system is asymmetric, there does not have to be an exchange
More informationPublic Key Algorithms
Public Key Algorithms 1 Public Key Algorithms It is necessary to know some number theory to really understand how and why public key algorithms work Most of the public key algorithms are based on modular
More informationLecture IV : Cryptography, Fundamentals
Lecture IV : Cryptography, Fundamentals Internet Security: Principles & Practices John K. Zao, PhD (Harvard) SMIEEE Computer Science Department, National Chiao Tung University Spring 2012 Basic Principles
More informationPublic Key Encryption. Modified by: Dr. Ramzi Saifan
Public Key Encryption Modified by: Dr. Ramzi Saifan Prime Numbers Prime numbers only have divisors of 1 and itself They cannot be written as a product of other numbers Prime numbers are central to number
More informationCryptography and Network Security. Sixth Edition by William Stallings
Cryptography and Network Security Sixth Edition by William Stallings Chapter 9 Public Key Cryptography and RSA Misconceptions Concerning Public-Key Encryption Public-key encryption is more secure from
More informationChapter 9. Public Key Cryptography, RSA And Key Management
Chapter 9 Public Key Cryptography, RSA And Key Management RSA by Rivest, Shamir & Adleman of MIT in 1977 The most widely used public-key cryptosystem is RSA. The difficulty of attacking RSA is based on
More informationCryptography. Submitted to:- Ms Poonam Sharma Faculty, ABS,Manesar. Submitted by:- Hardeep Gaurav Jain
Cryptography Submitted to:- Ms Poonam Sharma Faculty, ABS,Manesar Submitted by:- Hardeep Gaurav Jain Cryptography Cryptography, a word with Greek origins, means "secret writing." However, we use the term
More informationTuesday, January 17, 17. Crypto - mini lecture 1
Crypto - mini lecture 1 Cryptography Symmetric key cryptography (secret key crypto): sender and receiver keys identical Asymmetric key cryptography (public key crypto): encryption key public, decryption
More informationStudy Guide to Mideterm Exam
YALE UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE CPSC 467b: Cryptography and Computer Security Handout #7 Professor M. J. Fischer February 20, 2012 Study Guide to Mideterm Exam For the exam, you are responsible
More informationComputer Security. 08. Cryptography Part II. Paul Krzyzanowski. Rutgers University. Spring 2018
Computer Security 08. Cryptography Part II Paul Krzyzanowski Rutgers University Spring 2018 March 23, 2018 CS 419 2018 Paul Krzyzanowski 1 Block ciphers Block ciphers encrypt a block of plaintext at a
More informationChannel Coding and Cryptography Part II: Introduction to Cryptography
Channel Coding and Cryptography Part II: Introduction to Cryptography Prof. Dr.-Ing. habil. Andreas Ahrens Communications Signal Processing Group, University of Technology, Business and Design Email: andreas.ahrens@hs-wismar.de
More informationCSCI 454/554 Computer and Network Security. Topic 2. Introduction to Cryptography
CSCI 454/554 Computer and Network Security Topic 2. Introduction to Cryptography Outline Basic Crypto Concepts and Definitions Some Early (Breakable) Cryptosystems Key Issues 2 Basic Concepts and Definitions
More information9/30/2016. Cryptography Basics. Outline. Encryption/Decryption. Cryptanalysis. Caesar Cipher. Mono-Alphabetic Ciphers
Cryptography Basics IT443 Network Security Administration Slides courtesy of Bo Sheng Basic concepts in cryptography systems Secret cryptography Public cryptography 1 2 Encryption/Decryption Cryptanalysis
More informationCryptography Basics. IT443 Network Security Administration Slides courtesy of Bo Sheng
Cryptography Basics IT443 Network Security Administration Slides courtesy of Bo Sheng 1 Outline Basic concepts in cryptography systems Secret key cryptography Public key cryptography Hash functions 2 Encryption/Decryption
More informationOutline. Cryptography. Encryption/Decryption. Basic Concepts and Definitions. Cryptography vs. Steganography. Cryptography: the art of secret writing
Outline CSCI 454/554 Computer and Network Security Basic Crypto Concepts and Definitions Some Early (Breakable) Cryptosystems Key Issues Topic 2. Introduction to Cryptography 2 Cryptography Basic Concepts
More informationChapter 9 Public Key Cryptography. WANG YANG
Chapter 9 Public Key Cryptography WANG YANG wyang@njnet.edu.cn Content Introduction RSA Diffie-Hellman Key Exchange Introduction Public Key Cryptography plaintext encryption ciphertext decryption plaintext
More informationCS669 Network Security
UNIT II PUBLIC KEY ENCRYPTION Uniqueness Number Theory concepts Primality Modular Arithmetic Fermet & Euler Theorem Euclid Algorithm RSA Elliptic Curve Cryptography Diffie Hellman Key Exchange Uniqueness
More informationApplied Cryptography and Computer Security CSE 664 Spring 2018
Applied Cryptography and Computer Security Lecture 13: Public-Key Cryptography and RSA Department of Computer Science and Engineering University at Buffalo 1 Public-Key Cryptography What we already know
More informationIntroduction to Cryptography and Security Mechanisms: Unit 5. Public-Key Encryption
Introduction to Cryptography and Security Mechanisms: Unit 5 Public-Key Encryption Learning Outcomes Explain the basic principles behind public-key cryptography Recognise the fundamental problems that
More informationRSA (material drawn from Avi Kak Lecture 12, Lecture Notes on "Computer and Network Security" Used in asymmetric crypto.
RSA (material drawn from Avi Kak (kak@purdue.edu) Lecture 12, Lecture Notes on "Computer and Network Security" Used in asymmetric crypto. protocols The RSA algorithm is based on the following property
More informationCSCI 454/554 Computer and Network Security. Topic 5.2 Public Key Cryptography
CSCI 454/554 Computer and Network Security Topic 5.2 Public Key Cryptography Outline 1. Introduction 2. RSA 3. Diffie-Hellman Key Exchange 4. Digital Signature Standard 2 Introduction Public Key Cryptography
More informationOVE EDFORS ELECTRICAL AND INFORMATION TECHNOLOGY
1 Information Transmission Chapter 6 Cryptology OVE EDFORS ELECTRICAL AND INFORMATION TECHNOLOGY Learning outcomes After this lecture the student should undertand what cryptology is and how it is used,
More informationBasic Concepts and Definitions. CSC/ECE 574 Computer and Network Security. Outline
CSC/ECE 574 Computer and Network Security Topic 2. Introduction to Cryptography 1 Outline Basic Crypto Concepts and Definitions Some Early (Breakable) Cryptosystems Key Issues 2 Basic Concepts and Definitions
More informationSecurity+ Guide to Network Security Fundamentals, Third Edition. Chapter 11 Basic Cryptography
Security+ Guide to Network Security Fundamentals, Third Edition Chapter 11 Basic Cryptography Objectives Define cryptography Describe hashing List the basic symmetric cryptographic algorithms 2 Objectives
More informationLecture 6: Overview of Public-Key Cryptography and RSA
1 Lecture 6: Overview of Public-Key Cryptography and RSA Yuan Xue In this lecture, we give an overview to the public-key cryptography, which is also referred to as asymmetric cryptography. We will first
More informationOutline. CSCI 454/554 Computer and Network Security. Introduction. Topic 5.2 Public Key Cryptography. 1. Introduction 2. RSA
CSCI 454/554 Computer and Network Security Topic 5.2 Public Key Cryptography 1. Introduction 2. RSA Outline 3. Diffie-Hellman Key Exchange 4. Digital Signature Standard 2 Introduction Public Key Cryptography
More informationPublic Key Cryptography, OpenPGP, and Enigmail. 31/5/ Geek Girls Carrffots GVA
Public Key Cryptography, OpenPGP, and Enigmail Cryptography is the art and science of transforming (encrypting) a message so only the intended recipient can read it Symmetric Cryptography shared secret
More informationSecurity: Cryptography
Security: Cryptography Computer Science and Engineering College of Engineering The Ohio State University Lecture 38 Some High-Level Goals Confidentiality Non-authorized users have limited access Integrity
More informationEncryption Algorithms
Encryption Algorithms 1. Transposition Ciphers 2. Substitution Ciphers 3. Product Ciphers 4. Exponentiation Ciphers 5. Cryptography based on Discrete Logarithms 6. Advanced Encryption Standard (AES) 1.
More informationBehrang Noohi. 22 July Behrang Noohi (QMUL) 1 / 18
Behrang Noohi School of Mathematical Sciences Queen Mary University of London 22 July 2014 Behrang Noohi (QMUL) 1 / 18 Introduction Secure Communication How can one send a secret message? Steganography
More informationCryptographic Techniques. Information Technologies for IPR Protections 2003/11/12 R107, CSIE Building
Cryptographic Techniques Information Technologies for IPR Protections 2003/11/12 R107, CSIE Building Outline Data security Cryptography basics Cryptographic systems DES RSA C. H. HUANG IN CML 2 Cryptography
More informationChapter 3 Public Key Cryptography
Cryptography and Network Security Chapter 3 Public Key Cryptography Lectured by Nguyễn Đức Thái Outline Number theory overview Public key cryptography RSA algorithm 2 Prime Numbers A prime number is an
More informationCSE 127: Computer Security Cryptography. Kirill Levchenko
CSE 127: Computer Security Cryptography Kirill Levchenko October 24, 2017 Motivation Two parties want to communicate securely Secrecy: No one else can read messages Integrity: messages cannot be modified
More informationOutline. Public Key Cryptography. Applications of Public Key Crypto. Applications (Cont d)
Outline AIT 682: Network and Systems Security 1. Introduction 2. RSA 3. Diffie-Hellman Key Exchange 4. Digital Signature Standard Topic 5.2 Public Key Cryptography Instructor: Dr. Kun Sun 2 Public Key
More informationA Tour of Classical and Modern Cryptography
A Tour of Classical and Modern Cryptography Evan P. Dummit University of Rochester May 25, 2016 Outline Contents of this talk: Overview of cryptography (what cryptography is) Historical cryptography (how
More informationCryptography (DES+RSA) by Amit Konar Dept. of Math and CS, UMSL
Cryptography (DES+RSA) by Amit Konar Dept. of Math and CS, UMSL Transpositional Ciphers-A Review Decryption 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Encryption 1 2 3 4 5 6 7 8 A G O O D F R I E N D I S A T R E
More informationCryptographic Hash Functions
ECE458 Winter 2013 Cryptographic Hash Functions Dan Boneh (Mods by Vijay Ganesh) Previous Lectures: What we have covered so far in cryptography! One-time Pad! Definition of perfect security! Block and
More informationOverview. Public Key Algorithms I
Public Key Algorithms I Dr. Arjan Durresi Louisiana State University Baton Rouge, LA 70810 Durresi@csc.lsu.Edu These slides are available at: http://www.csc.lsu.edu/~durresi/csc4601-04/ Louisiana State
More informationIntroduction to Cryptography. Vasil Slavov William Jewell College
Introduction to Cryptography Vasil Slavov William Jewell College Crypto definitions Cryptography studies how to keep messages secure Cryptanalysis studies how to break ciphertext Cryptology branch of mathematics,
More informationClassical Cryptography
Classical Cryptography Chester Rebeiro IIT Madras STINSON : chapter 1 Ciphers Symmetric Algorithms Encryption and Decryption use the same key i.e. K E = K D Examples: Block Ciphers : DES, AES, PRESENT,
More informationComputer Security: Principles and Practice
Computer Security: Principles and Practice Chapter 2 Cryptographic Tools First Edition by William Stallings and Lawrie Brown Lecture slides by Lawrie Brown Cryptographic Tools cryptographic algorithms
More informationAPNIC elearning: Cryptography Basics
APNIC elearning: Cryptography Basics 27 MAY 2015 03:00 PM AEST Brisbane (UTC+10) Issue Date: Revision: Introduction Presenter Sheryl Hermoso Training Officer sheryl@apnic.net Specialties: Network Security
More informationClassical Cryptography. Thierry Sans
Classical Cryptography Thierry Sans Example and definitions of a cryptosystem Caesar Cipher - the oldest cryptosystem A shift cipher attributed to Julius Caesar (100-44 BC) MEET ME AFTER THE TOGA PARTY
More informationComputer Security 3/23/18
s s encrypt a block of plaintext at a time and produce ciphertext Computer Security 08. Cryptography Part II Paul Krzyzanowski DES & AES are two popular block ciphers DES: 64 bit blocks AES: 128 bit blocks
More informationCRYPTOGRAPHY & DIGITAL SIGNATURE
UNIT V CRYPTOGRAPHY & DIGITAL SIGNATURE What happens in real life? We have universal electronic connectivity via networks of our computers so allowing viruses and hackers to do eavesdropping. So both the
More informationIntroduction to Cryptography and Security Mechanisms. Abdul Hameed
Introduction to Cryptography and Security Mechanisms Abdul Hameed http://informationtechnology.pk Before we start 3 Quiz 1 From a security perspective, rather than an efficiency perspective, which of the
More informationChapter 3. Cryptography. Information Security/System Security p. 33/617
Chapter 3 Cryptography Information Security/System Security p. 33/617 Introduction A very important tool for security is cryptography Cryptography is the (art and) science of keeping information secure
More informationPublic Key Cryptography
Public Key Cryptography Giuseppe F. Italiano Universita` di Roma Tor Vergata italiano@disp.uniroma2.it Motivation Until early 70s, cryptography was mostly owned by government and military Symmetric cryptography
More informationIntroduction to Cryptography
Introduction to Cryptography Jiyou Li lijiyou at sjtu.edu.cn Department of Mathematics, Shanghai Jiao Tong University Sep. 17th, 2013 Cryptography Cryptography: the art and science of keeping message secure.
More informationComputer Security. 08r. Pre-exam 2 Last-minute Review Cryptography. Paul Krzyzanowski. Rutgers University. Spring 2018
Computer Security 08r. Pre-exam 2 Last-minute Review Cryptography Paul Krzyzanowski Rutgers University Spring 2018 March 26, 2018 CS 419 2018 Paul Krzyzanowski 1 Cryptographic Systems March 26, 2018 CS
More informationCryptography Introduction to Computer Security. Chapter 8
Cryptography Introduction to Computer Security Chapter 8 Introduction Cryptology: science of encryption; combines cryptography and cryptanalysis Cryptography: process of making and using codes to secure
More informationLECTURE 4: Cryptography
CSC 519 Information Security LECTURE 4: Cryptography Dr. Esam A. Alwagait alwagait@ksu.edu.sa Recap form previous Lecture We discussed more symmetric encryption. Books? Security Engineering, Ross Anderson
More information(a) Symmetric model (b) Cryptography (c) Cryptanalysis (d) Steganography
Code No: RR410504 Set No. 1 1. Write short notes on (a) Symmetric model (b) Cryptography (c) Cryptanalysis (d) Steganography 3. (a) Illustrate Diffie-hellman Key Exchange scheme for GF(P) [6M] (b) Consider
More informationIntroduction. CSE 5351: Introduction to cryptography Reading assignment: Chapter 1 of Katz & Lindell
Introduction CSE 5351: Introduction to cryptography Reading assignment: Chapter 1 of Katz & Lindell 1 Cryptography Merriam-Webster Online Dictionary: 1. secret writing 2. the enciphering and deciphering
More informationCryptographic Concepts
Outline Identify the different types of cryptography Learn about current cryptographic methods Chapter #23: Cryptography Understand how cryptography is applied for security Given a scenario, utilize general
More informationRef:
Cryptography & digital signature Dec. 2013 Ref: http://cis.poly.edu/~ross/ 2 Cryptography Overview Symmetric Key Cryptography Public Key Cryptography Message integrity and digital signatures References:
More informationCSC 474/574 Information Systems Security
CSC 474/574 Information Systems Security Topic 2.5 Public Key Algorithms CSC 474/574 Dr. Peng Ning 1 Public Key Algorithms Public key algorithms covered in this class RSA: encryption and digital signature
More informationASYMMETRIC CRYPTOGRAPHY
ASYMMETRIC CRYPTOGRAPHY CONTENT: 1. Number Theory 2. One Way Function 3. Hash Function 4. Digital Signature 5. RSA (Rivest-Shamir Adleman) References: 1. Applied Cryptography, Bruce Schneier 2. Cryptography
More informationL2. An Introduction to Classical Cryptosystems. Rocky K. C. Chang, 23 January 2015
L2. An Introduction to Classical Cryptosystems Rocky K. C. Chang, 23 January 2015 This and the next set of slides 2 Outline Components of a cryptosystem Some modular arithmetic Some classical ciphers Shift
More informationElements of Cryptography and Computer and Networking Security Computer Science 134 (COMPSCI 134) Fall 2016 Instructor: Karim ElDefrawy
Elements of Cryptography and Computer and Networking Security Computer Science 134 (COMPSCI 134) Fall 2016 Instructor: Karim ElDefrawy Homework 2 Due: Friday, 10/28/2016 at 11:55pm PT Will be posted on
More informationWhat did we talk about last time? Public key cryptography A little number theory
Week 4 - Friday What did we talk about last time? Public key cryptography A little number theory If p is prime and a is a positive integer not divisible by p, then: a p 1 1 (mod p) Assume a is positive
More informationUnderstanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl
Understanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 1 Introduction to Cryptography ver. October 27, 2009 These slides were
More informationPublic Key Algorithms
Public Key Algorithms CS 472 Spring 13 Lecture 6 Mohammad Almalag 2/19/2013 Public Key Algorithms - Introduction Public key algorithms are a motley crew, how? All hash algorithms do the same thing: Take
More informationPart VI. Public-key cryptography
Part VI Public-key cryptography Drawbacks with symmetric-key cryptography Symmetric-key cryptography: Communicating parties a priori share some secret information. Secure Channel Alice Unsecured Channel
More informationAn overview and Cryptographic Challenges of RSA Bhawana
An overview and Cryptographic Challenges of RSA Bhawana Department of CSE, Shanti Devi Institute of Technology & Management, Israna, Haryana India ABSTRACT: With the introduction of the computer, the need
More informationPublic Key Algorithms
CSE597B: Special Topics in Network and Systems Security Public Key Cryptography Instructor: Sencun Zhu The Pennsylvania State University Public Key Algorithms Public key algorithms RSA: encryption and
More informationCSC 474/574 Information Systems Security
CSC 474/574 Information Systems Security Topic 2.1 Introduction to Cryptography CSC 474/574 By Dr. Peng Ning 1 Cryptography Cryptography Original meaning: The art of secret writing Becoming a science that
More informationENEE 459-C Computer Security. Message authentication
ENEE 459-C Computer Security Message authentication Data Integrity and Source Authentication Encryption does not protect data from modification by another party. Why? Need a way to ensure that data arrives
More informationCCNA Security 1.1 Instructional Resource
CCNA Security 1.1 Instructional Resource Chapter 7 Cryptographic Systems 2012 Cisco and/or its affiliates. All rights reserved. 1 Explain how cryptology consists of cryptography (encoding messages) and
More informationCryptography (Overview)
Cryptography (Overview) Some history Caesar cipher, rot13 substitution ciphers, etc. Enigma (Turing) Modern secret key cryptography DES, AES Public key cryptography RSA, digital signatures Cryptography
More informationEncryption. INST 346, Section 0201 April 3, 2018
Encryption INST 346, Section 0201 April 3, 2018 Goals for Today Symmetric Key Encryption Public Key Encryption Certificate Authorities Secure Sockets Layer Simple encryption scheme substitution cipher:
More informationKurose & Ross, Chapters (5 th ed.)
Kurose & Ross, Chapters 8.2-8.3 (5 th ed.) Slides adapted from: J. Kurose & K. Ross \ Computer Networking: A Top Down Approach (5 th ed.) Addison-Wesley, April 2009. Copyright 1996-2010, J.F Kurose and
More informationAssignment 9 / Cryptography
Assignment 9 / Cryptography Michael Hauser March 2002 Tutor: Mr. Schmidt Course: M.Sc Distributed Systems Engineering Lecturer: Mr. Owens CONTENTS Contents 1 Introduction 3 2 Simple Ciphers 3 2.1 Vignère
More informationTraditional Symmetric-Key Ciphers. A Biswas, IT, BESU Shibpur
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
More informationISA 662 Internet Security Protocols. Outline. Prime Numbers (I) Beauty of Mathematics. Division (II) Division (I)
Outline ISA 662 Internet Security Protocols Some Math Essentials & History Asymmetric signatures and key exchange Asymmetric encryption Symmetric MACs Lecture 2 ISA 662 1 2 Beauty of Mathematics Demonstration
More informationCryptography and Network Security
Cryptography and Network Security Spring 2012 http://users.abo.fi/ipetre/crypto/ Lecture 14: Folklore, Course summary, Exam requirements Ion Petre Department of IT, Åbo Akademi University 1 Folklore on
More informationCryptographic Hash Functions
Cryptographic Hash Functions Cryptographic Hash Functions A cryptographic hash function takes a message of arbitrary length and creates a message digest of fixed length. Iterated Hash Function A (compression)
More informationMaking and Breaking Ciphers
Making and Breaking Ciphers Ralph Morelli Trinity College, Hartford (ralph.morelli@trincoll.edu) Smithsonian Institute October 31, 2009 2009 Ralph Morelli You are free to reuse and remix this presentation
More informationLecture 2 Applied Cryptography (Part 2)
Lecture 2 Applied Cryptography (Part 2) Patrick P. C. Lee Tsinghua Summer Course 2010 2-1 Roadmap Number theory Public key cryptography RSA Diffie-Hellman DSA Certificates Tsinghua Summer Course 2010 2-2
More informationWinter 2011 Josh Benaloh Brian LaMacchia
Winter 2011 Josh Benaloh Brian LaMacchia Symmetric Cryptography January 20, 2011 Practical Aspects of Modern Cryptography 2 Agenda Symmetric key ciphers Stream ciphers Block ciphers Cryptographic hash
More informationPublic Key Cryptography and the RSA Cryptosystem
Public Key Cryptography and the RSA Cryptosystem Two people, say Alice and Bob, would like to exchange secret messages; however, Eve is eavesdropping: One technique would be to use an encryption technique
More informationTechnological foundation
Technological foundation Carte à puce et Java Card 2010-2011 Jean-Louis Lanet Jean-louis.lanet@unilim.fr Cryptology Authentication Secure upload Agenda Cryptology Cryptography / Cryptanalysis, Smart Cards
More informationThe question paper contains 40 multiple choice questions with four choices and students will have to pick the correct one (each carrying ½ marks.).
Time: 3hrs BCA III Network security and Cryptography Examination-2016 Model Paper 2 M.M:50 The question paper contains 40 multiple choice questions with four choices and students will have to pick the
More informationCryptography Introduction
Cryptography Introduction Last Updated: Aug 20, 2013 Terminology Access Control o Authentication Assurance that entities are who they claim to be o Authorization Assurance that entities have permission
More information1.264 Lecture 28. Cryptography: Asymmetric keys
1.264 Lecture 28 Cryptography: Asymmetric keys Next class: Anderson chapters 20. Exercise due before class (Reading doesn t cover same topics as lecture) 1 Asymmetric or public key encryption Receiver
More informationCryptography and Network Security 2. Symmetric Ciphers. Lectured by Nguyễn Đức Thái
Cryptography and Network Security 2. Symmetric Ciphers Lectured by Nguyễn Đức Thái Outline Symmetric Encryption Substitution Techniques Transposition Techniques Steganography 2 Symmetric Encryption There
More informationUzzah and the Ark of the Covenant
Uzzah and the Ark of the Covenant And when they came to the threshing floor of Chidon, Uzzah put out his hand to take hold of the ark, for the oxen stumbled. 10 And the anger of the LORD was kindled against
More informationECE 646 Fall 2009 Final Exam December 15, Multiple-choice test
ECE 646 Fall 2009 Final Exam December 15, 2009 Multiple-choice test 1. (1 pt) Parallel processing can be used to speed up the following cryptographic transformations (please note that multiple answers
More informationCryptography Intro and RSA
Cryptography Intro and RSA Well, a gentle intro to cryptography, followed by a description of public key crypto and RSA. 1 Definition Cryptology is the study of secret writing Concerned with developing
More informationח'/סיון/תשע "א. RSA: getting ready. Public Key Cryptography. Public key cryptography. Public key encryption algorithms
Public Key Cryptography Kurose & Ross, Chapters 8.28.3 (5 th ed.) Slides adapted from: J. Kurose & K. Ross \ Computer Networking: A Top Down Approach (5 th ed.) AddisonWesley, April 2009. Copyright 19962010,
More informationGarantía y Seguridad en Sistemas y Redes
Garantía y Seguridad en Sistemas y Redes Tema 2. Cryptographic Tools Esteban Stafford Departamento de Ingeniería Informá2ca y Electrónica Este tema se publica bajo Licencia: Crea2ve Commons BY- NC- SA
More information