Channel Coding and Cryptography Part II: Introduction to Cryptography
|
|
- Madeleine Foster
- 6 years ago
- Views:
Transcription
1 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 Andreas Ahrens 113
2 Further Reading and Information Understanding Cryptography Menezes, A.; van Oorschot, P.; Vanstone, S. : Handbook of Applied Cryptography. London, New York: CRC Press, Tilborg, H. v.: Encyclopedia of Cryptography and Security. Berlin: Springer, Parr, C.; Pelzl, J.: Understanding Cryptography, A Textbook for Students and Practitioners. Heidelberg: Springer, Andreas Ahrens 114
3 Classification of the Field of Cryptology (1) Cryptography Symmetric Ciphers Asymmetric Ciphers Block Ciphers Stream Ciphers The majority of today s protocols are hybrid schemes, i.e., the use both symmetric ciphers (e.g., for encryption and message authentication) and asymmetric ciphers (e.g., for key exchange and digital signature). Andreas Ahrens 115
4 Classification of the Field of Cryptology (2) Symmetric Algorithms two parties have an encryption and decryption method for which they share a secret key Asymmetric (or Public-Key) Algorithms consist of a secret key (as in symmetric cryptography) as well as a public key Hybrid Schemes symmetric ciphers (e.g., for encryption and message authentication) and asymmetric ciphers (e.g., for key exchange and digital signature). Andreas Ahrens 116
5 Symmetric Cryptography Alternative names: private-key, single-key or secret-key cryptography Oscar (bad guy) Alice (good) x Unsecure channel (e.g. Internet) x Bob (good) Problem Statement: 1) Alice and Bob would like to communicate via an unsecure channel (e.g., WLAN or Internet). 2) A malicious third party Oscar (the bad guy) has channel access but should not be able to understand the communication. Andreas Ahrens 117
6 Symmetric Cryptography (to be cont.) Solution: Encryption with symmetric cipher. Oscar obtains only ciphertext y, that looks like random bits Syntax: Oscar (bad guy) y x is the plaintext y is the ciphertext K is called the key Alice (good) x Encryption e( ) y Unsecure channel (e.g. Internet) y Decryption d( ) x Bob (good) K K Key Generator Secure Channel Andreas Ahrens 118
7 Symmetric Cryptography (to be cont.) Symmetric Cryptography: Encryption equation y = e K (x) Decryption equation x = d K (y) Encryption and decryption are inverse operations if the same key K is used on both sides: d K (y) = d K (e K (x)) = x The key must be transmitted via a secure channel between Alice and Bob. The secure channel can be realized, e.g., by manually installing the key for the Wi-Fi Protected Access (WPA) protocol. However, the system is only secure if an attacker does not learn the key K! The problem of secure communication is reduced to secure transmission and storage of the key K. Andreas Ahrens 119
8 Substitution Cipher (1) Historical cipher Idea: replace each plaintext letter by a fixed other letter. Plaintext Ciphertext Example: A B C K D W ABBA would be encrypted as KDDK How secure is the Substitution Cipher? Let s have a look at how often the letter appear in the alphabet (Letter Frequency Analysis) Andreas Ahrens 120
9 Substitution Cipher (2) How secure is the Substitution Cipher? Let s have a look at how often the letter appear in the alphabet (Letter Frequency Analysis) Letter Frequency Analysis Letters have very different frequencies in the English language The frequency of plaintext letters is preserved in the ciphertext For Example: e is the most common letter in English; almost 13% of all letters in a typical English text are e In Practice: not only frequencies of individual letters can be used for an attack, but also the frequency of letter pairs (i.e., th is very common in English) Andreas Ahrens 121
10 Cryptoanalysis Attacks against cryptographic system: Bribing, blackmailing etc. can be used to obtain a secret key. Kerckhoff s Principle is paramount in modern cryptography: A cryptosystem should be secure even if the attacker (Oscar) knows all details about the system, with the exception of the secret key. The system should be secure when the attacker knows the encryption and decryption algorithms. Andreas Ahrens 122
11 Short Introduction to Modular Arithmetic Why do we need to study modular arithmetic? Important for asymmetric cryptography (RSA, elliptic curves, etc.) Most cryptosystems are based on sets of numbers that are discrete (sets with integers are particularly useful) finite (i.e., if we only compute with a finely many numbers) It is crucial to have an operation which keeps the numbers within limits, i.e., after addition and multiplication they should never leave the set. Let s have a look! Andreas Ahrens 123
12 Short Introduction to Modular Arithmetic (to be cont.) Modulo Operation Let a, r, m be integers and m > 0. We write a r mod m if (r-a) is divisible by m or if m divides a-r m is called the modulus and r is called the remainder It is always possible to write a = q m + r for 0 r < m with the quotient q and the remainder r. Examples: Let a = 11 and m = 9 : 11 2 mod 9 (11 = ) Let a = 19 and m = 9 : 19 1 mod 9 (19 = ) Andreas Ahrens 124
13 Short Introduction to Modular Arithmetic (to be cont.) How do we perform modular division? First, note that rather than performing a division, we prefer to multiply by the inverse. The inverse a -1 of a number a is defined such that: a a -1 1 mod m The inverse of 7 mod 9 is 4 since 7 x mod 9. How is the inverse compute? The multiplicative inverse of a number a mod m only exists if and only if: gcd (a, m) = 1 (gcd, greatest common divisor) (note that in the example above gcd(7, 9) = 1, so that the inverse of 7 exists modulo 9) Andreas Ahrens 125
14 Short Introduction to Modular Arithmetic (to be cont.) Modular Arithmetic There is the neutral element 0 with respect to addition, i.e., for all a a + 0 a mod m For all a, there is always an additive inverse element a such that a + (-a) 0 mod m There is the neutral element 1 with respect to multiplication, i.e., for all a a x 1 a mod m The multiplicative inverse a -1 is defined such that a x a -1 1 mod m Andreas Ahrens 126
15 Shift Cipher Replaces each plaintext letter by another one. Replacement rule: Take letter that follows after k positions in the alphabet Needs mapping from letters numbers: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Example for k = 7 Plaintext = ATTACK = 0, 19, 19, 0, 2, 10 Ciphertext = HAAHJR = 7, 0, 0, 7, 9, 17 Note that the letters wrap around at the end of the alphabet, which can mathematically be expressed as reduction modulo 26, e.g., = 26 0 mod 26 Andreas Ahrens 127
16 Shift Cipher (to be cont.) Mathematical description of the cipher Let k, x, y ε {0,1,, 25} Encryption: y = e k (x) x + k mod 26 Decryption: x = d k (x) y - k mod 26 How secure is the shift cipher? Exhaustive key search (key space is only 26!) Letter frequency analysis, similar to attack against substitution cipher Andreas Ahrens 128
17 Affine Cipher Extension of the shift cipher: rather than just adding the key to the plaintext, we also multiply by the key Key consists of two parts: k = (a, b) Let k, x, y ε {0,1,, 25} Encryption: y = e k (x) a x + b mod 26 Decryption: x = d k (x) a -1 (y b) mod 26 Since the inverse of a is needed for inversion, we can only use values for a for which: gcd(a, 26) = 1. There are 12 values for a that fulfill this condition a ε {1,3,5,7,9,11,15,17,19,21,23,25} Again, several attacks are possible, including: Exhaustive key search and letter frequency analysis, similar to the attack against the substitution cipher Andreas Ahrens 129
18 Affine Cipher (to be cont.) Example Let the key be k = (a,b) = (9,13) Plaintext = ATTACK = 0, 19, 19, 0, 2, 10 Ciphertext = NCCNFZ = 13, 2, 2, 13, 5, 25 Andreas Ahrens 130
19 Short Introduction to Modular Arithmetic (to be cont.) Modular Reduction Example: We want to compute 3 7 mod 7 (note that exponentiation is extremely important in public-key cryptography). 1. Approach: Exponentiation followed by modular reduction Example: 3 7 = mod 7 the intermediate result is 2187 even though we know that the final result can t be larger than 6. Andreas Ahrens 131
20 Short Introduction to Modular Arithmetic (to be cont.) 2. Approach: Exponentiation with intermediate modular reduction Example: 3 7 = = 27 x 81 At this point we reduce the intermediate results 27 modulo 7 and 81 mod = = 27 x 81 6 x 4 mod 7 6 x 4 = 24 3 mod 7 We can perform all these multiplications without pocket calculator, whereas mentally computing 3 7 = 2187 is a bit challenging for most of us For most algorithms it is advantageous to reduce intermediate results as soon as possible. Andreas Ahrens 132
21 RSA Cryptosystem Martin Hellman and Whitfield Diffie published their landmark publickey paper in 1976 Asymmetric RSA cryptosystem (Ronald Rivest, Adi Shamir and Leonard Adleman, 1977) Up to now, RSA is the most widely used asymmetric cryptosystem RSA is mainly used for two applications Transport of (i.e., symmetric) keys Digital signatures Andreas Ahrens 133
22 RSA Cryptosystem (to be cont.) RSA operations are done over the integer ring Z n (i.e., arithmetic modulo n), where n = p q, with p, q being large primes Encryption and decryption are simply exponentiations in the ring Encryption and Decryption Given the public key k pub = (n,e) and the private key k pr = d we write (x, y ε Z n ) y = e kpub (x) x e mod n x = d kpr (y) y d mod n We call e kpub () the encryption and d kpr (y) the decryption operation. In practice x, y, n and d are very long integer numbers ( 1024 bits). The security of the scheme relies on the fact that it is hard to derive the private exponent d given the public-key (n, e). Andreas Ahrens 134
23 RSA Cryptosystem (to be cont.) Key Generation Like all asymmetric schemes, RSA has set-up phase during which the private and public keys are computed Algorithm: RSA Key Generation Output: public key: k pub = (n,e) and private key k pr = d 1. Choose two large primes p, q 2. Compute n = p q 3. Compute Φ(n) = (p-1) (q-1) 4. Select the public exponent e ε {1, 2,, Φ(n)-1} such that gcd(e, Φ(n) ) = 1 5. Compute the private key d such that d e 1 mod Φ(n) 6. Result: public key k pub = (n,e) and private key k pr = d Remarks: Choosing two large, distinct primes p, q (in Step 1) is non-trivial gcd(e, Φ(n)) = 1 ensures that e has an inverse and, thus, that there is always a private key d Andreas Ahrens 135
24 RSA Cryptosystem (to be cont.) Example ALICE Bob Message x = 4 1. Choose p = 3 and q = Compute n = p q = Φ(n) = (3-1) (11-1) = Chose e = 3 5. d e -1 7 mod 20 k pub = (n,e) = (33,3) y = x e mod 33 y = 31 y d = = x mod 33 Andreas Ahrens 136
Understanding 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 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 28, 2010 These slides were
More informationDigital Communications. Basic Concepts in Cryptography
Basic Concepts in Cryptography Baltic Summer School Technical Informatics & Information Technology (BaSoTi) Vilnius (Lithuania) July/August 2013 Prof. Dr.-Ing. habil. Andreas Ahrens Communications Signal
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 informationUNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering. Introduction to Cryptography ECE 597XX/697XX. Part 1.
UNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering Introduction to Cryptography ECE 597XX/697XX Part 1 Introduction Israel Koren ECE597/697 Koren Part.1.1 Course Outline I. Introduction
More informationKey Exchange. Secure Software Systems
1 Key Exchange 2 Challenge Exchanging Keys &!"#h%&'() & & 1 2 6(6 1) 2 15! $ The more parties in communication, the more keys that need to be securely exchanged " # Do we have to use out-of-band methods?
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 informationUnderstanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl. Chapter 6 Introduction to Public-Key Cryptography
Understanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 6 Introduction to Public-Key Cryptography ver. November 18, 2010 These
More informationDigital Communications. Concepts in Cryptography
Concepts in Cryptography Baltic Summer School Technical Informatics & Information Technology (BaSoTi) Riga (Latvia) July/August 2014 Prof. Dr.-Ing. habil. Andreas Ahrens Communications Signal Processing
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 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 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 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 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 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 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 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 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 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 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 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 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 informationUnderstanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl. Chapter 6 Introduction to Public-Key Cryptography
Understanding Cryptography A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 6 Introduction to Public-Key Cryptography ver. November 18, 2010 These
More informationA SIGNATURE ALGORITHM BASED ON DLP AND COMPUTING SQUARE ROOTS
A SIGNATURE ALGORITHM BASED ON DLP AND COMPUTING SQUARE ROOTS Ounasser Abid 1 and Omar Khadir 2 1, 2 Laboratory of Mathematics, Cryptography and Mechanics, FSTM University Hassan II of Casablanca, Morocco
More informationA nice outline of the RSA algorithm and implementation can be found at:
Cryptography Lab: RSA Encryption and Decryption Lab Objectives: After this lab, the students should be able to Explain the simple concepts of encryption and decryption to protect information in transmission.
More informationCOMM1003. Information Theory. Dr. Wassim Alexan Spring Lecture 4
COMM1003 Information Theory Dr. Wassim Alexan Spring 2018 Lecture 4 Cryptology Cryptology is the most general term and it splits into two parts: Cryptography and Cryptanalysis Cryptography is the science
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 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 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 informationSome Stuff About Crypto
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
More informationNetwork Security. Chapter 4 Public Key Cryptography. Public Key Cryptography (4) Public Key Cryptography
Chair for Network Architectures and Services Department of Informatics TU München Prof. Carle Encryption/Decryption using Public Key Cryptography Network Security Chapter 4 Public Key Cryptography However,
More informationCryptosystems. Truong Tuan Anh CSE-HCMUT
Cryptosystems Truong Tuan Anh CSE-HCMUT anhtt@hcmut.edu.vn 2 In This Lecture Cryptography Cryptosystem: Definition Simple Cryptosystem Shift cipher Substitution cipher Affine cipher Cryptanalysis Cryptography
More informationChair for Network Architectures and Services Department of Informatics TU München Prof. Carle. Network Security
Chair for Network Architectures and Services Department of Informatics TU München Prof. Carle Network Security Chapter 2 Basics 2.2 Public Key Cryptography Encryption/Decryption using Public Key Cryptography
More informationThe Application of Elliptic Curves Cryptography in Embedded Systems
The Application of Elliptic Curves Cryptography in Embedded Systems Wang Qingxian School of Computer Science and Engineering University of Electronic Science and Technology China Introduction to Cryptography
More informationTECHNISCHE UNIVERSITEIT EINDHOVEN Faculty of Mathematics and Computer Science Exam Cryptology, Tuesday 31 October 2017
Faculty of Mathematics and Computer Science Exam Cryptology, Tuesday 31 October 2017 Name : TU/e student number : Exercise 1 2 3 4 5 6 total points Notes: Please hand in this sheet at the end of the exam.
More informationDiffie-Hellman Protocol as a Symmetric Cryptosystem
IJCSNS International Journal of Computer Science and Network Security, VOL.18 No.7, July 2018 33 Diffie-Hellman Protocol as a Symmetric Cryptosystem Karel Burda, Brno University of Technology, Brno, Czech
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 Cryptanalysis
http://www.di.ens.fr/ pnguyen INRIA and École normale supérieure, Paris, France MPRI, 2010 Outline 1 Introduction Asymmetric Cryptology Course Overview 2 Textbook RSA 3 Euclid s Algorithm Applications
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 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 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 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 informationCS Network Security. Nasir Memon Polytechnic University Module 7 Public Key Cryptography. RSA.
CS 393 - Network Security Nasir Memon Polytechnic University Module 7 Public Key Cryptography. RSA. Course Logistics Homework 2 revised. Due next Tuesday midnight. 2/26,28/02 Module 7 - Pubic Key Crypto
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 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 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 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 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 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 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 informationNumber Theory and RSA Public-Key Encryption
Number Theory and RSA Public-Key Encryption Dr. Natarajan Meghanathan Associate Professor of Computer Science Jackson State University E-mail: natarajan.meghanathan@jsums.edu CIA Triad: Three Fundamental
More informationThe Beta Cryptosystem
Bulletin of Electrical Engineering and Informatics Vol. 4, No. 2, June 2015, pp. 155~159 ISSN: 2089-3191 155 The Beta Cryptosystem Chandrashekhar Meshram Department of Mathematics, RTM Nagpur University,
More informationSide-Channel Attacks on RSA with CRT. Weakness of RSA Alexander Kozak Jared Vanderbeck
Side-Channel Attacks on RSA with CRT Weakness of RSA Alexander Kozak Jared Vanderbeck What is RSA? As we all know, RSA (Rivest Shamir Adleman) is a really secure algorithm for public-key cryptography.
More informationENCRYPTION USING LESTER HILL CIPHER ALGORITHM
ENCRYPTION USING LESTER HILL CIPHER ALGORITHM Thangarasu.N Research Scholar in Department of Computer Science Bharathiar University,Coimbatore Dr.Arul Lawrence SelvaKumar Dean & Professor, Department of
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 informationPublic-Key Cryptography. Professor Yanmin Gong Week 3: Sep. 7
Public-Key Cryptography Professor Yanmin Gong Week 3: Sep. 7 Outline Key exchange and Diffie-Hellman protocol Mathematical backgrounds for modular arithmetic RSA Digital Signatures Key management Problem:
More informationC - Cryptography
Coordinating unit: 270 - FIB - Barcelona School of Informatics Teaching unit: 749 - MAT - Department of Mathematics Academic year: Degree: 2018 BACHELOR'S DEGREE IN INFORMATICS ENGINEERING (Syllabus 2010).
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 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 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 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 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 informationCPSC 467b: Cryptography and Computer Security
CPSC 467b: Cryptography and Computer Security Michael J. Fischer Lecture 7 January 30, 2012 CPSC 467b, Lecture 7 1/44 Public-key cryptography RSA Factoring Assumption Computing with Big Numbers Fast Exponentiation
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 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 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 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 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 information- 0 - CryptoLib: Cryptography in Software John B. Lacy 1 Donald P. Mitchell 2 William M. Schell 3 AT&T Bell Laboratories ABSTRACT
- 0 - CryptoLib: Cryptography in Software John B. Lacy 1 Donald P. Mitchell 2 William M. Schell 3 AT&T Bell Laboratories ABSTRACT With the capacity of communications channels increasing at the current
More informationTopics. Number Theory Review. Public Key Cryptography
Public Key Cryptography Topics 1. Number Theory Review 2. Public Key Cryptography 3. One-Way Trapdoor Functions 4. Diffie-Helman Key Exchange 5. RSA Cipher 6. Modern Steganography Number Theory Review
More informationIntroduction. Cambridge University Press Mathematics of Public Key Cryptography Steven D. Galbraith Excerpt More information
1 Introduction Cryptography is an interdisciplinary field of great practical importance. The subfield of public key cryptography has notable applications, such as digital signatures. The security of a
More informationCrypto CS 485/ECE 440/CS 585 Fall 2017
Crypto CS 485/ECE 440/CS 585 Fall 2017 SSL/TLS Secure Sockets Layer, Transport Layer Security Web (HTTPS), email, any application based on sockets Key ideas Authentication Secure key exchange End-to-end
More informationPublic-Key Cryptography
Computer Security Spring 2008 Public-Key Cryptography Aggelos Kiayias University of Connecticut A paradox Classic cryptography (ciphers etc.) Alice and Bob share a short private key using a secure channel.
More informationPrime Field over Elliptic Curve Cryptography for Secured Message Transaction
Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology ISSN 2320 088X IMPACT FACTOR: 5.258 IJCSMC,
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 informationDavenport University ITS Lunch and Learn February 2, 2012 Sneden Center Meeting Hall Presented by: Scott Radtke
Davenport University ITS Lunch and Learn February 2, 2012 Sneden Center Meeting Hall Presented by: Scott Radtke A discussion on the mathematics behind coding and decoding using RSA Public-Key Cryptography.
More information10.1 Introduction 10.2 Asymmetric-Key Cryptography Asymmetric-Key Cryptography 10.3 RSA Cryptosystem
[Part 2] Asymmetric-Key Encipherment Asymmetric-Key Cryptography To distinguish between two cryptosystems: symmetric-key and asymmetric-key; To discuss the RSA cryptosystem; To introduce the usage of asymmetric-key
More informationRSA. Public Key CryptoSystem
RSA Public Key CryptoSystem DIFFIE AND HELLMAN (76) NEW DIRECTIONS IN CRYPTOGRAPHY Split the Bob s secret key K to two parts: K E, to be used for encrypting messages to Bob. K D, to be used for decrypting
More informationICT 6541 Applied Cryptography. Hossen Asiful Mustafa
ICT 6541 Applied Cryptography Hossen Asiful Mustafa Basic Communication Alice talking to Bob Alice Bob 2 Eavesdropping Eve listening the conversation Alice Bob 3 Secure Communication Eve listening the
More informationUnderstanding Cryptography by Christof Paar and Jan Pelzl. Chapter 9 Elliptic Curve Cryptography
Understanding Cryptography by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 9 Elliptic Curve Cryptography ver. February 2nd, 2015 These slides were prepared by Tim Güneysu, Christof Paar
More informationIntroduction to Cryptography Lecture 7
Introduction to Cryptography Lecture 7 Public-Key Encryption: El-Gamal, RSA Benny Pinkas page 1 1 Public key encryption Alice publishes a public key PK Alice. Alice has a secret key SK Alice. Anyone knowing
More informationC - Cryptography
Coordinating unit: 270 - FIB - Barcelona School of Informatics Teaching unit: 749 - MAT - Department of Mathematics Academic year: Degree: 2017 BACHELOR'S DEGREE IN INFORMATICS ENGINEERING (Syllabus 2010).
More informationApplications of The Montgomery Exponent
Applications of The Montgomery Exponent Shay Gueron 1,3 1 Dept. of Mathematics, University of Haifa, Israel (shay@math.haifa.ac.il) Or Zuk 2,3 2 Dept. of Physics of Complex Systems, Weizmann Institute
More informationLECTURE NOTES ON PUBLIC- KEY CRYPTOGRAPHY. (One-Way Functions and ElGamal System)
Department of Software The University of Babylon LECTURE NOTES ON PUBLIC- KEY CRYPTOGRAPHY (One-Way Functions and ElGamal System) By College of Information Technology, University of Babylon, Iraq Samaher@itnet.uobabylon.edu.iq
More informationLecture 2 Algorithms with numbers
Advanced Algorithms Floriano Zini Free University of Bozen-Bolzano Faculty of Computer Science Academic Year 2013-2014 Lecture 2 Algorithms with numbers 1 RSA Algorithm Why does RSA work? RSA is based
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 informationJournal of Computer Engineering & Technology (JCET) ISSN (Print), ISSN (Online), Volume 1, Issue 1, July-December (2013)
JOURNAL OF COMPUTER ENGINEERING & TECHNOLOGY (JCET) JCET I A E M E ISSN 2347-3908 (Print) ISSN 2347-3916 (Online) Volume 1, Issue 1, July-December (2013), pp.10-17 IAEME: http://www.iaeme.com/jcet.asp
More informationIntroduction to Medical Computing
CS 2125 Introduction to Medical Computing Stephen M. Watt The University of Western Ontario Topic 3 Cryptography University of Western Ontario CS 2125. Stephen M. Watt Cryptography Some things should be
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, 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 informationOther Topics in Cryptography. Truong Tuan Anh
Other Topics in Cryptography Truong Tuan Anh 2 Outline Public-key cryptosystem Cryptographic hash functions Signature schemes Public-Key Cryptography Truong Tuan Anh CSE-HCMUT 4 Outline Public-key cryptosystem
More informationPUBLIC KEY CRYPTO. Anwitaman DATTA SCSE, NTU Singapore CX4024. CRYPTOGRAPHY & NETWORK SECURITY 2018, Anwitaman DATTA
PUBLIC KEY CRYPTO Anwitaman DATTA SCSE, NTU Singapore Acknowledgement: The following lecture slides are based on, and uses material from the text book Cryptography and Network Security (various eds) by
More informationIntroduction to Cryptography Lecture 7
Introduction to Cryptography Lecture 7 El Gamal Encryption RSA Encryption Benny Pinkas page 1 1 Public key encryption Alice publishes a public key PK Alice. Alice has a secret key SK Alice. Anyone knowing
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 informationUNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering. Introduction to Cryptography ECE 597XX/697XX
UNIVERSITY OF MASSACHUSETTS Dept. of Electrical & Computer Engineering Introduction to Cryptography ECE 597XX/697XX Part 10 Digital Signatures Israel Koren ECE597/697 Koren Part.10.1 Content of this part
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 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 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 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 informationIntro to Public Key Cryptography Diffie & Hellman Key Exchange
Intro to Public Key Cryptography Diffie & Hellman Key Exchange Course Summary Introduction Stream & Block Ciphers Block Ciphers Modes (ECB,CBC,OFB) Advanced Encryption Standard (AES) Message Authentication
More information