Applied Cryptography Public Key Algorithms
|
|
- Pierce Richard
- 8 years ago
- Views:
Transcription
1 Applied Cryptography Public Key Algorithms Sape J. Mullender Huygens Systems Research Laboratory Universiteit Twente Enschede 1
2 Public Key Cryptography Independently invented by Whitfield Diffie & Martin Hellmann and Ralph Merkle in 1976 Only three algorithms appear to work well: RSA, ElGamal, Rabin Chosen plaintext attack trivial: the encryption key is public 2
3 Knapsack Algorithm No longer secure, but still interesting Given a set of weights (all different), find a subset with a given weight. Given a set of values M 1,..., M n, and a sum S, find b 1,..., b n, (b i {0, 1}) such that n S = b i M i Solving this is NP hard. i=1 3
4 Knapsack Algorithm The plaintext is the string of b i and specifies which weights to put in the knapsack. The key is the list of weights. The ciphertext is the resulting sum. The algorithm relies on there being two knapsacks, one solvable in linear time, the other not. The easy one is modifiable into the hard one. The public key is the hard one. The easy one is used to decrypt. 4
5 Superincreasing Knapsack If the list of weights increases so fast that each subsequent weight weighs more than all the previous ones together, we have a superincreasing knapsack. With such weights, the knapsack problem is easy to solve: Take the total weight, compare to the largest weight. If greater, then that weight must be included, substract from total and proceed with the next weight. If the total weight becomes zero in this process, the problem is solved. If not, there is no solution. 5
6 Normal Knapsacks If the weights are not superincreasing, the problem becomes hard, essentially only solvable by trial and error. For n weights, there are 2 n sets of weights to be tried. Add one weight and finding the solution takes twice as long. 6
7 Creating a Knapsack Pair We begin by creating a superincreasing knapsack W = {W 1,..., W k } and construct a normal one, by defining a modulus n > k 1 W i and a multiplier m that is co-prime with n (gcd(n, m) = 1). The new weights w = {w 1,..., w k } are calculated by w i = W i m mod n. The sequence W, together with n, and m is the private key, the sequence w is the public one. contain at least 250 items. Real knapsacks should 7
8 Encryption To encrypt a message, break it up into blocks of k bits and compute the total weight of the knapsack using weights w (a one bit indicates presence, a zero bit absence of the corresponding weight). 8
9 Decryption Multiply each of the total weights by m 1 mod n and solve the superincreasing knapsack problem to recover the weights (and the bits). See example on p. 464/465. 9
10 Security The Knapsack algorithm has been broken by Shamir and Zippel (± 1982). They found ways to reconstruct the superincreasing knapsack from the original one. Most variations on the knapsack algorithm have been broken by techniques very similar to those of Shamir and Zippel. 10
11 RSA Named after Rivest, Shamir and Adleman this one is nice and simple and quite secure to boot. This is how it works: Choose two big primes p and q and use its product n as the modulus of the algorithm. Also choose e and d so that e d 1(mod φ(n)). This is Euler s totient function again. Remember that φ(p q) = (p 1) (q 1), and note that d e 1 (mod φ(n)) The public key is (n, e), the private key is (n, d). Encryption: c = m e mod n Decryption: m = c d mod n, 11
12 Because c d mod n = (m e mod n) d mod n = (m e ) d mod n = m e d mod n = m φ(n)+1 mod n = m m φ(n) mod n = m mod n 12
13 Speed RSA is a thousand times slower than DES. Choosing a small e helps (e.g., 3, 17, or (just two one bits)). 13
14 Security Depends on the difficulty of factoring n. equivalent to this. Guessing φ(n) is The largest product of primes ever factored had 129 digits. Progress in factoring is constantly made, but at a rate of a few digits per year. Choosing n to have 300 digits or more (1000 bits or more) will keep the number theorists busy for quite some years. If p and q are probabilistic primes, and they happen not to be, encryption and decryption won t work properly. You may or may not notice. In any case, the probabilty of p and q not being prime can easily be made small enough that you won t have to worry about it. 14
15 There is much more about attacks in the book, but time is currently our enemy. Read up on it if you re interested. 15
16 Rabin Depends on the difficulty of finding modular square roots which is just as hard as factoring. Choose n = p q where p and q are large primes and p, q 3 mod 4. p and q are the private key, n is the public key. Encryption: c = m 2 mod n Decryption is more cumbersome... 16
17 Decryption Let a = q(q 1 mod p) and b = p(p 1 mod q) m 1 = c (p+1)/4 mod p m 2 = (p c (p+1)/4 ) mod p m 3 = c (q+1)/4 mod q m 4 = (q c (q+1)/4 ) mod q M 1 = (am 1 + bm 3 ) mod n M 3 = (am 2 + bm 3 ) mod n M 2 = (am 1 + bm 4 ) mod n M 4 = (am 2 + bm 4 ) mod n One of M 1,..., M 4 is the plaintext message. Redundancy will reveal which. Williams invented refinements that eliminate having to choose one of four possible solutions. 17
18 El Gamal ElGamal depends of the difficulty of finding logarithms in a finite field (finding x, such that x a y(mod n)). Choose p prime and g, x less than p. Calculate y = g x mod p. The public key is (y, g, p). The secret key is (x, g, p). 18
19 Signing with ElGamal 1. Choose random k 2. Compute a = g k mod p 3. Use the extended Euclidean algorithm to solve for b in M = (xa + kb) mod (p 1) 4. The signature is (a, b); k must be kept secret. To verify, confirm that y a a b g M mod p. Note that k can be used to recover x, so it must be kept just as secret as the secret key itself. It s best to discard k immediately after signing. 19
20 Encrypting with ElGamal 1. Choose random k co-prime with p 1 2. Compute a = g k mod p and b = y k M mod p 3. The ciphertext is (a, b) (it s twice the size of the plaintext) To decrypt: M = b a x mod p 20
21 Patents All these public-key systems are patented (in the US) with the exception of ElGamal. It has not yet been tested whether these patents stand up in court. 21
The Mathematics of the RSA Public-Key Cryptosystem
The Mathematics of the RSA Public-Key Cryptosystem Burt Kaliski RSA Laboratories ABOUT THE AUTHOR: Dr Burt Kaliski is a computer scientist whose involvement with the security industry has been through
More informationCryptography and Network Security Chapter 9
Cryptography and Network Security Chapter 9 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 9 Public Key Cryptography and RSA Every Egyptian received two names,
More informationCSCE 465 Computer & Network Security
CSCE 465 Computer & Network Security Instructor: Dr. Guofei Gu http://courses.cse.tamu.edu/guofei/csce465/ Public Key Cryptogrophy 1 Roadmap Introduction RSA Diffie-Hellman Key Exchange Public key and
More informationPublic Key (asymmetric) Cryptography
Public-Key Cryptography UNIVERSITA DEGLI STUDI DI PARMA Dipartimento di Ingegneria dell Informazione Public Key (asymmetric) Cryptography Luca Veltri (mail.to: luca.veltri@unipr.it) Course of Network Security,
More informationOverview of Public-Key Cryptography
CS 361S Overview of Public-Key Cryptography Vitaly Shmatikov slide 1 Reading Assignment Kaufman 6.1-6 slide 2 Public-Key Cryptography public key public key? private key Alice Bob Given: Everybody knows
More informationSecure Network Communication Part II II Public Key Cryptography. Public Key Cryptography
Kommunikationssysteme (KSy) - Block 8 Secure Network Communication Part II II Public Key Cryptography Dr. Andreas Steffen 2000-2001 A. Steffen, 28.03.2001, KSy_RSA.ppt 1 Secure Key Distribution Problem
More informationLecture Note 5 PUBLIC-KEY CRYPTOGRAPHY. Sourav Mukhopadhyay
Lecture Note 5 PUBLIC-KEY CRYPTOGRAPHY Sourav Mukhopadhyay Cryptography and Network Security - MA61027 Modern/Public-key cryptography started in 1976 with the publication of the following paper. W. Diffie
More informationAn Introduction to the RSA Encryption Method
April 17, 2012 Outline 1 History 2 3 4 5 History RSA stands for Rivest, Shamir, and Adelman, the last names of the designers It was first published in 1978 as one of the first public-key crytographic systems
More informationNotes on Network Security Prof. Hemant K. Soni
Chapter 9 Public Key Cryptography and RSA Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared by both sender and receiver if this key is disclosed communications
More informationPrinciples of Public Key Cryptography. Applications of Public Key Cryptography. Security in Public Key Algorithms
Principles of Public Key Cryptography Chapter : Security Techniques Background Secret Key Cryptography Public Key Cryptography Hash Functions Authentication Chapter : Security on Network and Transport
More informationShor s algorithm and secret sharing
Shor s algorithm and secret sharing Libor Nentvich: QC 23 April 2007: Shor s algorithm and secret sharing 1/41 Goals: 1 To explain why the factoring is important. 2 To describe the oldest and most successful
More informationElements of Applied Cryptography Public key encryption
Network Security Elements of Applied Cryptography Public key encryption Public key cryptosystem RSA and the factorization problem RSA in practice Other asymmetric ciphers Asymmetric Encryption Scheme Let
More informationNetwork Security. Computer Networking Lecture 08. March 19, 2012. HKU SPACE Community College. HKU SPACE CC CN Lecture 08 1/23
Network Security Computer Networking Lecture 08 HKU SPACE Community College March 19, 2012 HKU SPACE CC CN Lecture 08 1/23 Outline Introduction Cryptography Algorithms Secret Key Algorithm Message Digest
More informationA SOFTWARE COMPARISON OF RSA AND ECC
International Journal Of Computer Science And Applications Vol. 2, No. 1, April / May 29 ISSN: 974-13 A SOFTWARE COMPARISON OF RSA AND ECC Vivek B. Kute Lecturer. CSE Department, SVPCET, Nagpur 9975549138
More informationOutline. Computer Science 418. Digital Signatures: Observations. Digital Signatures: Definition. Definition 1 (Digital signature) Digital Signatures
Outline Computer Science 418 Digital Signatures Mike Jacobson Department of Computer Science University of Calgary Week 12 1 Digital Signatures 2 Signatures via Public Key Cryptosystems 3 Provable 4 Mike
More informationCRYPTOGRAPHY IN NETWORK SECURITY
ELE548 Research Essays CRYPTOGRAPHY IN NETWORK SECURITY AUTHOR: SHENGLI LI INSTRUCTOR: DR. JIEN-CHUNG LO Date: March 5, 1999 Computer network brings lots of great benefits and convenience to us. We can
More informationCIS 5371 Cryptography. 8. Encryption --
CIS 5371 Cryptography p y 8. Encryption -- Asymmetric Techniques Textbook encryption algorithms In this chapter, security (confidentiality) is considered in the following sense: All-or-nothing secrecy.
More informationCryptography and Network Security
Cryptography and Network Security Fifth Edition by William Stallings Chapter 9 Public Key Cryptography and RSA Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared
More informationSecure File Transfer Using USB
International Journal of Scientific and Research Publications, Volume 2, Issue 4, April 2012 1 Secure File Transfer Using USB Prof. R. M. Goudar, Tushar Jagdale, Ketan Kakade, Amol Kargal, Darshan Marode
More informationLecture 3: One-Way Encryption, RSA Example
ICS 180: Introduction to Cryptography April 13, 2004 Lecturer: Stanislaw Jarecki Lecture 3: One-Way Encryption, RSA Example 1 LECTURE SUMMARY We look at a different security property one might require
More information1720 - Forward Secrecy: How to Secure SSL from Attacks by Government Agencies
1720 - Forward Secrecy: How to Secure SSL from Attacks by Government Agencies Dave Corbett Technical Product Manager Implementing Forward Secrecy 1 Agenda Part 1: Introduction Why is Forward Secrecy important?
More informationLukasz Pater CMMS Administrator and Developer
Lukasz Pater CMMS Administrator and Developer EDMS 1373428 Agenda Introduction Why do we need asymmetric ciphers? One-way functions RSA Cipher Message Integrity Examples Secure Socket Layer Single Sign
More informationMathematics of Internet Security. Keeping Eve The Eavesdropper Away From Your Credit Card Information
The : Keeping Eve The Eavesdropper Away From Your Credit Card Information Department of Mathematics North Dakota State University 16 September 2010 Science Cafe Introduction Disclaimer: is not an internet
More informationPrimality Testing and Factorization Methods
Primality Testing and Factorization Methods Eli Howey May 27, 2014 Abstract Since the days of Euclid and Eratosthenes, mathematicians have taken a keen interest in finding the nontrivial factors of integers,
More informationSoftware Implementation of Gong-Harn Public-key Cryptosystem and Analysis
Software Implementation of Gong-Harn Public-key Cryptosystem and Analysis by Susana Sin A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master
More informationEmbedding more security in digital signature system by using combination of public key cryptography and secret sharing scheme
International Journal of Computer Sciences and Engineering Open Access Research Paper Volume-4, Issue-3 E-ISSN: 2347-2693 Embedding more security in digital signature system by using combination of public
More informationSECURITY IMPROVMENTS TO THE DIFFIE-HELLMAN SCHEMES
www.arpapress.com/volumes/vol8issue1/ijrras_8_1_10.pdf SECURITY IMPROVMENTS TO THE DIFFIE-HELLMAN SCHEMES Malek Jakob Kakish Amman Arab University, Department of Computer Information Systems, P.O.Box 2234,
More informationCS 758: Cryptography / Network Security
CS 758: Cryptography / Network Security offered in the Fall Semester, 2003, by Doug Stinson my office: DC 3122 my email address: dstinson@uwaterloo.ca my web page: http://cacr.math.uwaterloo.ca/~dstinson/index.html
More informationThe application of prime numbers to RSA encryption
The application of prime numbers to RSA encryption Prime number definition: Let us begin with the definition of a prime number p The number p, which is a member of the set of natural numbers N, is considered
More informationPublic Key Cryptography. c Eli Biham - March 30, 2011 258 Public Key Cryptography
Public Key Cryptography c Eli Biham - March 30, 2011 258 Public Key Cryptography Key Exchange All the ciphers mentioned previously require keys known a-priori to all the users, before they can encrypt
More information7! Cryptographic Techniques! A Brief Introduction
7! Cryptographic Techniques! A Brief Introduction 7.1! Introduction to Cryptography! 7.2! Symmetric Encryption! 7.3! Asymmetric (Public-Key) Encryption! 7.4! Digital Signatures! 7.5! Public Key Infrastructures
More informationNetwork Security. Gaurav Naik Gus Anderson. College of Engineering. Drexel University, Philadelphia, PA. Drexel University. College of Engineering
Network Security Gaurav Naik Gus Anderson, Philadelphia, PA Lectures on Network Security Feb 12 (Today!): Public Key Crypto, Hash Functions, Digital Signatures, and the Public Key Infrastructure Feb 14:
More informationPublic Key Cryptography: RSA and Lots of Number Theory
Public Key Cryptography: RSA and Lots of Number Theory Public vs. Private-Key Cryptography We have just discussed traditional symmetric cryptography: Uses a single key shared between sender and receiver
More informationLUC: A New Public Key System
LUC: A New Public Key System Peter J. Smith a and Michael J. J. Lennon b a LUC Partners, Auckland UniServices Ltd, The University of Auckland, Private Bag 92019, Auckland, New Zealand. b Department of
More informationA Factoring and Discrete Logarithm based Cryptosystem
Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 11, 511-517 HIKARI Ltd, www.m-hikari.com A Factoring and Discrete Logarithm based Cryptosystem Abdoul Aziz Ciss and Ahmed Youssef Ecole doctorale de Mathematiques
More informationSoftware Tool for Implementing RSA Algorithm
Software Tool for Implementing RSA Algorithm Adriana Borodzhieva, Plamen Manoilov Rousse University Angel Kanchev, Rousse, Bulgaria Abstract: RSA is one of the most-common used algorithms for public-key
More informationRSA Question 2. Bob thinks that p and q are primes but p isn t. Then, Bob thinks Φ Bob :=(p-1)(q-1) = φ(n). Is this true?
RSA Question 2 Bob thinks that p and q are primes but p isn t. Then, Bob thinks Φ Bob :=(p-1)(q-1) = φ(n). Is this true? Bob chooses a random e (1 < e < Φ Bob ) such that gcd(e,φ Bob )=1. Then, d = e -1
More informationRSA Attacks. By Abdulaziz Alrasheed and Fatima
RSA Attacks By Abdulaziz Alrasheed and Fatima 1 Introduction Invented by Ron Rivest, Adi Shamir, and Len Adleman [1], the RSA cryptosystem was first revealed in the August 1977 issue of Scientific American.
More informationNetwork Security. Chapter 2 Basics 2.2 Public Key Cryptography. Public Key Cryptography. 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 2 Basics 2.2 Public Key Cryptography
More informationMathematical Model Based Total Security System with Qualitative and Quantitative Data of Human
Int Jr of Mathematics Sciences & Applications Vol3, No1, January-June 2013 Copyright Mind Reader Publications ISSN No: 2230-9888 wwwjournalshubcom Mathematical Model Based Total Security System with Qualitative
More informationPublic Key Cryptography and RSA. Review: Number Theory Basics
Public Key Cryptography and RSA Murat Kantarcioglu Based on Prof. Ninghui Li s Slides Review: Number Theory Basics Definition An integer n > 1 is called a prime number if its positive divisors are 1 and
More informationDigital Signatures. Meka N.L.Sneha. Indiana State University. nmeka@sycamores.indstate.edu. October 2015
Digital Signatures Meka N.L.Sneha Indiana State University nmeka@sycamores.indstate.edu October 2015 1 Introduction Digital Signatures are the most trusted way to get documents signed online. A digital
More informationPublic Key Cryptography Overview
Ch.20 Public-Key Cryptography and Message Authentication I will talk about it later in this class Final: Wen (5/13) 1630-1830 HOLM 248» give you a sample exam» Mostly similar to homeworks» no electronic
More informationNetwork Security. Abusayeed Saifullah. CS 5600 Computer Networks. These slides are adapted from Kurose and Ross 8-1
Network Security Abusayeed Saifullah CS 5600 Computer Networks These slides are adapted from Kurose and Ross 8-1 Public Key Cryptography symmetric key crypto v requires sender, receiver know shared secret
More informationMATH 168: FINAL PROJECT Troels Eriksen. 1 Introduction
MATH 168: FINAL PROJECT Troels Eriksen 1 Introduction In the later years cryptosystems using elliptic curves have shown up and are claimed to be just as secure as a system like RSA with much smaller key
More informationAdvanced Cryptography
Family Name:... First Name:... Section:... Advanced Cryptography Final Exam July 18 th, 2006 Start at 9:15, End at 12:00 This document consists of 12 pages. Instructions Electronic devices are not allowed.
More informationCIS 6930 Emerging Topics in Network Security. Topic 2. Network Security Primitives
CIS 6930 Emerging Topics in Network Security Topic 2. Network Security Primitives 1 Outline Absolute basics Encryption/Decryption; Digital signatures; D-H key exchange; Hash functions; Application of hash
More information159.334 Computer Networks. Network Security 1. Professor Richard Harris School of Engineering and Advanced Technology
Network Security 1 Professor Richard Harris School of Engineering and Advanced Technology Presentation Outline Overview of Identification and Authentication The importance of identification and Authentication
More informationCryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur
Cryptography and Network Security Department of Computer Science and Engineering Indian Institute of Technology Kharagpur Module No. # 01 Lecture No. # 05 Classic Cryptosystems (Refer Slide Time: 00:42)
More informationCS549: Cryptography and Network Security
CS549: Cryptography and Network Security by Xiang-Yang Li Department of Computer Science, IIT Cryptography and Network Security 1 Notice This lecture note (Cryptography and Network Security) is prepared
More informationSECURITY IN NETWORKS
SECURITY IN NETWORKS GOALS Understand principles of network security: Cryptography and its many uses beyond confidentiality Authentication Message integrity Security in practice: Security in application,
More informationCryptography and Network Security Chapter 10
Cryptography and Network Security Chapter 10 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 10 Other Public Key Cryptosystems Amongst the tribes of Central
More informationLecture 6 - Cryptography
Lecture 6 - Cryptography CSE497b - Spring 2007 Introduction Computer and Network Security Professor Jaeger www.cse.psu.edu/~tjaeger/cse497b-s07 Question 2 Setup: Assume you and I don t know anything about
More informationEXAM questions for the course TTM4135 - Information Security June 2010. Part 1
EXAM questions for the course TTM4135 - Information Security June 2010 Part 1 This part consists of 6 questions all from one common topic. The number of maximal points for every correctly answered question
More informationComputer Security: Principles and Practice
Computer Security: Principles and Practice Chapter 20 Public-Key Cryptography and Message Authentication First Edition by William Stallings and Lawrie Brown Lecture slides by Lawrie Brown Public-Key Cryptography
More informationLecture 13 - Basic Number Theory.
Lecture 13 - Basic Number Theory. Boaz Barak March 22, 2010 Divisibility and primes Unless mentioned otherwise throughout this lecture all numbers are non-negative integers. We say that A divides B, denoted
More informationCryptography: Authentication, Blind Signatures, and Digital Cash
Cryptography: Authentication, Blind Signatures, and Digital Cash Rebecca Bellovin 1 Introduction One of the most exciting ideas in cryptography in the past few decades, with the widest array of applications,
More informationNumber Theory and the RSA Public Key Cryptosystem
Number Theory and the RSA Public Key Cryptosystem Minh Van Nguyen nguyenminh2@gmail.com 05 November 2008 This tutorial uses to study elementary number theory and the RSA public key cryptosystem. A number
More informationCryptography and Network Security
Cryptography and Network Security Spring 2012 http://users.abo.fi/ipetre/crypto/ Lecture 7: Public-key cryptography and RSA Ion Petre Department of IT, Åbo Akademi University 1 Some unanswered questions
More informationAn Introduction to RSA Public-Key Cryptography
An Introduction to RSA Public-Key Cryptography David Boyhan August 5, 2008 According to the U.S. Census Bureau, in the 1st quarter of 2008, approximately $33 billion worth of retail sales were conducted
More informationPublic-Key Cryptanalysis
To appear in Recent Trends in Cryptography, I. Luengo (Ed.), Contemporary Mathematics series, AMS-RSME, 2008. Public-Key Cryptanalysis Phong Q. Nguyen Abstract. In 1976, Diffie and Hellman introduced the
More informationNumber Theory and Cryptography using PARI/GP
Number Theory and Cryptography using Minh Van Nguyen nguyenminh2@gmail.com 25 November 2008 This article uses to study elementary number theory and the RSA public key cryptosystem. Various commands will
More informationNetwork Security. Security Attacks. Normal flow: Interruption: 孫 宏 民 hmsun@cs.nthu.edu.tw Phone: 03-5742968 國 立 清 華 大 學 資 訊 工 程 系 資 訊 安 全 實 驗 室
Network Security 孫 宏 民 hmsun@cs.nthu.edu.tw Phone: 03-5742968 國 立 清 華 大 學 資 訊 工 程 系 資 訊 安 全 實 驗 室 Security Attacks Normal flow: sender receiver Interruption: Information source Information destination
More informationNetwork Security. HIT Shimrit Tzur-David
Network Security HIT Shimrit Tzur-David 1 Goals: 2 Network Security Understand principles of network security: cryptography and its many uses beyond confidentiality authentication message integrity key
More informationCapture Resilient ElGamal Signature Protocols
Capture Resilient ElGamal Signature Protocols Hüseyin Acan 1, Kamer Kaya 2,, and Ali Aydın Selçuk 2 1 Bilkent University, Department of Mathematics acan@fen.bilkent.edu.tr 2 Bilkent University, Department
More informationFactoring integers, Producing primes and the RSA cryptosystem Harish-Chandra Research Institute
RSA cryptosystem HRI, Allahabad, February, 2005 0 Factoring integers, Producing primes and the RSA cryptosystem Harish-Chandra Research Institute Allahabad (UP), INDIA February, 2005 RSA cryptosystem HRI,
More informationPeer-to-Peer Networks Anonymity (1st part) 8th Week
Peer-to-Peer Networks Anonymity (1st part) 8th Week Department of Computer Science 1 Motivation Society Free speech is only possible if the speaker does not suffer negative consequences Thus, only an anonymous
More informationSymmetric Key cryptosystem
SFWR C03: Computer Networks and Computer Security Mar 8-11 200 Lecturer: Kartik Krishnan Lectures 22-2 Symmetric Key cryptosystem Symmetric encryption, also referred to as conventional encryption or single
More informationTiming Attacks on software implementation of RSA
Timing Attacks on software implementation of RSA Project Report Harshman Singh 903-40-5260 singhha@cs.orst.edu June 07, 2004 Abstract Timing attacks enable an attacker to extract secret information from
More informationNEW DIGITAL SIGNATURE PROTOCOL BASED ON ELLIPTIC CURVES
NEW DIGITAL SIGNATURE PROTOCOL BASED ON ELLIPTIC CURVES Ounasser Abid 1, Jaouad Ettanfouhi 2 and Omar Khadir 3 1,2,3 Laboratory of Mathematics, Cryptography and Mechanics, Department of Mathematics, Fstm,
More informationFinal Exam. IT 4823 Information Security Administration. Rescheduling Final Exams. Kerberos. Idea. Ticket
IT 4823 Information Security Administration Public Key Encryption Revisited April 5 Notice: This session is being recorded. Lecture slides prepared by Dr Lawrie Brown for Computer Security: Principles
More informationReview of methods for secret sharing in cloud computing
Review of methods for secret sharing in cloud computing Dnyaneshwar Supe Amit Srivastav Dr. Rajesh S. Prasad Abstract:- Cloud computing provides various IT services. Many companies especially those who
More informationDigital Signature. Raj Jain. Washington University in St. Louis
Digital Signature Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 Jain@cse.wustl.edu Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-11/
More informationDigital signatures are one of the most important inventions/applications of modern cryptography.
CHAPTER 7: DIGITAL SIGNATURES Digital signatures are one of the most important inventions/applications of modern cryptography. Part VII Digital signatures The problem is how can a user sign (electronically)
More informationChapter 7: Network security
Chapter 7: Network security Foundations: what is security? cryptography authentication message integrity key distribution and certification Security in practice: application layer: secure e-mail transport
More informationOutline. CSc 466/566. Computer Security. 8 : Cryptography Digital Signatures. Digital Signatures. Digital Signatures... Christian Collberg
Outline CSc 466/566 Computer Security 8 : Cryptography Digital Signatures Version: 2012/02/27 16:07:05 Department of Computer Science University of Arizona collberg@gmail.com Copyright c 2012 Christian
More informationSecurity in communication networks
Security in communication networks by MARTIN E. HELLMAN Stanford University Stanford, California INTRODUCTION It may seem anomolous that electronic mail and other computer communication systems require
More informationNetwork Security. Omer Rana
Network Security Omer Rana CM0255 Material from: Cryptography Components Sender Receiver Plaintext Encryption Ciphertext Decryption Plaintext Encryption algorithm: Plaintext Ciphertext Cipher: encryption
More informationComputer Networks 1 (Mạng Máy Tính 1) Lectured by: Dr. Phạm Trần Vũ MEng. Nguyễn CaoĐạt
Computer Networks 1 (Mạng Máy Tính 1) Lectured by: Dr. Phạm Trần Vũ MEng. Nguyễn CaoĐạt 1 Lecture 11: Network Security Reference: Chapter 8 - Computer Networks, Andrew S. Tanenbaum, 4th Edition, Prentice
More informationAC76/AT76 CRYPTOGRAPHY & NETWORK SECURITY DEC 2014
Q.2a. Define Virus. What are the four phases of Viruses? In addition, list out the types of Viruses. A virus is a piece of software that can infect other programs by modifying them; the modification includes
More informationAn Introduction to Cryptography as Applied to the Smart Grid
An Introduction to Cryptography as Applied to the Smart Grid Jacques Benoit, Cooper Power Systems Western Power Delivery Automation Conference Spokane, Washington March 2011 Agenda > Introduction > Symmetric
More informationMulti-Layered Cryptographic Processor for Network Security
International Journal of Scientific and Research Publications, Volume 2, Issue 10, October 2012 1 Multi-Layered Cryptographic Processor for Network Security Pushp Lata *, V. Anitha ** * M.tech Student,
More informationNetwork Security [2] Plain text Encryption algorithm Public and private key pair Cipher text Decryption algorithm. See next slide
Network Security [2] Public Key Encryption Also used in message authentication & key distribution Based on mathematical algorithms, not only on operations over bit patterns (as conventional) => much overhead
More informationNumber Theory. Proof. Suppose otherwise. Then there would be a finite number n of primes, which we may
Number Theory Divisibility and Primes Definition. If a and b are integers and there is some integer c such that a = b c, then we say that b divides a or is a factor or divisor of a and write b a. Definition
More informationModule: Applied Cryptography. Professor Patrick McDaniel Fall 2010. CSE543 - Introduction to Computer and Network Security
CSE543 - Introduction to Computer and Network Security Module: Applied Cryptography Professor Patrick McDaniel Fall 2010 Page 1 Key Distribution/Agreement Key Distribution is the process where we assign
More information3-6 Toward Realizing Privacy-Preserving IP-Traceback
3-6 Toward Realizing Privacy-Preserving IP-Traceback The IP-traceback technology enables us to trace widely spread illegal users on Internet. However, to deploy this attractive technology, some problems
More informationVoteID 2011 Internet Voting System with Cast as Intended Verification
VoteID 2011 Internet Voting System with Cast as Intended Verification September 2011 VP R&D Jordi Puiggali@scytl.com Index Introduction Proposal Security Conclusions 2. Introduction Client computers could
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 Introduction to Cryptography What is cryptography?
More informationCh.9 Cryptography. The Graduate Center, CUNY.! CSc 75010 Theoretical Computer Science Konstantinos Vamvourellis
Ch.9 Cryptography The Graduate Center, CUNY! CSc 75010 Theoretical Computer Science Konstantinos Vamvourellis Why is Modern Cryptography part of a Complexity course? Short answer:! Because Modern Cryptography
More informationCenter for Internet Security. INTEGRATED INTELLIGENCE CENTER Technical White Paper William F. Pelgrin, CIS President and CEO
INTEGRATED INTELLIGENCE CENTER Technical White Paper William F. Pelgrin, CIS President and CEO Private and Public Key Cryptography and Ransomware December 2014 Authored by:ted Fischer (CIS) Security Operations
More informationAN IMPLEMENTATION OF HYBRID ENCRYPTION-DECRYPTION (RSA WITH AES AND SHA256) FOR USE IN DATA EXCHANGE BETWEEN CLIENT APPLICATIONS AND WEB SERVICES
HYBRID RSA-AES ENCRYPTION FOR WEB SERVICES AN IMPLEMENTATION OF HYBRID ENCRYPTION-DECRYPTION (RSA WITH AES AND SHA256) FOR USE IN DATA EXCHANGE BETWEEN CLIENT APPLICATIONS AND WEB SERVICES Kalyani Ganesh
More informationEXAM questions for the course TTM4135 - Information Security May 2013. Part 1
EXAM questions for the course TTM4135 - Information Security May 2013 Part 1 This part consists of 5 questions all from one common topic. The number of maximal points for every correctly answered question
More informationCryptography & Digital Signatures
Cryptography & Digital Signatures CS 594 Special Topics/Kent Law School: Computer and Network Privacy and Security: Ethical, Legal, and Technical Consideration Prof. Sloan s Slides, 2007, 2008 Robert H.
More informationHow To Know If A Message Is From A Person Or A Machine
The RSA Algorithm Evgeny Milanov 3 June 2009 In 1978, Ron Rivest, Adi Shamir, and Leonard Adleman introduced a cryptographic algorithm, which was essentially to replace the less secure National Bureau
More informationModeling and verification of security protocols
Modeling and verification of security protocols Part I: Basics of cryptography and introduction to security protocols Dresden University of Technology Martin Pitt martin@piware.de Paper and slides available
More informationCIS 433/533 - Computer and Network Security Public Key Crypto/ Cryptographic Protocols
CIS 433/533 - Computer and Network Security Public Key Crypto/ Cryptographic Protocols Professor Kevin Butler Winter 2010 Computer and Information Science Key Distribution/Agreement Key Distribution is
More informationIntroduction. Digital Signature
Introduction Electronic transactions and activities taken place over Internet need to be protected against all kinds of interference, accidental or malicious. The general task of the information technology
More informationDigital Signatures. Murat Kantarcioglu. Based on Prof. Li s Slides. Digital Signatures: The Problem
Digital Signatures Murat Kantarcioglu Based on Prof. Li s Slides Digital Signatures: The Problem Consider the real-life example where a person pays by credit card and signs a bill; the seller verifies
More informationMessage Authentication Codes
2 MAC Message Authentication Codes : and Cryptography Sirindhorn International Institute of Technology Thammasat University Prepared by Steven Gordon on 28 October 2013 css322y13s2l08, Steve/Courses/2013/s2/css322/lectures/mac.tex,
More informationPublic-key cryptography RSA
Public-key cryptography RSA NGUYEN Tuong Lan LIU Yi Master Informatique University Lyon 1 Objective: Our goal in the study is to understand the algorithm RSA, some existence attacks and implement in Java.
More information