Lecture IV : Cryptography, Fundamentals
|
|
- Rose Cain
- 5 years ago
- Views:
Transcription
1 Lecture IV : Cryptography, Fundamentals Internet Security: Principles & Practices John K. Zao, PhD (Harvard) SMIEEE Computer Science Department, National Chiao Tung University Spring 2012
2 Basic Principles Kerckhoff s Principle: Internet Security - Cryptography Basics 2 A cryptosystem should be secure even if everything about the system, except the key, is public knowledge. Shannon's Maxim: Your enemy knows your system!
3 Internet Security - Cryptography Basics 3 Outlines Basic Concepts Information Theoretic Cryptography Computational Difficult Cryptography One Way Functions One Way Trapdoor Functions Cyptanalytic Attacks Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
4 Internet Security - Cryptography Basics 4 Information Theoretic Cryptography Basic Cryptography Tenet Proper application of cryptography should make it infeasible for cryptanalysis to infer plaintext and/or crypto-keys using ciphertext, known-plaintext or chosen-plaintext attacks What does it mean by infeasible? What does it mean by infer? Information Theoretic Cryptography [Shannon 1949] Infeasible means Mathematically impossible (regardless of available resources) Cryptanalyst does not have enough information to decipher Infer means Obtaining partial/probabilistic information about plaintext
5 Internet Security - Cryptography Basics 5 Computational Difficult Cryptography Foundation of Modern Cryptography Infeasible means Computationally infeasible with existing technology & available resources Cryptanalyst does have enough information to decipher, but may not have time, machines or energy to crack the codes Infer means Obtaining partial/probabilistic information about plaintext Computationally difficult cryptosystems are based upon One-Way Functions One-Way Functions are functions that are easy to evaluate but hard to invert x f(x)
6 Internet Security - Cryptography Basics 6 Outlines Basic Concepts Information Theoretic Cryptography Computational Difficult Cryptography One Way Functions One Way Trapdoor Functions Cyptanalytic Attacks Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
7 7 One-Way Function Spring 2012 Internet Security - Cryptography Basics Definition : A one-to-one mapping x S, y S y = f (x) of which Forward Mapping f is computationally feasible Inverse Mapping f -1 is computationally infeasible Characteristics : Cryptographically Strong / Secure Inverse Infeasibility f -1 is computationally infeasible Collision Improbability Example : Given a, b S, P ( f (a) = f (b) ) #(S)/2 Modular Exponentiation Message Digest (Cryptographically Strong Hashing)
8 8 Spring 2012 One-Way Trapdoor Function Internet Security - Cryptography Basics Definition : A one-to-one parameterized mapping x S, y S y = f k (x) of which Question : Forward Mapping f k is computationally feasible if k is known Inverse Mapping f k -1 is Computationally infeasible if k is unknown, but Computationally feasible if k is known Does such function ever exist? Diffie and Hellman thought so! Diffie, W. and Hellman, M.E., New Directions in Cryptography, IEEE Transaction on Information Theory 22(6): , 1976.
9 Internet Security - Cryptography Basics 9 Outlines Basic Concepts Information Theoretic Cryptography Computational Difficult Cryptography One Way Functions One Way Trapdoor Functions Cyptanalytic Attacks Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
10 Attack Models When performing cryptanalytic attacks, we have to determine adversary s capability (Attack Model) and define a successful attack (Goal Model). Ciphertext-Only Attack (COA) Attackers have access only to a set of ciphertexts Known-Plaintext Attack (KPA) Attackers have samples of both the plaintext, and its encrypted version (ciphertext) Chosen-Plaintext Attack (CPA) Attackers have the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts Chosen-Ciphertext Attack (CCA) Internet Security - Cryptography Basics 10 Attackers have the capability to choose a ciphertext and obtaining its decryption under an unknown key
11 Internet Security - Cryptography Basics 11 Attack Goals Corresponding plaintext is deduced Part of plaintext or the whole plaintext of target ciphertext Unintended ciphertext/plaintext is generated One or more valid ciphertext/plaintext pair Users private keys are found Attackers can do anything. Also known as total break.
12 Example: Caesar Cipher Ciphertext-Only Attack (COA) Attacker gains one ciphertext. He can tries all 26 possible key (shift amount) to see if meaningful plaintext appears. Known-Plaintext Attack (KPA) Attacker gains several plaintext/ciphertext pair. He could easily find which one letter maps to the other. Chosen-Plaintext Attack (CPA) Attacker chooses one letter to be encrypted and retrieve the ciphertext. He could deduce the key from the ciphertext. Chosen-Ciphertext Attack (CCA) Work basically the same way since the operation is symmetric. Internet Security - Cryptography Basics 12
13 Ciphertext Attack Concept Internet Security - Cryptography Basics 13 Attempts to discover cipher key(s) or plaintext(s) from known ciphertext(s) Most common cipher attacks Definition Given ciphertext of N unknown plaintext under same unknown key c i = E k (m i ), i = [ 1..N ] Discover or infer key k or some subset(s) of plaintext { m i } Example Mono-alphabetic Cipher : encipher English text by mapping the alphabets to a chosen permutation { a, b, c, x, y, z } { e, r, p, h, g, m } Relatively difficult to break based on exhaustive key search (26! 1) Easy to break based on letter frequencies of English alphabets
14 Known Plaintext Attack Concept Internet Security - Cryptography Basics 14 Attempts to discover cipher key(s) or new plaintext(s) from known plaintext and ciphertext pairs Definition Given N pairs of known plaintext and ciphertext under same unknown key ( m i, c i = E k (m i ) ), i = [ 1..N ] Discover or infer key k or some new ciphertext-plaintext pair Example k or ( c N+1, m N+1 ) Key or plaintext discovery from special control messages Mono-alphabetic Cipher : Easy to break if known plaintext-ciphertext pairs contain all alphabets
15 Chosen Plaintext Attacks Concept Internet Security - Cryptography Basics 15 Attempts to discover cipher key(s) or new plaintext(s) from knowing corresponding plaintexts of chosen ciphertexts Definition Given ciphertext of N chosen plaintext under same unknown key ( m i (chosen), c i = E k (m i ) ), i = [ 1..N ] Discover or infer key k or some new ciphertext-plaintext pair Example ( c N+1, m N+1 ) Mono-alphabetic Cipher : Easy to break by having the corresponding ciphertext of plaintext abcd xyz or any sub-string of 25 alphabets Challenge-Response Attacks SSL Million Message Attack
16 Internet Security - Cryptography Basics 16 Outlines Basic Concepts Cyptanalytic Attacks Information Theoretic Crypto Computational Difficult Crypto One Way Functions One Way Trapdoor Functions Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
17 17 Spring 2012 Internet Security - Cryptography Basics Wonderful World of Modular Arithmetic Integers : = { -2, -1, 0, 1, 2, } Addition (+) Identity : z, 0 z + 0 = z Inverse : z, -z z + (-z) = 0 Multiplication (x) Identity : z, 1 z x 1 = z Inverse :? is a (commutative) ring
18 18 Spring 2012 Internet Security - Cryptography Basics Modular Arithmetic Addition (+) a, b, n ( a + b ) mod n remainder ( a + b ) n Ex: ( ) mod 10 = 1
19 Modular Arithmetic Multiplication ( ) Internet Security - Cryptography Basics 19 a, b, n ( a b ) mod n remainder ( a b ) n Ex: ( 2 7 ) mod 10 = 4
20 Internet Security - Cryptography Basics 20 Outlines Basic Concepts Cyptanalytic Attacks Information Theoretic Crypto Computational Difficult Crypto One Way Functions One Way Trapdoor Functions Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
21 21 Finite Fields Spring 2012 Internet Security - Cryptography Basics Addition (+) Identity : z p, 0 p ( z + 0 ) mod p = z Inverse : z p, -z p z + (-z) = 0 Multiplication ( ) Identity : z p, 1 p z 1 = z Inverse : z p, z -1 p z z -1 = 0
22 22 Spring 2012 Internet Security - Cryptography Basics Finite Field, p Integer Prime-Modulo Sets : p = { 0, 1, 2, p-1 } Addition (+) Identity : z p, 0 p ( z + 0 ) mod p = z Inverse : z p, -z p z + (-z) = 0 Ex: ( ) mod 5 = 0 Multiplication ( ) Identity : z p, 1 p z 1 = z Inverse : z p, z -1 p z z -1 = 1 Ex: ( 3 2 ) mod 5 = 1! p is a FINITE FIELD
23 Internet Security - Cryptography Basics 23 Outlines Basic Concepts Cyptanalytic Attacks Information Theoretic Crypto Computational Difficult Crypto One Way Functions One Way Trapdoor Functions Mathematical Foundation Modular Arithmetic Finite Fields Computationally Hard Problems
24 Internet Security - Cryptography Basics 24 Hard Problem : Discrete Logarithm Modular Exponentiation (x y ) Definition : x, y, n x y mod p remainder ( x y ) n How about Inverse? z p, p is prime, Is there y p x y mod p = z? y is known as log x z (mod p) Discrete Logarithm Inverse of Modular Exponentiation Like factoring problem, discrete logarithm problem (DLP) is believed to be difficult. Thus, modular exponentiation is regarded as a one-way function, and used as the basis of several public-key cryptosystems. Yet, nobody admitted to have proven that DLP cannot be solved quickly.
25 Internet Security Cryptography Basics 25 Discrete Logarithm, Properties NOT all columns contain unique results! ONLY those share no common factor with n = 10 contain unique results. α x mod n α x+n mod n α x mod n = α x+κφ(n) mod n
26 NP-Intermediate Problems Internet Security - Cryptography Basics 26 It s a problem in NP but not known to be in P or NP-complete If P NP then there exist problems in NP that are neither P nor NPcomplete. These problems are called NP-intermediate problems. - Ladner Examples: Graph Isomorphism Discrete Logarithm Integer Factorization
27 Best Algorithms Internet Security - Cryptography Basics 27 Both integer factoring and discrete logarithm can be solved by sub-exponential algorithms Integer Factoring General_number_field_sieve: L n [1/3, (64/9) 1/3 ]= L n [1/3, ] Special_number_field_sieve: L n [1/3, (32/9) 1/3 ]=L n [1/3, ] Discrete Logarithms Index_calculus_algorithm: L 2 m[1/3,c] 0<c<1.587 for F * 2m, let n=2m
Introduction 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 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 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 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 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 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 informationFoundations of Cryptology
Multimedia Security Mauro Barni University of Siena Cryptography Cryptography is the art or science of keeping messages secret; the word cryptography is derived from Greek and literally means secret (crypto-)
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 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 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 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 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 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 informationClassical Encryption Techniques. CSS 322 Security and Cryptography
Classical Encryption Techniques CSS 322 Security and Cryptography Contents Terminology and Models Requirements, Services and Attacks Substitution Ciphers Caesar, Monoalphabetic, Polyalphabetic, One-time
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 informationIntroduction to Cryptology. Lecture 2
Introduction to Cryptology Lecture 2 Announcements Access to Canvas? 2 nd Edition vs. 1 st Edition HW1 due on Tuesday, 2/7 Discrete Math Readings/Quizzes on Canvas due on Tuesday, 2/14 Agenda Last time:
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 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 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 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 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 information1-7 Attacks on Cryptosystems
1-7 Attacks on Cryptosystems In the present era, not only business but almost all the aspects of human life are driven by information. Hence, it has become imperative to protect useful information from
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 informationLecture III : Communication Security Mechanisms
Lecture III : Communication Security Mechanisms Internet Security: Principles & Practices John K. Zao, PhD (Harvard) SMIEEE Computer Science Department, National Chiao Tung University 2 X.800 : Security
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 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 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 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 informationMath236 Discrete Maths with Applications
Math236 Discrete Maths with Applications P. Ittmann UKZN, Pietermaritzburg Semester 1, 2012 Ittmann (UKZN PMB) Math236 2012 1 / 1 Block Ciphers A block cipher is an encryption scheme in which the plaintext
More informationSecurity Models: Proofs, Protocols and Certification
Security Models: Proofs, Protocols and Certification Florent Autrau - Yassine Lakhnech - Jean-Louis Roch Master-2 Security, Cryptology and Coding of Information Systems ENSIMAG/Grenoble-INP UJF Grenoble
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 informationKey Exchange. References: Applied Cryptography, Bruce Schneier Cryptography and Network Securiy, Willian Stallings
Key Exchange References: Applied Cryptography, Bruce Schneier Cryptography and Network Securiy, Willian Stallings Outlines Primitives Root Discrete Logarithm Diffie-Hellman ElGamal Shamir s Three Pass
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 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 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 informationIntroduction to Cryptographic Systems. Asst. Prof. Mihai Chiroiu
Introduction to Cryptographic Systems Asst. Prof. Mihai Chiroiu Vocabulary In cryptography, cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Decryption
More informationPrivate-Key Encryption
Private-Key Encryption Ali El Kaafarani Mathematical Institute Oxford University 1 of 32 Outline 1 Historical Ciphers 2 Probability Review 3 Security Definitions: Perfect Secrecy 4 One Time Pad (OTP) 2
More informationCS408 Cryptography & Internet Security
CS408 Cryptography & Internet Security Lectures 16, 17: Security of RSA El Gamal Cryptosystem Announcement Final exam will be on May 11, 2015 between 11:30am 2:00pm in FMH 319 http://www.njit.edu/registrar/exams/finalexams.php
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 informationIntroduction to Cryptography. In the News: Hacker exposes embassies'
T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography EECE 412 Copyright 2004-2007 Konstantin Beznosov In the News: Hacker exposes embassies' e-mail A Swedish security
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 information2/7/2013. CS 472 Network and System Security. Mohammad Almalag Lecture 2 January 22, Introduction To Cryptography
CS 472 Network and System Security Mohammad Almalag malmalag@cs.odu.edu Lecture 2 January 22, 2013 Introduction To Cryptography 1 Definitions Cryptography = the science (art) of encryption Cryptanalysis
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 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 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 informationIntroduction to Cryptography
T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography EECE 412 Session 3 Copyright 2004 Konstantin Beznosov Session Outline Historical background Caesar and Vigenère
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 informationS. Erfani, ECE Dept., University of Windsor Network Security. 2.3-Cipher Block Modes of operation
2.3-Cipher Block Modes of operation 2.3-1 Model of Conventional Cryptosystems The following figure, which is on the next page, illustrates the conventional encryption process. The original plaintext is
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 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 informationT H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A. Introduction to Cryptography
T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography 1 Module Outline Historical background Classic ciphers One-time pad The Random Oracle model Random functions: Hash
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 informationCS573 Data Privacy and Security. Cryptographic Primitives and Secure Multiparty Computation. Li Xiong
CS573 Data Privacy and Security Cryptographic Primitives and Secure Multiparty Computation Li Xiong Outline Cryptographic primitives Symmetric Encryption Public Key Encryption Secure Multiparty Computation
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 informationCryptanalysis. Ed Crowley
Cryptanalysis Ed Crowley 1 Topics Cryptanalysis History Modern Cryptanalysis Characterization of Cryptanalysis Attacks Attack Types 2 Cryptanalysis Science of cracking ciphers and codes, decoding secrets,
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 informationCPSC 467: Cryptography and Computer Security
CPSC 467: Cryptography and Computer Michael J. Fischer Lecture 4 September 11, 2017 CPSC 467, Lecture 4 1/23 Analyzing Confidentiality of Cryptosystems Secret ballot elections Information protection Adversaries
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 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 informationIntroduction to Cryptography CS 136 Computer Security Peter Reiher October 9, 2014
Introduction to Cryptography CS 136 Computer Security Peter Reiher October 9, 2014 Page 1 Outline What is data encryption? Cryptanalysis Basic encryption methods Substitution ciphers Permutation ciphers
More informationCryptography ThreeB. Ed Crowley. Fall 08
Cryptography ThreeB Ed Crowley Fall 08 Cryptanalysis History Modern Cryptanalysis Characterization of Cryptanalysis Attacks Attack Types Cryptanalysis. Science of cracking ciphers and codes, decoding secrets,
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 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 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 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 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 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 informationEEC-484/584 Computer Networks
EEC-484/584 Computer Networks Lecture 23 wenbing@ieee.org (Lecture notes are based on materials supplied by Dr. Louise Moser at UCSB and Prentice-Hall) Outline 2 Review of last lecture Introduction to
More informationLecture 6 - Cryptography
Lecture 6 - Cryptography CMPSC 443 - Spring 2012 Introduction Computer and Network Security Professor Jaeger www.cse.psu.edu/~tjaeger/cse443-s12 Question Setup: Assume you and I donʼt know anything about
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 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 informationB) Symmetric Ciphers. B.a) Fundamentals B.b) Block Ciphers B.c) Stream Ciphers
1 B) Symmetric Ciphers B.a) Fundamentals B.b) Block Ciphers B.c) Stream Ciphers B.a) Fundamentals 2 B.1 Definition 3 A mapping Enc: P K C for which ϕ k := Enc(,k): P C is bijective for each k K is called
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 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 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 information(8) Cryptanalysis. Close-up of the rotors in a Fialka cipher machine
(8) Cryptanalysis Definition: Close-up of the rotors in a Fialka cipher machine Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") : is the study of methods for obtaining
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 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 informationHardware Design and Software Simulation for Four Classical Cryptosystems
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 21 (2013 ) 500 505 The 4 th International Conference on Emerging Ubiquitous Systems and Pervasive Networks (EUSPN-2013)
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 informationSubstitution Ciphers, continued. 3. Polyalphabetic: Use multiple maps from the plaintext alphabet to the ciphertext alphabet.
Substitution Ciphers, continued 3. Polyalphabetic: Use multiple maps from the plaintext alphabet to the ciphertext alphabet. Non-periodic case: Running key substitution ciphers use a known text (in a standard
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 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 informationComputational Security, Stream and Block Cipher Functions
Computational Security, Stream and Block Cipher Functions 18 March 2019 Lecture 3 Most Slides Credits: Steve Zdancewic (UPenn) 18 March 2019 SE 425: Communication and Information Security 1 Topics for
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 informationClassical Encryption Techniques
Encryption CSS322: Security and Cryptography Sirindhorn International Institute of Technology Thammasat University Prepared by Steven Gordon on 29 December 2011 CSS322Y11S2L02, Steve/Courses/2011/S2/CSS322/Lectures/classical.tex,
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 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 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 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 informationOutline Basics of Data Encryption CS 239 Computer Security January 24, 2005
Outline Basics of Data Encryption CS 239 Computer Security January 24, 2005 What is data encryption? Basic encryption mechanisms Stream and block ciphers Characteristics of good ciphers Page 1 Page 2 Data
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 informationECEN 5022 Cryptography
Introduction University of Colorado Spring 2008 Historically, cryptography is the science and study of secret writing (Greek: kryptos = hidden, graphein = to write). Modern cryptography also includes such
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 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 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 informationCSCE 813 Internet Security Symmetric Cryptography
CSCE 813 Internet Security Symmetric Cryptography Professor Lisa Luo Fall 2017 Previous Class Essential Internet Security Requirements Confidentiality Integrity Authenticity Availability Accountability
More informationCSC/ECE 774 Advanced Network Security
Computer Science CSC/ECE 774 Advanced Network Security Topic 2. Network Security Primitives CSC/ECE 774 Dr. Peng Ning 1 Outline Absolute basics Encryption/Decryption; Digital signatures; D-H key exchange;
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 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 information