# Proofs in Cryptography

Save this PDF as:

Size: px
Start display at page:

## Transcription

5 2.3 Semantic Security against CPA 2.4 PRGs 2.5 PRFs 2.6 Block Ciphers or Pseudorandom Functions 2.7 Message Authentication Codes 2.8 Collision-resistant Hash functions 3 Public Key Cryptography 3.1 CCA 3.2 OWFs 3.3 Signature schemes 4 Advanced Topics* 4.1 Hybrid Arguments* 4.2 Randomized Self Reductions* 5 Exercises 1. Prove that flipping bits of a PRG is still secure. Given a PRG G that is secure (i.e., satisfies the indistinguishability game) construct a PRG G (x) := b 1 b 2 b n where (b 1 b 2 b n ) = G(x), the output of G on x and b is the bit b flipped. Show that G is still secure. To do this, construct an adversary B that given a string decides whether it is from G (i.e., G evaluated on a random input) or completely random with probability better than 1/2. To do this, it uses A who claims to break the distinguishability test for G. Therefore, B must somehow use its challenge string w and concoct a string for A to help it decide whether it is random or not. 2. Prove that permuting the bits of a PRG is still secure. Given a PRG G, and a permutation π (and its inverse permutation π 1 ) 5, consider G π (x) = (b π(1) b π(2) b π(n) ) where (b 1 b 2 b n ) = G(x). Show, largely along the lines of Exercise 1 that G π is secure. In particular if π is the identity this is trivial. If π(i) = n + 1 i, i.e., G simply reverses the bits of the output, the proof is covered in the section. You need to use π Prove that a l-expanding PRG is a small domain PRF. This is HW1 problem 7b. The formal statement can be found on the website. Here, to prove the security, given an adversary A for the small domain PRF, you are required to construct an adversary B that interacts with the PRG-Challenger and distinguishes whether the string given were random or pseudorandom. Remember, B must present a PRF-Challenger Chal to A and ensure that he is faithfully simulating either a random function or a pseudorandom function. 5 I.e., π 1 (π(i)) = i for all i. 5

### Introduction to Security Proof of Cryptosystems

Introduction to Security Proof of Cryptosystems D. J. Guan November 16, 2007 Abstract Provide proof of security is the most important work in the design of cryptosystems. Problem reduction is a tool to

### Lecture 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

### Midterm Exam Solutions CS161 Computer Security, Spring 2008

Midterm Exam Solutions CS161 Computer Security, Spring 2008 1. To encrypt a series of plaintext blocks p 1, p 2,... p n using a block cipher E operating in electronic code book (ECB) mode, each ciphertext

### 1 Pseudorandom Permutations

Theoretical Foundations of Cryptography Lecture 9 Georgia Tech, Spring 2010 PRPs, Symmetric Encryption 1 Pseudorandom Permutations Instructor: Chris Peikert Scribe: Pushkar Tripathi In the first part of

### Lecture 15 - Digital Signatures

Lecture 15 - Digital Signatures Boaz Barak March 29, 2010 Reading KL Book Chapter 12. Review Trapdoor permutations - easy to compute, hard to invert, easy to invert with trapdoor. RSA and Rabin signatures.

### Cryptography CS 555. Topic 3: One-time Pad and Perfect Secrecy. CS555 Spring 2012/Topic 3 1

Cryptography CS 555 Topic 3: One-time Pad and Perfect Secrecy CS555 Spring 2012/Topic 3 1 Outline and Readings Outline One-time pad Perfect secrecy Limitation of perfect secrecy Usages of one-time pad

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.

### Lecture 9 - Message Authentication Codes

Lecture 9 - Message Authentication Codes Boaz Barak March 1, 2010 Reading: Boneh-Shoup chapter 6, Sections 9.1 9.3. Data integrity Until now we ve only been interested in protecting secrecy of data. However,

### Lecture 10: CPA Encryption, MACs, Hash Functions. 2 Recap of last lecture - PRGs for one time pads

CS 7880 Graduate Cryptography October 15, 2015 Lecture 10: CPA Encryption, MACs, Hash Functions Lecturer: Daniel Wichs Scribe: Matthew Dippel 1 Topic Covered Chosen plaintext attack model of security MACs

### PUBLIC KEY ENCRYPTION

PUBLIC KEY ENCRYPTION http://www.tutorialspoint.com/cryptography/public_key_encryption.htm Copyright tutorialspoint.com Public Key Cryptography Unlike symmetric key cryptography, we do not find historical

### CSA E0 235: Cryptography (29/03/2015) (Extra) Lecture 3

CSA E0 235: Cryptography (29/03/2015) Instructor: Arpita Patra (Extra) Lecture 3 Submitted by: Mayank Tiwari Review From our discussion of perfect secrecy, we know that the notion of perfect secrecy has

### Victor Shoup Avi Rubin. fshoup,rubing@bellcore.com. Abstract

Session Key Distribution Using Smart Cards Victor Shoup Avi Rubin Bellcore, 445 South St., Morristown, NJ 07960 fshoup,rubing@bellcore.com Abstract In this paper, we investigate a method by which smart

### Ch.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

### Lecture 5 - CPA security, Pseudorandom functions

Lecture 5 - CPA security, Pseudorandom functions Boaz Barak October 2, 2007 Reading Pages 82 93 and 221 225 of KL (sections 3.5, 3.6.1, 3.6.2 and 6.5). See also Goldreich (Vol I) for proof of PRF construction.

### Introduction. 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

### 1 Message Authentication

Theoretical Foundations of Cryptography Lecture Georgia Tech, Spring 200 Message Authentication Message Authentication Instructor: Chris Peikert Scribe: Daniel Dadush We start with some simple questions

### 1 Signatures vs. MACs

CS 120/ E-177: Introduction to Cryptography Salil Vadhan and Alon Rosen Nov. 22, 2006 Lecture Notes 17: Digital Signatures Recommended Reading. Katz-Lindell 10 1 Signatures vs. MACs Digital signatures

### 1 Construction of CCA-secure encryption

CSCI 5440: Cryptography Lecture 5 The Chinese University of Hong Kong 10 October 2012 1 Construction of -secure encryption We now show how the MAC can be applied to obtain a -secure encryption scheme.

### MTAT.07.003 Cryptology II. Digital Signatures. Sven Laur University of Tartu

MTAT.07.003 Cryptology II Digital Signatures Sven Laur University of Tartu Formal Syntax Digital signature scheme pk (sk, pk) Gen (m, s) (m,s) m M 0 s Sign sk (m) Ver pk (m, s)? = 1 To establish electronic

### Overview of Cryptographic Tools for Data Security. Murat Kantarcioglu

UT DALLAS Erik Jonsson School of Engineering & Computer Science Overview of Cryptographic Tools for Data Security Murat Kantarcioglu Pag. 1 Purdue University Cryptographic Primitives We will discuss the

### Provably Secure Cryptography: State of the Art and Industrial Applications

Provably Secure Cryptography: State of the Art and Industrial Applications Pascal Paillier Gemplus/R&D/ARSC/STD/Advanced Cryptographic Services French-Japanese Joint Symposium on Computer Security Outline

### cryptography s642 computer security adam everspaugh

cryptography s642 adam everspaugh ace@cs.wisc.edu computer security today Cryptography intro Crypto primitives / Symmetric and asymmetric crypto / MACs / Digital signatures / Key exchange Provable security

### Computational Soundness of Symbolic Security and Implicit Complexity

Computational Soundness of Symbolic Security and Implicit Complexity Bruce Kapron Computer Science Department University of Victoria Victoria, British Columbia NII Shonan Meeting, November 3-7, 2013 Overview

### 1 Domain Extension for MACs

CS 127/CSCI E-127: Introduction to Cryptography Prof. Salil Vadhan Fall 2013 Reading. Lecture Notes 17: MAC Domain Extension & Digital Signatures Katz-Lindell Ÿ4.34.4 (2nd ed) and Ÿ12.0-12.3 (1st ed).

### Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption

Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption Ronald Cramer Victor Shoup December 12, 2001 Abstract We present several new and fairly practical public-key

### COM S 687 Introduction to Cryptography October 19, 2006

COM S 687 Introduction to Cryptography October 19, 2006 Lecture 16: Non-Malleability and Public Key Encryption Lecturer: Rafael Pass Scribe: Michael George 1 Non-Malleability Until this point we have discussed

### Security usually depends on the secrecy of the key, not the secrecy of the algorithm (i.e., the open design model!)

1 A cryptosystem has (at least) five ingredients: 1. 2. 3. 4. 5. Plaintext Secret Key Ciphertext Encryption algorithm Decryption algorithm Security usually depends on the secrecy of the key, not the secrecy

### Key Privacy for Identity Based Encryption

Key Privacy for Identity Based Encryption Internet Security Research Lab Technical Report 2006-2 Jason E. Holt Internet Security Research Lab Brigham Young University c 2006 Brigham Young University March

### Public-Key Encryption (Asymmetric Encryption)

Public-Key Encryption (Asymmetric Encryption) Summer School, Romania 2014 Marc Fischlin 13. Oktober 2010 Dr.Marc Fischlin Kryptosicherheit 1 The story so far (Private-Key Crypto) Alice establish secure

### Asymmetric Encryption. With material from Jonathan Katz, David Brumley, and Dave Levin

Asymmetric Encryption With material from Jonathan Katz, David Brumley, and Dave Levin Warmup activity Overview of asymmetric-key crypto Intuition for El Gamal and RSA And intuition for attacks Digital

### Non-Black-Box Techniques In Crytpography. Thesis for the Ph.D degree Boaz Barak

Non-Black-Box Techniques In Crytpography Introduction Thesis for the Ph.D degree Boaz Barak A computer program (or equivalently, an algorithm) is a list of symbols a finite string. When we interpret a

### 1 Digital Signatures. 1.1 The RSA Function: The eth Power Map on Z n. Crypto: Primitives and Protocols Lecture 6.

1 Digital Signatures A digital signature is a fundamental cryptographic primitive, technologically equivalent to a handwritten signature. In many applications, digital signatures are used as building blocks

### Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs

Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs Enes Pasalic University of Primorska Koper, 2014 Contents 1 Preface 3 2 Problems 4 2 1 Preface This is a

### Cryptography. Jonathan Katz, University of Maryland, College Park, MD 20742.

Cryptography Jonathan Katz, University of Maryland, College Park, MD 20742. 1 Introduction Cryptography is a vast subject, addressing problems as diverse as e-cash, remote authentication, fault-tolerant

MACs Message authentication and integrity Foundations of Cryptography Computer Science Department Wellesley College Table of contents Introduction MACs Constructing Secure MACs Secure communication and

### Chapter 10 Asymmetric-Key Cryptography

Chapter 10 Asymmetric-Key Cryptography Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.1 Chapter 10 Objectives To distinguish between two cryptosystems: symmetric-key

### SYMMETRIC ENCRYPTION. Mihir Bellare UCSD 1

SYMMETRIC ENCRYPTION Mihir Bellare UCSD 1 Syntax A symmetric encryption scheme SE = (K,E,D) consists of three algorithms: K and E may be randomized, but D must be deterministic. Mihir Bellare UCSD 2 Correct

### Outline. 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

### Lecture 2: Complexity Theory Review and Interactive Proofs

600.641 Special Topics in Theoretical Cryptography January 23, 2007 Lecture 2: Complexity Theory Review and Interactive Proofs Instructor: Susan Hohenberger Scribe: Karyn Benson 1 Introduction to Cryptography

### A Chosen Ciphertext Attack on RSA Optimal Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1 v2.0

A Chosen Ciphertext Attack on RSA Optimal Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1 v2.0 James Manger Telstra Research Laboratories, Level 7, 242 Exhibition Street, Melbourne 3000,

### Introduction to Cryptography

Introduction to Cryptography Part 2: public-key cryptography Jean-Sébastien Coron January 2007 Public-key cryptography Invented by Diffie and Hellman in 1976. Revolutionized the field. Each user now has

### Dr. 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?

### Hash Functions. Integrity checks

Hash Functions EJ Jung slide 1 Integrity checks Integrity vs. Confidentiality! Integrity: attacker cannot tamper with message! Encryption may not guarantee integrity! Intuition: attacker may able to modify

### Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #10 Symmetric Key Ciphers (Refer

### Identity-based Encryption with Post-Challenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks

Identity-based Encryption with Post-Challenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks Tsz Hon Yuen - Huawei, Singapore Ye Zhang - Pennsylvania State University, USA Siu Ming

### Technische Universität München Winter term 2010 Theoretische Informatik Dr. M. Luttenberger / A. Gaiser SOLUTION. Cryptography Endterm

Technische Universität München Winter term 2010 Theoretische Informatik Dr. M. Luttenberger / A. Gaiser SOLUTION Cryptography Endterm Last name: First name: Student ID no.: Signature: Code {A,..., Z} 6

### Asymmetric Cryptography. Mahalingam Ramkumar Department of CSE Mississippi State University

Asymmetric Cryptography Mahalingam Ramkumar Department of CSE Mississippi State University Mathematical Preliminaries CRT Chinese Remainder Theorem Euler Phi Function Fermat's Theorem Euler Fermat's Theorem

### 9/17/2015. Cryptography Basics. Outline. Encryption/Decryption. Cryptanalysis. Caesar Cipher. Mono-Alphabetic Ciphers

Cryptography Basics IT443 Network Security Administration Instructor: Bo Sheng Outline Basic concepts in cryptography system Secret cryptography Public cryptography Hash functions 1 2 Encryption/Decryption

### Network security and all ilabs

Network security and all ilabs Modern cryptography for communications security part 1 Benjamin Hof hof@in.tum.de Lehrstuhl für Netzarchitekturen und Netzdienste Fakultät für Informatik Technische Universität

### Security and Cryptography 1. Stefan Köpsell, Thorsten Strufe. Module 4: Basic Crypto, Stream Ciphers

Security and Cryptography 1 Stefan Köpsell, Thorsten Strufe Module 4: Basic Crypto, Stream Ciphers Disclaimer: Günter Schäfer, Mark Manulis, large parts from Dan Boneh Dresden, WS 16/17 Reprise from the

### 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

### The Order of Encryption and Authentication for Protecting Communications (Or: How Secure is SSL?)

The Order of Encryption and Authentication for Protecting Communications (Or: How Secure is SSL?) Hugo Krawczyk Abstract. We study the question of how to generically compose symmetric encryption and authentication

### Multi-Input Functional Encryption for Unbounded Arity Functions

Multi-Input Functional Encryption for Unbounded Arity Functions Saikrishna Badrinarayanan, Divya Gupta, Abhishek Jain, and Amit Sahai Abstract. The notion of multi-input functional encryption (MI-FE) was

### Leakage-Resilient Authentication and Encryption from Symmetric Cryptographic Primitives

Leakage-Resilient Authentication and Encryption from Symmetric Cryptographic Primitives Olivier Pereira Université catholique de Louvain ICTEAM Crypto Group B-1348, Belgium olivier.pereira@uclouvain.be

### Digital Signatures. Prof. Zeph Grunschlag

Digital Signatures Prof. Zeph Grunschlag (Public Key) Digital Signatures PROBLEM: Alice would like to prove to Bob, Carla, David,... that has really sent them a claimed message. E GOAL: Alice signs each

### Improved Online/Offline Signature Schemes

Improved Online/Offline Signature Schemes Adi Shamir and Yael Tauman Applied Math. Dept. The Weizmann Institute of Science Rehovot 76100, Israel {shamir,tauman}@wisdom.weizmann.ac.il Abstract. The notion

### Overview 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

### Computational Complexity: A Modern Approach

i Computational Complexity: A Modern Approach Draft of a book: Dated January 2007 Comments welcome! Sanjeev Arora and Boaz Barak Princeton University complexitybook@gmail.com Not to be reproduced or distributed

### 1 Formulating The Low Degree Testing Problem

6.895 PCP and Hardness of Approximation MIT, Fall 2010 Lecture 5: Linearity Testing Lecturer: Dana Moshkovitz Scribe: Gregory Minton and Dana Moshkovitz In the last lecture, we proved a weak PCP Theorem,

### Post-Quantum Cryptography #4

Post-Quantum Cryptography #4 Prof. Claude Crépeau McGill University http://crypto.cs.mcgill.ca/~crepeau/waterloo 185 ( 186 Attack scenarios Ciphertext-only attack: This is the most basic type of attack

### MESSAGE AUTHENTICATION IN AN IDENTITY-BASED ENCRYPTION SCHEME: 1-KEY-ENCRYPT-THEN-MAC

MESSAGE AUTHENTICATION IN AN IDENTITY-BASED ENCRYPTION SCHEME: 1-KEY-ENCRYPT-THEN-MAC by Brittanney Jaclyn Amento A Thesis Submitted to the Faculty of The Charles E. Schmidt College of Science in Partial

### Chapter 10 Asymmetric-Key Cryptography

Chapter 10 Asymmetric-Key Cryptography Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.1 Chapter 10 Objectives Present asymmetric-key cryptography. Distinguish

### CIS433/533 - Computer and Network Security Cryptography

CIS433/533 - Computer and Network Security Cryptography Professor Kevin Butler Winter 2011 Computer and Information Science A historical moment Mary Queen of Scots is being held by Queen Elizabeth and

### Lecture 9. Lecturer: Yevgeniy Dodis Spring 2012

CSCI-GA.3210-001 MATH-GA.2170-001 Introduction to Cryptography Macrh 21, 2012 Lecture 9 Lecturer: Yevgeniy Dodis Spring 2012 Last time we introduced the concept of Pseudo Random Function Family (PRF),

### Solving systems of linear equations over finite fields

Solving systems of linear equations over finite fields June 1, 2007 1 Introduction 2 3 4 Basic problem Introduction x 1 + x 2 + x 3 = 1 x 1 + x 2 = 1 x 1 + x 2 + x 4 = 1 x 2 + x 4 = 0 x 1 + x 3 + x 4 =

### Provable-Security Analysis of Authenticated Encryption in Kerberos

Provable-Security Analysis of Authenticated Encryption in Kerberos Alexandra Boldyreva Virendra Kumar Georgia Institute of Technology, School of Computer Science 266 Ferst Drive, Atlanta, GA 30332-0765

### Cryptographic Hash Functions Message Authentication Digital Signatures

Cryptographic Hash Functions Message Authentication Digital Signatures Abstract We will discuss Cryptographic hash functions Message authentication codes HMAC and CBC-MAC Digital signatures 2 Encryption/Decryption

### Cryptography 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)

### Introduction to Modern Cryptography

Introduction to Modern Cryptography 3rd lecture: Computational Security of Private-Key Encryption and Pseudorandomness some of these slides are copied from or heavily inspired by the University College

### Message Authentication Codes 133

Message Authentication Codes 133 CLAIM 4.8 Pr[Mac-forge A,Π (n) = 1 NewBlock] is negligible. We construct a probabilistic polynomial-time adversary A who attacks the fixed-length MAC Π and succeeds in

### Introduction to Cryptography CS 355

Introduction to Cryptography CS 355 Lecture 30 Digital Signatures CS 355 Fall 2005 / Lecture 30 1 Announcements Wednesday s lecture cancelled Friday will be guest lecture by Prof. Cristina Nita- Rotaru

### Fundamentals of Computer Security

Fundamentals of Computer Security Spring 2015 Radu Sion Intro Encryption Hash Functions A Message From Our Sponsors Fundamentals System/Network Security, crypto How do things work Why How to design secure

### Applied Cryptology. Ed Crowley

Applied Cryptology Ed Crowley 1 Basics Topics Basic Services and Operations Symmetric Cryptography Encryption and Symmetric Algorithms Asymmetric Cryptography Authentication, Nonrepudiation, and Asymmetric

### The mathematics of cryptology

The mathematics of cryptology Paul E. Gunnells Department of Mathematics and Statistics University of Massachusetts, Amherst Amherst, MA 01003 www.math.umass.edu/ gunnells April 27, 2004 What is Cryptology?

6.857 Computer and Network Security Fall Term, 1997 Lecture 4 : 16 September 1997 Lecturer: Ron Rivest Scribe: Michelle Goldberg 1 Conditionally Secure Cryptography Conditionally (or computationally) secure

### On-Line/Off-Line Digital Signatures

J. Cryptology (996) 9: 35 67 996 International Association for Cryptologic Research On-Line/Off-Line Digital Signatures Shimon Even Computer Science Department, Technion Israel Institute of Technology,

### Digital 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

### Cryptography and Network Security: Summary

Cryptography and Network Security: Summary Timo Karvi 12.2013 Timo Karvi () Cryptography and Network Security: Summary 12.2013 1 / 17 Summary of the Requirements for the exam The advices are valid for

### Verifiable Delegation of Computation over Large Datasets

Verifiable Delegation of Computation over Large Datasets Siavosh Benabbas University of Toronto Rosario Gennaro IBM Research Yevgeniy Vahlis AT&T Cloud Computing Data D Code F Y F(D) Cloud could be malicious

### CPSC 467b: Cryptography and Computer Security

CPSC 467b: Cryptography and Computer Security Michael J. Fischer Lecture 1 January 9, 2012 CPSC 467b, Lecture 1 1/22 Course Overview Symmetric Cryptography CPSC 467b, Lecture 1 2/22 Course Overview CPSC

### OHJ-2306 Introduction to Theoretical Computer Science, Fall 2012 8.11.2012

276 The P vs. NP problem is a major unsolved problem in computer science It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a \$ 1,000,000 prize for the

### Network 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:

### Message Authentication Code

Message Authentication Code Ali El Kaafarani Mathematical Institute Oxford University 1 of 44 Outline 1 CBC-MAC 2 Authenticated Encryption 3 Padding Oracle Attacks 4 Information Theoretic MACs 2 of 44

### CIS 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

### Lecture 11: The Goldreich-Levin Theorem

COM S 687 Introduction to Cryptography September 28, 2006 Lecture 11: The Goldreich-Levin Theorem Instructor: Rafael Pass Scribe: Krishnaprasad Vikram Hard-Core Bits Definition: A predicate b : {0, 1}

### Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No. # 11 Block Cipher Standards (DES) (Refer Slide

### Yale University Department of Computer Science

Yale University Department of Computer Science On Backtracking Resistance in Pseudorandom Bit Generation (preliminary version) Michael J. Fischer Michael S. Paterson Ewa Syta YALEU/DCS/TR-1466 October

### Lecture 17: Re-encryption

600.641 Special Topics in Theoretical Cryptography April 2, 2007 Instructor: Susan Hohenberger Lecture 17: Re-encryption Scribe: Zachary Scott Today s lecture was given by Matt Green. 1 Motivation Proxy

### Non-interactive and Reusable Non-malleable Commitment Schemes

Non-interactive and Reusable Non-malleable Commitment Schemes Ivan Damgård a Jens Groth b June 16, 2003 Abstract We consider non-malleable (NM) and universally composable (UC) commitment schemes in the

### Counter Expertise Review on the TNO Security Analysis of the Dutch OV-Chipkaart. OV-Chipkaart Security Issues Tutorial for Non-Expert Readers

Counter Expertise Review on the TNO Security Analysis of the Dutch OV-Chipkaart OV-Chipkaart Security Issues Tutorial for Non-Expert Readers The current debate concerning the OV-Chipkaart security was

### Lecture 13: Message Authentication Codes

Lecture 13: Message Authentication Codes Last modified 2015/02/02 In CCA security, the distinguisher can ask the library to decrypt arbitrary ciphertexts of its choosing. Now in addition to the ciphertexts

### The 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

### Introduction to computer science

Introduction to computer science Michael A. Nielsen University of Queensland Goals: 1. Introduce the notion of the computational complexity of a problem, and define the major computational complexity classes.

### Cryptography & 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.

### Department Informatik. Privacy-Preserving Email Forensics. Technical Reports / ISSN 2191-5008. Frederik Armknecht, Andreas Dewald

Department Informatik Technical Reports / ISSN 2191-5008 Frederik Armknecht, Andreas Dewald Privacy-Preserving Email Forensics Technical Report CS-2015-03 April 2015 Please cite as: Frederik Armknecht,

### Introduction. Chapter 1

Chapter 1 Introduction This is a chapter from version 1.1 of the book Mathematics of Public Key Cryptography by Steven Galbraith, available from http://www.isg.rhul.ac.uk/ sdg/crypto-book/ The copyright

### Digital Signatures. What are Signature Schemes?

Digital Signatures Debdeep Mukhopadhyay IIT Kharagpur What are Signature Schemes? Provides message integrity in the public key setting Counter-parts of the message authentication schemes in the public