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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 in a computational setting Definition of collision resistant hash functions 2 Recap of last lecture - PRGs for one time pads Last lecture, we saw how a PRG could be used to use keys to encrypt messages of a larger size with a one-time-pad. Given a key k and a message m where k < m, we use a PRG G with at least m k bit stretch to generate a one time pad G(k). Then, we do bitwise XORing with m to achieve our ciphertext. Formally, our encryption and decryption functions are: Enc(k, m) = G(k) m Dec(k, c) = G(k) c Disregarding other properties, the above still has the problem of not working for more than one message. Our goal for the next section will be to define a model of security that provides multi-message encryption security, and to provide a scheme which achieves it. 3 Chosen Plaintext Attack (CPA) We will now consider a new model of security in which an adversary has blackbox access to our encryption function with the same key we are using. The adversary can make a polynomial number of queries with any plaintext message they want, and will receive the corresponding ciphertext. The adversary also gets to provide two messages m 0 and m 1. One of them (unknown to the adversary) is chosen, and an encryption of it is returned. The adversary must then determine which message, m 0 or m 1, was encrypted and returned to it. Lecture 10, Page 1

2 3.1 CPA Definition In order to analyze such a scenario, we will consider two experiments, CPA-Exp-0 and CPA-Exp-1. In both experiments the adversary can query a encryption oracle by choosing arbitrary messages m i and getting back ciphertexts c i Enc(k, m i ). The adversary can query the oracle as many times as it wants. At some point the adversary chooses two challenge messages M 0, M 1 and gets back an encryption of M b where b = 0 in experiment 0 and b = 1 in experiment 1, It will then be the job of the adversary to correctly conclude which experiment he is in. For a bit b 0, 1, an adversary A and a security parameter n, we define CPA-Exp b A (n) as the following procedure: CPA-Exp b A (n) Challenger k {0, 1} n Repeat poly(n) times{ Repeat poly(n) times{ m i Enc(k, m i ) M 0, M 1 C = Enc(k, M b ) m i Enc(k, m i ) b {0, 1} The output of the experiment is b Adversary A picks M 0, M 1 of equal length Definition 1 A symmetric-key encryption scheme (Enc, Dec) is CPA secure if for any PPT adversary A we have Pr[CPA-Exp b A(n) = 1] Pr[CPA-Exp b A(n) = 1] = negl(n). Experiment Indistinguishability. We already defined the computational indisitinguishability of two distribution (ensambles) X Y. Let s extend this definition to interactive experiments such as the ones defined above. If Exp A (n) and Exp A (n) are two experiments parametrized by an adversary A and a security parameter n, we write Exp Exp as a shorthand notation to denote that for all PPT adversary A Pr[Exp A (n) = 1] Pr[Exp A(n) = 1] = negl(n). With this notation, the definition of CPA security for encryption can be written simply as: CPA-Exp 0 CPA-Exp A randomized encryption scheme with CPA security First, it is worth noting that no deterministic encryption protocol can satisfy this definition. This is because the adversary is not limited in what it is allowed to query with its oracle Lecture 10, Page 2

3 access to O(m) = Enc(k, m). Thus, an adversary could first query O(M 0 ) and O(M 1 ) before passing these messages to the experiment as its choices of M 0 and M 1. Whichever experiment it is in, it will either be returned O(M 0 ) or O(M 1 ) exactly as the oracle originally returned to him. Thus with probability 1 it can distinguish between the experiments it is in. To get around this, we create a randomized encryption scheme, in which, for fixed k and m, Enc(k, m) is a random variable, satisfying Pr [Dec(k, Enc(k, m)) = m] = 1. Let F k : {0, 1} n {0, 1} l(n) be a PRF. Then we can define Enc and Dec as follows: Enc(k, m) : x {0, 1} n c = (x, F k (x) m) Dec(k, c) : c = (x, y) m = y F k (x) Where in the above schemes, Enc samples a uniformly random x and returns c, while Dec unpacks c as described and returns m. The intuition for the above schemes is that, reusing one time pads is insecure, but access to a PRF gives us an exponential supply of pads we can use. If we wish to decrypt the message, then knowing k will let us use F k to reconstruct the pad, but to an adversary who can only see x, the pad is indistinguishable from being chosen completely at random, providing encryption similar to a randomly chosen one time pad. 3.3 Proof of Security To prove the CPA security of our above scheme, we will proceed by a hybrid argument. First, we will define the hybrids. Then, we will prove that each one is indistinguishable from the next. Each hybrid will essentially be a variation of one of the experiments, where we modify how the encryption procedure works. H 0 : CPA-Exp-0 : Enc(k, m) = (x, F k (x) m) H 1 : CPA-Exp-0 : Enc(k, m) = (x, R(x) m), R(x) is a true random function H 2 : CPA-Exp-0 : Enc(k, m) = (x, y), y {0, 1} l(n) H 2 : CPA-Exp-1 : Enc(k, m) = (x, y), y {0, 1}l(n) H 3 : CPA-Exp-1 : Enc(k, m) = (x, R(x) m), R(x) is a true random function H 4 : CPA-Exp-1 : Enc(k, m) = (x, F k (x) m) Note that we labeled H 2, H 2 in this manner because they are trivially identical experiments, so the hybrid step is a one liner. In particular, H 0 is exactly CPA-Exp-0, and H 4 is exactly CPA-Exp-1. Lemma 1 H 0 H 1 Proof: Suppose A could distinguish between H 0 and H 1. Since they are both running in CPA-Exp-0, this is the same as distinguishing between (x, F k (x)), and (x, R(x)). Formally, we could have B A distinguish between F k (X) and R(x) by using A as a black box, where whenever A would access the encryption oracle O, B A will proxy for the result by passing Lecture 10, Page 3

4 the input to its unknown function, and giving the output back to A as the result. Since we should have F k (x) R(x), then H 0 H 1. Lemma 2 H 1 H 2 Proof: First, note that the distribution for R(x) and R(x)XORm are the same, since R(x) is truly random. The difference between H 1 and H 2 is the difference between R(x)XORm R(x) and y. The only way we could tell the difference between R(x) and y is if we chose the same x at least twice. In this case, R(x) would be consistent, but y will, with probability nearly 1, be a different value. However, x is chosen randomly. If we make q queries to the oracle, then by a union bound, the probability that we choose the same x more than once is Pr [ i, j : x i = x j ] q 2 /2 n negl(n). Thus we can only differentiate H 1 and H 2 with negligible probability. Lemma 3 H 2 H 2 Proof: The encryption oracle ignores the inputs, so there is no correlation between what the oracle gives as an answer and whether we are in CPA-Exp-0 or CPA-Exp-1. The experiments are identical. Lemma 4 H 2 H 3 Proof: The same argument that H 1 H 2 applies. Lemma 5 H 3 H 4 Proof: The same argument that H 0 H 1 applies. Thus by a hybrid argument, we have that H 0 = CPA-Exp-0 CPA-Exp-1 = H 4, as desired. Due to the randomization, it is not possible for a computationally bounded adversary to tell which M 0, M 1 was encrypted and returned. The only real attack is to keep querying on M 0 and M 1 repeatedly, and hope to get the same random parameter x that the experiment used for its encryption of M b. 4 MACs in a computational setting Previously, we defined 1-time MACs which had information theoretic security, even in the face of unbounded computational power, but could only be used to authenticate a single message. We also saw that we can extend this construction to any a-priori bounded number of messages t, but the size of the key had to grow with t. In this section, we will update our definition by viewing our adversary as being computationally bounded. This new definition will allow us to securely generate tags for arbitrarily many messages with a short key. Lecture 10, Page 4

5 4.1 Computational secure MAC definition As before, the key k is chosen uniformly at random. However, this time, the adversary A has oracle access to MAC(k, m). After making a polynomial number of queries, A can pick any message m, and must attempt to generate a correct tag σ. If MAC(k, m ) = σ and m = m i for any of the previously queried m i, then the result of the experiment is 1. Else, it is 0. We define this experiment as AuthExp A. The flow diagram for this is below: Challenger k {0, 1} n Repeat poly(n) times{ AuthExp m i MAC(k, m i ) (m, σ ) Returns 1 if MAC(k, m ) = σ and m m i from previous queries Else returns 0 Adversary A Generates (m, σ ) pair Definition 2 A MAC is computationally secure if for all PPT adversaries A, we have that: Pr [AuthExp A (n) = 1] negl(n). 4.2 MACs with AuthExp security Given our above definition, it is true that any PRF F k (x) will suffice as a MAC. We formalize this and prove it below. Theorem 1 Let F k (m) be any P RF. Define a MAC function as MAC(k, m) = F k (m). Then M AC(k, m) is computationally secure. Proof: First, we will show that AuthExp is indistinguishable from an experiment where in place of F k we use a truly random function. Then the desired conclusion follows from the security of the modified experiment. Define the following two hybrids: H 0 : AuthExp H 1 : AuthExp, replace F k with R(m) // R is a truly random function Lemma 6 H 0 H 1. In other words, for all PPT A, Pr [H 0 (A, n) = 1] Pr [H 1 (A, n) = 1] negl(n). Proof: If we could distinguish H 0 and H 1, then we could distinguish any PRF from a random function by plugging them into H 0 and H 1 and distinguishing those experiments. Lemma 7 For all adversaries A: Pr[H 1 (A, n) = 1] 2 n Lecture 10, Page 5

6 Proof: Since the MAC function is a truly random function, no matter what queries A makes in experimet H 1, if m was not queried then the final tag MAC k (m ) = R(m ) will be random and unknown to the adversary. Thus no matter what tag σ the adversary chooses, the probability of it being correct σ = R(m ) is at most 2 n. Combining the two lemmas we get that for all PPT A: as we wanted to show. Pr [AuthExp A (n) = 1] = Pr [H 0 (A, n) = 1] Pr [H 1 (A, n) = 1] + negl(n) By Lemma 6 2 n + negl(n) negl(n) By Lemma 7 5 Combining encryption and authenticity In previous lectures, we had viewed encryption and authenticity as separate problems. In reality, these two processes are combined to create encryption schemes where messages can also be verified. Not only that, but they are more related than they appear. Consider the following simple protocol between parties A and B: A has a message (b, m) to encrypt for B. If m is a top secret message, she will set b = 1, indicating to B that it is not to be shared. If m can be freely shared after B is done with it, she will set b = 0. A uses proper encryption to send Enc(k, (b, m)) to B, who then uses his decryption function to obtain the original (b, m) and act according to the value of b. Suppose an actively malicious party E could intercept ciphertexts, and although cannot read them, could flip any bit of the plaintext message by appropriately tampering with the ciphertext. Then E could flip the first bit of the plaintext, changing the behavior of B. If this was a top secret message, B would mistakingly publish it for all to see. Although this example may seem forced, in practice there have been attacks on cryptography implementations which work in a way very similar to the above. The key problem in the above example is that B will act differently based on what he reads from the plaintext message. B could also be viewed as a system, which decrypts incoming ciphertexts and acts according to the plaintext. For example, imagine a bank server which receives encrypted transactions, and must make transfers according to the plaintext descriptions. In order for correctness of this system to be guaranteed, the cryptography schemes must provide their own guarantees as to what can and cannot be decrypted into a plaintext message. This is the role of the MACs in the cryptography schemes. The question to answer is, in what way should encryption and authenticate be composed, so that neither is compromised? To motivate this question, consider the following incorrect combination: c = Enc(k, m) σ MAC((, k), m) Send (σ, c) Lecture 10, Page 6

7 In this case, we are signing the plaintext, not the ciphertext. B can only authenticate after decrypting c. There are two potential problems with this. First, we have no guarantees that σ doesn t reveal any information about the message, which we want to hide. Second, it is still possible that just by decrypting c, information about the message or the secret key can be revealed. This is mostly due to Dec(k, c) having undefined behavior if c is not in its domain, which can occur if it was tampered with by an active eavesdropper. What we really want is to make sure that bad cipher texts do not get to be passed to the decryption function. Thus, we do the following: c = Enc(k, m) σ MAC((, k), c) Send (σ, c) When B receives (σ, c), he first checks that MAC(k, c) = σ, and only attempts decryption if this is the case. This prevents both the MAC from leaking information about m, and accidental decryption of faulty ciphertexts. To reiterate, the main point is to not decrypt bad cipher texts. 6 Collision Resistant Hash Functions A collision resistant hash function is used to compress a long message x to a short digest y = H(x). Since H is compressing, there are neceserally collisions x x such that H(x) = H(x ). However, we require that such collisions are hard to find. More formally, we consider a family of functions H s : {0, 1} l(n) {0, 1} n, where l(n) > n and s {0, 1} n. We think of s as a public seed of the hash function which is chosen randomly but known to everyone. Then we say H s is a collision resistant family of hash functions if: 1. H s (x) can be computed in polynomial (in s, x ) time. 2. For all PPT A, the following experiment has negligible probability of returning 1: s {0, 1} n A gets s. A outputs x, x {0, 1} l(n). The experiment returns 1 iff x x and H s (x) = H s (x ), 0 otherwise. More compactly, we can write that for all PPT A we have: Pr[(H s (x) = H s (x )) (x x ) : s {0, 1} n, (x, x ) A(s)] = negl(n). Lecture 10, Page 7

8 Discussion on seeds. One might ask whether the seed s is needed at all - couldn t we have just a single hash function H for which it s hard to find collisions? Intuitively this seems possible and is actually done in practice. However, for a technical reason, we need the formal definition to have a random seed. The reason is that, if we had a single fixed hash function H then there would always be a very simple (non-uniform) adversary A that has a hard-coded collision x x such that H(x) = H(x ) and simply outputs x, x without doing any computation. By choosing a random seed s, we prevent this since the adversary would need to know a different collision for each s (or at least many seeds s) which would require an exponential amount of data. In practice, it seems unnecessary to have a seed since, even though there exists some A with the hard-coded collision x, x, we as humans do not know the code of this A. However, we do not have very good ways of formalizing this mathematically. Lecture 10, Page 8

### 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 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.

### 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

### 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.

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

### Talk announcement please consider attending!

Talk announcement please consider attending! Where: Maurer School of Law, Room 335 When: Thursday, Feb 5, 12PM 1:30PM Speaker: Rafael Pass, Associate Professor, Cornell University, Topic: Reasoning Cryptographically

### 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,

### 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

### 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

### 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

### Security Aspects of. Database Outsourcing. Vahid Khodabakhshi Hadi Halvachi. Dec, 2012

Security Aspects of Database Outsourcing Dec, 2012 Vahid Khodabakhshi Hadi Halvachi Security Aspects of Database Outsourcing Security Aspects of Database Outsourcing 2 Outline Introduction to Database

### Authentication and Encryption: How to order them? Motivation

Authentication and Encryption: How to order them? Debdeep Muhopadhyay IIT Kharagpur Motivation Wide spread use of internet requires establishment of a secure channel. Typical implementations operate in

### 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

### 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

### 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

### 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

### MAC. SKE in Practice. Lecture 5

MAC. SKE in Practice. Lecture 5 Active Adversary Active Adversary An active adversary can inject messages into the channel Active Adversary An active adversary can inject messages into the channel Eve

### 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

### 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).

### Cryptography and Network Security, PART IV: Reviews, Patches, and11.2012 Theory 1 / 53

Cryptography and Network Security, PART IV: Reviews, Patches, and Theory Timo Karvi 11.2012 Cryptography and Network Security, PART IV: Reviews, Patches, and11.2012 Theory 1 / 53 Key Lengths I The old

### One-Way Encryption and Message Authentication

One-Way Encryption and Message Authentication Cryptographic Hash Functions Johannes Mittmann mittmann@in.tum.de Zentrum Mathematik Technische Universität München (TUM) 3 rd Joint Advanced Student School

### 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

### 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

### 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

### 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

### Network Security Technology Network Management

COMPUTER NETWORKS Network Security Technology Network Management Source Encryption E(K,P) Decryption D(K,C) Destination The author of these slides is Dr. Mark Pullen of George Mason University. Permission

### CSC474/574 - Information Systems Security: Homework1 Solutions Sketch

CSC474/574 - Information Systems Security: Homework1 Solutions Sketch February 20, 2005 1. Consider slide 12 in the handout for topic 2.2. Prove that the decryption process of a one-round Feistel cipher

### Authenticated encryption

Authenticated encryption Dr. Enigma Department of Electrical Engineering & Computer Science University of Central Florida wocjan@eecs.ucf.edu October 16th, 2013 Active attacks on CPA-secure encryption

### Outline. 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

### 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

### 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

### Security Analysis of DRBG Using HMAC in NIST SP 800-90

Security Analysis of DRBG Using MAC in NIST SP 800-90 Shoichi irose Graduate School of Engineering, University of Fukui hrs shch@u-fukui.ac.jp Abstract. MAC DRBG is a deterministic random bit generator

### 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.

### 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

### Cryptography. Lecture Notes from CS276, Spring 2009. Luca Trevisan Stanford University

Cryptography Lecture Notes from CS276, Spring 2009 Luca Trevisan Stanford University Foreword These are scribed notes from a graduate course on Cryptography offered at the University of California, Berkeley,

### 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

### Fuzzy Identity-Based Encryption

Fuzzy Identity-Based Encryption Janek Jochheim June 20th 2013 Overview Overview Motivation (Fuzzy) Identity-Based Encryption Formal definition Security Idea Ingredients Construction Security Extensions

### GCM-SIV: Full Nonce Misuse-Resistant Authenticated Encryption at Under One Cycle per Byte. Yehuda Lindell Bar-Ilan University

GCM-SIV: Full Nonce Misuse-Resistant Authenticated Encryption at Under One Cycle per Byte Shay Gueron Haifa Univ. and Intel Yehuda Lindell Bar-Ilan University Appeared at ACM CCS 2015 How to Encrypt with

### Message 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,

### Overview of Symmetric Encryption

CS 361S Overview of Symmetric Encryption Vitaly Shmatikov Reading Assignment Read Kaufman 2.1-4 and 4.2 slide 2 Basic Problem ----- ----- -----? Given: both parties already know the same secret Goal: send

### 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

### 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

### CIS 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.

### Security Analysis for Order Preserving Encryption Schemes

Security Analysis for Order Preserving Encryption Schemes Liangliang Xiao University of Texas at Dallas Email: xll052000@utdallas.edu Osbert Bastani Harvard University Email: obastani@fas.harvard.edu I-Ling

### Designing Hash functions. Reviewing... Message Authentication Codes. and message authentication codes. We have seen how to authenticate messages:

Designing Hash functions and message authentication codes Reviewing... We have seen how to authenticate messages: Using symmetric encryption, in an heuristic fashion Using public-key encryption in interactive

### 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

### Network Security (2) CPSC 441 Department of Computer Science University of Calgary

Network Security (2) CPSC 441 Department of Computer Science University of Calgary 1 Friends and enemies: Alice, Bob, Trudy well-known in network security world Bob, Alice (lovers!) want to communicate

### 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

### 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

### Authenticated Encryption: Relations among Notions and Analysis of the Generic Composition Paradigm By Mihir Bellare and Chanathip Namprempre

Authenticated Encryption: Relations among Notions and Analysis of the Generic Composition Paradigm By Mihir Bellare and Chanathip Namprempre Some slides were also taken from Chanathip Namprempre's defense

### Capture 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

### YALE UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE

YALE UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE CPSC 467a: Cryptography and Computer Security Notes 1 (rev. 1) Professor M. J. Fischer September 3, 2008 1 Course Overview Lecture Notes 1 This course is

### 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

### 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

### 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}

### First Semester Examinations 2011/12 INTERNET PRINCIPLES

PAPER CODE NO. EXAMINER : Martin Gairing COMP211 DEPARTMENT : Computer Science Tel. No. 0151 795 4264 First Semester Examinations 2011/12 INTERNET PRINCIPLES TIME ALLOWED : Two Hours INSTRUCTIONS TO CANDIDATES

### 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

### 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. # 02 Overview on Modern Cryptography

### Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015

Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015 Chapter 2: Introduction to Cryptography What is cryptography? It is a process/art of mangling information in such a way so as to make it

### A Survey and Analysis of Solutions to the. Oblivious Memory Access Problem. Erin Elizabeth Chapman

A Survey and Analysis of Solutions to the Oblivious Memory Access Problem by Erin Elizabeth Chapman A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in

### Chapter 11. Asymmetric Encryption. 11.1 Asymmetric encryption schemes

Chapter 11 Asymmetric Encryption The setting of public-key cryptography is also called the asymmetric setting due to the asymmetry in key information held by the parties. Namely one party has a secret

### Network 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

### 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

### 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

### CS155. Cryptography Overview

CS155 Cryptography Overview Cryptography Is n A tremendous tool n The basis for many security mechanisms Is not n The solution to all security problems n Reliable unless implemented properly n Reliable

### Error oracle attacks and CBC encryption. Chris Mitchell ISG, RHUL http://www.isg.rhul.ac.uk/~cjm

Error oracle attacks and CBC encryption Chris Mitchell ISG, RHUL http://www.isg.rhul.ac.uk/~cjm Agenda 1. Introduction 2. CBC mode 3. Error oracles 4. Example 1 5. Example 2 6. Example 3 7. Stream ciphers

### Message Authentication Codes. Lecture Outline

Message Authentication Codes Murat Kantarcioglu Based on Prof. Ninghui Li s Slides Message Authentication Code Lecture Outline 1 Limitation of Using Hash Functions for Authentication Require an authentic

### 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

### CSCE 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

### SECURITY 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,

### Cryptography Lecture 8. Digital signatures, hash functions

Cryptography Lecture 8 Digital signatures, hash functions A Message Authentication Code is what you get from symmetric cryptography A MAC is used to prevent Eve from creating a new message and inserting

### Sample or Random Security A Security Model for Segment-Based Visual Cryptography

Sample or Random Security A Security Model for Segment-Based Visual Cryptography Sebastian Pape Dortmund Technical University March 5th, 2014 Financial Cryptography and Data Security 2014 Sebastian Pape

### 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

### 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

### Identity-Based Encryption from the Weil Pairing

Appears in SIAM J. of Computing, Vol. 32, No. 3, pp. 586-615, 2003. An extended abstract of this paper appears in the Proceedings of Crypto 2001, volume 2139 of Lecture Notes in Computer Science, pages

### Message authentication

Message authentication -- Hash based MAC unctions -- MAC unctions based on bloc ciphers -- Authenticated encryption (c) Levente Buttyán (buttyan@crysys.hu) Secret preix method MAC (x) = H( x) insecure!

### VoteID 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

### 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

### Cryptography: 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,

### 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

### CS 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

### Key Agreement from Close Secrets over Unsecured Channels Winter 2010

Key Agreement from Close Secrets over Unsecured Channels Winter 2010 Andreas Keller Contens 1. Motivation 2. Introduction 3. Building Blocks 4. Protocol Extractor Secure Sketches (MAC) message authentication

### CSE/EE 461 Lecture 23

CSE/EE 461 Lecture 23 Network Security David Wetherall djw@cs.washington.edu Last Time Naming Application Presentation How do we name hosts etc.? Session Transport Network Domain Name System (DNS) Data

### Client Server Registration Protocol

Client Server Registration Protocol The Client-Server protocol involves these following steps: 1. Login 2. Discovery phase User (Alice or Bob) has K s Server (S) has hash[pw A ].The passwords hashes are

### Proofs in Cryptography

Proofs in Cryptography Ananth Raghunathan Abstract We give a brief overview of proofs in cryptography at a beginners level. We briefly cover a general way to look at proofs in cryptography and briefly

### Symmetric Crypto MAC. Pierre-Alain Fouque

Symmetric Crypto MAC Pierre-Alain Fouque Birthday Paradox In a set of D elements, by picking at random D elements, we have with high probability a collision two elements are equal D=365, about 23 people

### a Course in Cryptography

a Course in Cryptography rafael pass abhi shelat c 2010 Pass/shelat All rights reserved Printed online 11 11 11 11 11 15 14 13 12 11 10 9 First edition: June 2007 Second edition: September 2008 Third edition:

### 2.1 Complexity Classes

15-859(M): Randomized Algorithms Lecturer: Shuchi Chawla Topic: Complexity classes, Identity checking Date: September 15, 2004 Scribe: Andrew Gilpin 2.1 Complexity Classes In this lecture we will look

### RSA 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.

### Lecture 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

### Order-Preserving Encryption Revisited: Improved Security Analysis and Alternative Solutions

A preliminary version of this paper appears in Advances in Cryptology - CRYPTO 0, 3st Annual International Cryptology Conference, P. Rogaway ed., LNCS, Springer, 0. Order-Preserving Encryption Revisited:

### Public 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

### 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

### Secure Deduplication of Encrypted Data without Additional Independent Servers

Secure Deduplication of Encrypted Data without Additional Independent Servers Jian Liu Aalto University jian.liu@aalto.fi N. Asokan Aalto University and University of Helsinki asokan@acm.org Benny Pinkas

### Signature Schemes. CSG 252 Fall 2006. Riccardo Pucella

Signature Schemes CSG 252 Fall 2006 Riccardo Pucella Signatures Signatures in real life have a number of properties They specify the person responsible for a document E.g. that it has been produced by

### 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