Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 8
Spring 11
Instructor: Mihir Bellare
May 25, 2011
Problem Set 8
Due: Wednesday June 1, 2011, in class.
Problem 1. [60 points] In an identitybased, noninteractive key distri
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 4 Solutions
Spring 11
Instructor: Mihir Bellare
May 4, 2011
Problem Set 4 Solutions
Problem 1. [30 points] Let E : cfw_0, 1k cfw_0, 1l cfw_0, 1l be a block cipher. Let D be th
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 5 Solutions
Spring 11
Instructor: Mihir Bellare
May 11, 2011
Problem Set 5 Solutions
Problem 1. [50 points] Let G = g b e a cyclic group of order m, and let k = log2 (m) . The
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 1
Spring 11
Instructor: Mihir Bellare
March 28, 2011
Problem Set 1
Due: Wednesday April 6, 2011, in class.
Problem 1. [30 points] Let K be a 56bit DES key, let L be a 64bit
Writing 4A The Critical Essay: Literature and the Arts
Week 1
Sunday, July 17
Introductions/Class rules/ Plagiarism Contract/ Student and Teacher
expectations
Monday, July 18
Morning:
Writing Diagnostic
Read Alice Walker, Everyday Use
Talk about story and
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 2 Solutions
Spring 11
Instructor: Mihir Bellare
April 13, 2011
Problem Set 2 Solutions
Problem 1. [20 points] Dene the family of functions F : cfw_0, 1128 cfw_0, 1128 cfw_0, 1
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 1 Solutions
Spring 11
Instructor: Mihir Bellare
April 6, 2010
Problem Set 1 Solutions
Problem 1. [30 points] Let K be a 56bit DES key, let L be a 64bit string, and let M be
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 7
Spring 11
Instructor: Mihir Bellare
May 18, 2011
Problem Set 7
Due: Wednesday May 25, 2011, in class.
Problem 1. [45 points] Generation of random numbers on systems is dicul
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 6
Spring 11
Instructor: Mihir Bellare
May 11, 2011
Problem Set 6
Due: Wednesday May 18, 2011, in class.
Problem 1. [35 points] Let p 3 be a prime and g Z a generator of Z . (T
Course Information
CSE 207 Modern Cryptography
Instructor: Mihir Bellare
Website: http:/wwwcse.ucsd.edu/users/mihir/cse207
1/1
Cryptography usage
Did you use any cryptography
today?
2/1
Cryptography usage
Did you use any cryptography
today?
over the l
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 3 Solutions
Spring 11
Instructor: Mihir Bellare
April 20, 2011
Problem Set 3 Solutions
Problem 1. [80 points] Let E : cfw_0, 1k cfw_0, 1n cfw_0, 1n be a block cipher and let a
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 6 Solutions
Spring 11
Instructor: Mihir Bellare
May 18, 2011
Problem Set 6 Solutions
Problem 1. [35 points] Let p 3 be a prime and g Z a generator of Z . (These are
p
p
public
AUTHENTICATED ENCRYPTION
1 / 55
So Far .
We have looked at methods to provide privacy and integrity/authenticity separately:
Goal Data privacy Data integrity/authenticity Primitive symmetric encryption MA scheme/MAC Security notions INDCPA, INDCCA UFCM
ASYMMETRIC ENCRYPTION
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Recommended Book
Steven Levy. Crypto. Penguin books. 2001. A nontechnical account of the history of publickey cryptography and the colorful characters involved.
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Recall Symmetric Cryptography
Before Alice and Bob ca
BLOCK CIPHERS
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Permutations and Inverses
A function f : cfw_0, 1 cfw_0, 1 is a permutation if there is an inverse function f 1 : cfw_0, 1 cfw_0, 1 satisfying x cfw_0, 1 : f 1 (f (x ) = x This means f must be onetoone and onto, meaning for every y
COMPUTATIONAL NUMBER THEORY
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Notation
Z = cfw_. . . , 2, 1, 0, 1, 2, . . .
N = cfw_0, 1, 2, . . .
Z+ = cfw_1, 2, 3, . . .
d a means d divides a
Example: 24.
For a, N Z let gcd(a, N ) be the largest d Z+ such that d a and d N .
Example: gcd(30
HASH FUNCTIONS
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What is a hash function?
By a hash function we usually mean a map h : D cfw_0, 1n that is compressing, meaning D > 2n . E.g. D = cfw_0, 12
64
is the set of all strings of length at most 264 . h MD4 MD5 SHA1 RIPEMD RIPEMD160 SHA25
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 5
Spring 11
Instructor: Mihir Bellare
May 4, 2011
Problem Set 5
Due: Wednesday May 11, 2011, in class.
Problem 1. [50 points] Let G = g b e a cyclic group of order m, and let
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 4
Spring 11
Instructor: Mihir Bellare
April 25, 2011
Problem Set 4
Due: Wednesday May 4, 2011, in class.
Problem 1. [30 points] Let E : cfw_0, 1k cfw_0, 1l cfw_0, 1l be a bloc
Computer Science and Engineering, UCSD
CSE 207: Modern Cryptography
Problem Set 3
Spring 11
Instructor: Mihir Bellare
October 13, 2011
Problem Set 3
Due: Wednesday April 20, 2011, in class.
Problem 1. [80 points] Let E : cfw_0, 1k cfw_0, 1n cfw_0, 1n be a
MESSAGE AUTHENTICATION
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Integrity and authenticity
The goal is to ensure that
M really originates with Alice and not someone else M has not been modified in transit
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Integrity and authenticity example
Alice Alice Pay $100 to Charlie

Bob (
PSEUDORANDOM FUNCTIONS
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Recall
We studied security of a block cipher against key recovery. But we saw that security against key recovery is not sufficient to ensure that natural usages of a block cipher are secure. We want to answer the question: W
STREAM CIPHERS and PRGs
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Stateful Generators
Initially, St is a random seed
St G X
St
Operation:
St[0] G X[1] St[1] G X[2] St[2] G X[3] St[3]
X [1]X [2]X [3]. is the output sequence and should be pseudorandom.
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Notation
(X [1] . . . X [m], St)
SYMMETRIC ENCRYPTION
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Syntax
A symmetric encryption scheme SE = (K, E , D ) consists of three
algorithms:
K is randomized
E can be randomized or stateful
D is deterministic
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Correct decryption requirement
Formally: For all K and M we have
Chapter 11 Asymmetric Encryption
The setting of publickey cryptography is also called the "asymmetric" setting due to the asymmetry in key information held by the parties. Namely one party has a secret key while another has the public key that matches th
Chapter 2 Block Ciphers
Blockciphers are the central tool in the design of protocols for sharedkey cryptography (aka. symmetric) cryptography. They are the main available "technology" we have at our disposal. This chapter will take a look at these object
Chapter 9 Computational Number Theory
9.1
The basic groups
We let Z = cfw_. . . , 2, 1, 0, 1, 2, . . . denote the set of integers. We let Z+ = cfw_1, 2, . . . denote the set of positive integers and N = cfw_0, 1, 2, . . . the set of nonnegative integer
Chapter 12 Digital signatures
In the public key setting, the primitive used to provide data integrity is a digital signature scheme. In this chapter we look at security notions and constructions for this primitive.
12.1
Digital signature schemes
A digital
Chapter 6 Hash Functions
A hash function usually means a function that compresses, meaning the output is shorter than the input. Often, such a function takes an input of arbitrary or almost arbitrary length to one whose length is a fixed number, like 160
Chapter 1 Introduction
Historically, cryptography arose as a means to enable parties to maintain privacy of the information they send to each other, even in the presence of an adversary with access to the communication channel. While providing privacy rem