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 p
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
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
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. [3
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 Diagnost
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 f
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
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 p
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 p
Course Information
CSE 207 Modern Cryptography
Instructor: Mihir Bellare
Website: http:/www-cse.ucsd.edu/users/mihir/cse207
1/1
Cryptography usage
Did you use any cryptography
today?
2/1
Cryptography
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 : cf
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
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 encryptio
ASYMMETRIC ENCRYPTION
1 / 135
Recommended Book
Steven Levy. Crypto. Penguin books. 2001. A non-technical account of the history of public-key cryptography and the colorful characters involved.
2 / 135
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 me
COMPUTATIONAL NUMBER THEORY
1 / 70
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: 2|4.
For a, N Z let gcd(a, N ) be the
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 lengt
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 po
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
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.
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
2 / 103
Integrity and authe
PSEUDO-RANDOM 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 blo
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 b
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
2 / 116
Correct d
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 secr
Chapter 2 Block Ciphers
Blockciphers are the central tool in the design of protocols for shared-key cryptography (aka. symmetric) cryptography. They are the main available "technology" we have at our
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
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 t
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
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