CSci 5471: Modern Cryptography, Spring 2010 Homework #1
Yongdae Kim
Due: Feb. 2 9:00 AM
Type up your solution (either text or pdf) and send it to me and TA by email. (kyd(atmark)cs.umn.edu,
yongdaek(atmark)gmail.com,hkang(atmark)cs.umn.edu)
Show all st
Admin Stuff
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Modern
Cryptography
Lecture 7
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Modern
Cryptography
Lecture 8
Yongdae Kim
Admin Stuff
E-mail
Office hours
5th assignment will be posted this week (programming).
Study Guide
Interim Report due: Mar 30 (Firm Deadline: Read instruction)
4th assignment is due: 3/23 9:00 AM.
Me: T 1:30 ~ 2:3
Admin Stuff
E-mail
Modern
Cryptography
Lecture 8
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Diffie, Hellman,
Elgamal
Discrete Logarithm
Problem
G: cyclic group of order p
g: a generator of G
Discrete logarithm problem
Find logg(h) with non-negligible
probability, for a uniform random hG
Solvers performance measured by success
probability
2
Discr
Diffie, Hellman,
Elgamal
Discrete Logarithm
Problem
G: cyclic group of order p
g: a generator of G
Discrete logarithm problem
Find logg(h) with non-negligible
probability, for a uniform random hG
Solvers performance measured by success
probability
2
Discr
Admin Stuff
E-mail
Modern
Cryptography
Lecture 10
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Modern
Cryptography
Lecture 11
Yongdae Kim
Admin Stuff
E-mail
Office hours
Final Report due: May 6 (Firm Deadline: NO EXTENSION)
6th assignment is due: 4/20 9:00 AM.
Study Guide
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~ 2:15
Admin Stuff
E-mail
Modern
Cryptography
Lecture 11
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Modern
Cryptography
Lecture 12
Yongdae Kim
Admin Stuff
E-mail
Office hours
Final Report due: May 6 (Firm Deadline: NO EXTENSION)
6th assignment is due: 4/20 9:00 AM.
Study Guide
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~ 2:15
Admin Stuff
E-mail
Modern
Cryptography
Lecture 12
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Modern
Cryptography
Lecture 13
Yongdae Kim
Admin Stuff
E-mail
Office hours
Final Report due: May 6 (Firm Deadline: NO EXTENSION)
6th assignment is due: 4/20 9:00 AM. (Today)
Study Guide
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 P
Admin Stuff
E-mail
Modern
Cryptography
Lecture 13
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:00 ~ 2:00, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
MAC & AE
MAC
Message Authentication Code
keyed hash function H (x)
k: secret key, x: message of any length,
k
Hk(x): xed length (say, 128 bits)
deterministic
Purpose: to prove to someone who has
the secret key k, that x is written by
How to use?
A
2/23/10
What is a hash
function?
Hash functions
Arbitrary length input, xed length output
efcient
one-wayness, 2nd preimage resistance,
collision resistance
What else?
Probability
A random function?
Recall that MD5 outputs 128-bit bitstrings.
What i
Hash functions
What is a hash
function?
Arbitrary length input, xed length output
efcient
one-wayness, 2nd preimage resistance,
collision resistance
What else?
Probability
Recall that MD5 outputs 128-bit bitstrings.
What is the probability that
MD5(
CSci 5471: Modern Cryptography, Spring 2010 Homework #2
Yongdae Kim
Due: Thursday, Feb. 16, 9:00 AM
Show all steps. Please ask any questions, if the problems are not clear.
Total 120 points.
1. Number Theory! (30 points)
(a) (7 pts) Show that ax + by =
CSci 5471: Modern Cryptography, Fall 2010 Homework #3
Yongdae Kim
Due: Mar. 2 9:00 AM
Show all steps. Please ask any questions, if the problems are not clear.
Send me your solution by e-mail.
Total 100 + 40 points.
1. Number Theory! (20 points) In the fol
CSci 5471: Modern Cryptography, Fall 2010 Homework #4
Yongdae Kim
Due: Mar. 23 9:00 AM
Show all steps. Please ask any questions, if the problems are not clear.
Send me your solution by e-mail.
Total 100 + 40 points.
1. Number Theory (45 points): Try to us
CSci 5471: Modern Cryptography, Spring 2010 Homework #5
Yongdae Kim
Due: Apr 6th. 9:00 AM.
Show all steps. Please ask any questions, if the problems are not clear.
Total 2 pages, 160 possible points.
Problem 4 could be subject to change. Check class web s
CSci 5471: Modern Cryptography, Spring 2010 Homework #6
Yongdae Kim
Due: Apr 20th (Tuesday) 9:00 AM
Show all steps. Please ask any questions, if the problems are not clear.
1. ElGamal vs. Dife-Hellman Algorithm (30 pt total) Suppose you have an algorith
Modern
Cryptography
Lecture 1
Yongdae Kim
Whos who?
2
Some movies :-)
3
Introduction
Class Information
Title:
Modern Cryptography
Course Number: CSci 5471
Lectures: TTh 11:15 PM - 12:30 PM, ME 212
Has been experimental and challenging to teach
this cou
Whos who?
Modern
Cryptography
Lecture 1
Yongdae Kim
2
Some movies :-)
Introduction
Class Information
Title:
Modern Cryptography
Number: CSci 5471
Lectures: TTh 11:15 PM - 12:30 PM, ME 212
Course
Has been experimental and challenging to teach
this cours
Modern
Cryptography
Lecture 2
Yongdae Kim
Admin Stuff
E-mail
Subject
should have [5471] in front, e.g. [5471] Project
proposal
CC TA and PostDoc: hkang@cs.umn.edu,
aaram@cs.umn.edu
Office hours
Me:
T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by
appointment)
Admin Stuff
E-mail
Subject
should have [5471] in front, e.g. [5471] Project
proposal
CC TA and PostDoc: hkang@cs.umn.edu,
aaram@cs.umn.edu
Modern
Cryptography
Lecture 2
Office hours
Me:
T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by
appointment)
TA: M 1:15 P
Modern
Cryptography
Lecture 3
Yongdae Kim
Admin Stuff
E-mail
Office hours
Pre-proposal due: Feb 9
2nd assignment will be on-line tonight (due: 2/16 9:00 AM)
Study Guide: Quiz this Thursday
Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:1
Admin Stuff
E-mail
Modern
Cryptography
Lecture 3
Subject should have [5471] in front, e.g. [5471] Project proposal
CC TA and PostDoc: hkang@cs.umn.edu, aaram@cs.umn.edu
Office hours
Me: T 1:30 ~ 2:30, Th 10:00 ~ 11:00 (and by appointment)
TA: M 1:15 PM ~
Modern
Cryptography
Lecture 4
Yongdae Kim
Admin Stuff
E-mail
Office hours
Third assignment will be posted early. (Programming)
Study Guide
Pre-proposal due: Feb 9 (Passed Deadline)
Meeting with groups: This week and next week
2nd assignment is due: 2/16 9