CS151: Intro to Cryptography and Computer Security
February 4, 2013
Homework 2 Solutions
Instructor: Anna Lysyanskaya
Due: February 11, 2013
Problem 1: Negligible functions
a. A function like (k) = 2k is certainly negligible, and also always positive.
b.
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CS151: Intro to Cryptography and Computer Security
Jan 28, 2014
Homework 1
Instructor: Anna Lysyanskaya
Due: Feb 4, 2014
Problem 1: True/False: This is a true/false problem.
Your friends Alice and Bob are both talented testtakers, but they can sometimes
CS151: Intro to Cryptography and Computer Security
April 30th, 2014
Final Exam
Instructor: Anna Lysyanskaya
Due: May 7, 2014
This is a noncollaborative assignment. You may not discuss the problems with any
other students and you may not use any resources
CS151: Intro to Cryptography and Computer Security
Jan 28, 2014
Homework 1 Solutions
Instructor: Anna Lysyanskaya
Due: Feb 4, 2014
Problem 1: True/False: This is a true/false problem.
a. Any percentage between 33.3%  50% would achieve this.
As an example
CS151: Intro to Cryptography and Computer Security
February 5, 2014
Homework 2
Instructor: Anna Lysyanskaya
Due: February 11, 2014
Problem 1: Negligible Functions
In cryptography, we usually dene security by requiring that the probability of some undesira
CS151: Intro to Cryptography and Computer Security
Feb 28, 2014
Homework 4 Solutions
Instructor: Anna Lysyanskaya
Due: Mar 6, 2014
Problem 1: Adaptive Security
a. (Solution by Nicolas Schank.) We can construct such a cryptosystem (G , E , D ) in the
follo
CS151: Intro to Cryptography and Computer Security
Feb 18, 2014
Homework 3
Instructor: Anna Lysyanskaya
Due: Feb 25, 2014
Problem 1: The Extended Euclidean GCD Algorithm
On input integers x and y, the extended Euclidean GCD algorithm nds integers a and b
CS151: Intro to Cryptography and Computer Security
April 21, 2014
Homework 8  Solutions
Instructor: Anna Lysyanskaya
Due: April 28, 2014
Problem 1: Broken Signatures
a. We want to show that if factoring is hard, it is also hard to make the scheme target
CS151: Intro to Cryptography and Computer Security
April 1, 2014
Homework 6  Solutions
Instructor: Anna Lysyanskaya
Due: April 8, 2014
Problem 1: Pseudorandom Fun(ctions)
We know that we want the output of Fs (x) to be of the form y0 y2 . . . yk1 , where
CS151: Intro to Cryptography and Computer Security
March 18, 2014
Homework 5 Solutions
Instructor: Anna Lysyanskaya
Due: April 1, 2014
Problem 1: Fun with PRGs
a. This is a PRG. Suppose that Ga (s) is not a PRG then there exists an adversary A that
distin
CS151: Intro to Cryptography and Computer Security
Feb 28, 2014
Homework 4
Instructor: Anna Lysyanskaya
Due: Mar 6, 2014
Problem 1: Adaptive Security
Recall the denition of secure publickey encryption that we saw in class.
Denition 1. A cryptosystem (G,
CS151: Intro to Cryptography and Computer Security
Mar 18, 2014
Homework 5
Instructor: Anna Lysyanskaya
Due: Apr 1, 2014
Problem 1: Fun with PRGs
Let G, G1 , G2 : cfw_0, 1n cfw_0, 12n be PRGs (for every n), and let s, s1 , s2 cfw_0, 1k . For each of the
f
CS151: Intro to Cryptography and Computer Security
April 10, 2014
Homework 7  Solutions
Instructor: Anna Lysyanskaya
Due: April 17, 2014
Problem 1: Damaging a CCASecure Cryptosystem
a. As always, we prove this using a reduction. In this case, we assume