15.082 and 6.855J
The Shortest Augmenting Path
Algorithm for the Maximum Flow
Problem
Shortest Augmenting Path
4
2
3
s
5
1
1
2
3
4
1
1
4
2
t
3
This is the original network,
and the original residual
network.
3
Initialize Distances
2
5
3
4
3
s
2
2
2 s
1
3
15.082J and 6.855J
March 4, 2003
Introduction to Maximum Flows
The Max Flow Problem
G
xij =
=
(N,A)
flow on arc (i,j)
uij
=
capacity of flow in arc (i,j)
s
t
=
=
source node
sink node
Maximize
v
Subject to
j xij
j xsj
=

k xki=
0 for each i s,t
v
0 xi
(2,4) Trees
What are they?
They are search Trees (but not binary search trees)
They are also known as 24, 234 trees
Multiway Search Trees
Each internal node of a multiway search tree T:
has at least two children
stores a collection of items of the
A simple example
finding the maximum of a set S of n numbers
Time complexity
Time complexity:
T(n)=
Calculation of T(n):
Assume n = 2k,
T(n) = 2T(n/2)+1
= 2(2T(n/4)+1)+1
= 4T(n/4)+2+1
:
=2k1T(2)+2k2+4+2+1
=2k1+2k2+4+2+1
=2k1 = n1
2T(n/2)+1 , n>2
AVL Trees
AVL Trees
1
Insertion
Inserting a node, v, into an AVL tree changes the
heights of some of the nodes in T.
The only nodes whose heights can increase are
the ancestors of node v.
If insertion causes T to become unbalanced, then
some ancestor of
15.082 and 6.855J
The Shortest Augmenting Path
Algorithm for the Maximum Flow
Problem
Shortest Augmenting Path
4
2
3
s
5
1
1
2
3
4
1
1
4
2
t
3
This is the original network,
and the original residual
network.
3
Initialize Distances
2
5
3
4
3
s
2
2
2 s
1
3
Problem Set 3
Instructions: Answer the questions below and submit your solutions in class on October 28. Late
submission will attract a penalty of 1 mark/hr. You have to solve the problems on you own. You
cannot consult your friends/enemies/internet.
The
15.082 and 6.855J
The FordFulkerson Augmenting
Path Algorithm for the Maximum
Flow Problem
1
FordFulkerson Max Flow
4
2
3
s
5
1
1
2
3
4
1
1
2
2
t
3
This is the original network,
and the original residual
network.
3
FordFulkerson Max Flow
4
2
3
s
5
1
1
CSL 201, IIT Delhi
Assignment 4  Part III
Searching Points in Multidimensional Range
Announce Date : 12.04.2014
Due Date : 21.04.2014
This part of assignment is based on multi dimensional range search. The
following sections contain brief introduction t
CSL 201, IIT Delhi
Assignment 4  Part I
Searching Points in a one dimensional(1D) range
Announce Date : 04.04.2014
Due Date : 12.04.2014
This part of the assignment is based on one dimensional(1D) range search.
1
Problem Intuition
1D range searches ar
1
Stack Controller
The stack controller is a device which when given an input either accepts the
input or rejects it. Internally the stack controller maintains a
set of rules,
stack
lookup table generated from the set of rules.
There are only two kinds
Assignment 1 (Total marks 13+2) : Here 2 marks are reserved for well documented and
correct program for all kinds of inputs data.
Last date of submission: 22nd Jan by 5pm ; Last date for Demo : latest by 25th Jan
(5) Write complete program in C / C+ to im
Simulation of Memory Allocator Module
Posting date: 6/March/14
Submission date: 19/March/14 by 10pm
Demo: 2024th March/14
Total: 20 Marks
Problem statement:
Write a C/C+ program to allocate memory to the processes from the list of available memory
chunks
Course Information
CSE 207 Modern Cryptography
Instructor: Mihir Bellare
Website: http:/cseweb.ucsd.edu/ mihir/cse207
1 / 56
Cryptography usage
Did you use any cryptography
today?
2 / 56
Cryptography usage
Did you use any cryptography
today?
over the l
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
1 / 135
Recommended Book
Steven Levy. Crypto. Penguin books. 2001. A nontechnical account of the history of publickey cryptography and the colorful characters involved.
2 / 135
Recall Symmetric Cryptography
Before Alice and Bob ca
Supplementary Material: A Computational Introduction to Number
Theory and Algebra (Version 1)
Last updated: 10/15/2006.
This document contains supplementary exercises, examples, and a few alternative proofs
of theorems that would make nice additions to th
DIGITAL SIGNATURES
1 / 74
Signing by hand
COSMO
ALICE
Cosmo
ALICE
Pay Bob $100
Alice
Alice
Bank
=?
no
Dont
yes
pay Bob
2 / 74
Signing electronically
SIGFILE
scan
Alice
101 1
Bank
Internet
ALICE
Pay Bob $100
3 / 74
Signing electronically
SIGFILE
scan
Alice
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Key Distribution
Diffie Hellman Key Exchange
^
^
Both parties share ^cfw_ which is the secret key for the session.
Authentication
Diffie Hellman Key Exchange
^
^cfw_
^
^
The adversar
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Minor1 Exam
Problem 1
Let : 0,1 128 0,1 128 0,1 128 be a (, , )
secure PRF. Consider the function family : 0,1 128
0,1 128 0,1 128 defined as () = (). Is
a secure PRF? Discuss.
CSL 759: Cryptography
Instructor: Ragesh Jaiswal
Course Information
Description: Cryptography has a very long history and there are evidences to suggest its existence
even around 4000 years back. Classical cryptography deals mainly with secret communicati
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
The Factoring Problem
The Factoring Problem
We would like to understand the success of polynomial time
algorithms in factoring integers. We formally define this in
terms of an exper
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Message Authentication
PRF as MAC
Suppose we have a secure PRF : 0,1 0,1
0,1 and suppose we only need to authenticate messages
of size , then consider the MAC associated with :
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Course Project
Course Project
Let me know your team (at most 2 students per project) and
your project topic by tomorrow (12th Mar.).
We will set up meetings this WedFri and early
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Hash Functions
Hash Functions: Introduction
A hash function is a map : 0,1 that is compressing,
i.e., > 2 .
Usually 2 and is small.
Example:
64
= 0,1 2 i.e., all binary strings o
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Block Ciphers
Block Ciphers: Introduction
Block ciphers work on blocks of message bits rather than a
stream of message bits.
Main Idea:
Suppose we encrypt in blocks of size .
Let
CSL759: Cryptography and Computer
Security
Ragesh Jaiswal
CSE, IIT Delhi
Message Authentication
Message Integrity/Authenticity
Accept/Reject
,
Key exchange protocol
Cryptographic goals:
was sent by Alice and no one else.
was not modified during transi