Cryptographic Hash Functions
Murat Kantarcioglu
Based on Prof. Ninghui Lis Slides
Lecture Outline
Hash functions
Security properties
Iterative Hash
Functions
Merkle-Damgard
construction
SHA1
1
Data Integrity and Source
Authentication
Encryption does
CS 555 Fall 2016 Homework 2 Solutions
Alexander R Block
November 14, 2016
Department of Computer Science, Purdue University. [email protected]
1
1. (10 + 10 points) Let Gn,` : cfw_0, 1n cfw_0, 1` and Hn,` : cfw_0, 1n cfw_0, 1` be efficient functions.
(a)
Cryptography- grad problem set 1
Maryam Honari Jahrom V00871627
Atousa Tangestanipour V00874196
Question 1:
1-a:
We have this equation from perfect secrecy:
P r [ P=mC=c ]=P r [ P=m ] H (M C )=H ( M )
We should prove both direction of above formulation
1-
Homework 2 - Due Thursday October 22, by 5pm - in my mailbox
Problem 1
Prove that if the discrete logarithm assumption holds, then it is hard to compute x given g xy and g y .
Formally, prove that if the discrete logarithm assumption holds, then for any p
Cryptography- grad problem set 1
Maryam Honari Jahrom V00871627
Atousa Tangestanipour V00874196
Question 1:
1-a:
We have this equation from perfect secrecy:
[ = = ] = [ = ] ( ) = ()
We should prove both direction of above formulation
1[ = = ] = [ = ] ( )
1. Suppose we have a message space P = cfw_m1 , m2 , m3 , m4 , and a distribution P on P given by Pr[P = m1 ] = 1/2, Pr[P = m2 ] = 1/4,
Pr[P = m3 ] = 1/8, Pr[P = m4 ] = 1/8. Let C be the corresponding
distribution on ciphertext space C = cfw_c1 , c2 , c3
Homework 3 - Due Monday November 2, by 5pm - in my mailbox
Problem 1
This problem gives an example of whats wrong with deterministic encryption. Suppose Bob and
David have two independent Rabin public keys nB and nD , respectively. Suppose Alice has a sin
Homework 4 - Comp150 - Due Friday Nov 20, by 5pm
Problem 1
So far, the adversaries we have considered have been limited to observing ciphertexts. A stronger
adversary is one endowed with the power to obtain decryptions of some ciphertexts. This is known
a
Math 110 Problem Set 1 Solutions
2.2 The ciphertext U CR was encrypted using the affine function 9x + 2 mod
26. Find the plaintext.
Solution: Given y, we need to solve
y 9x + 2 mod 26
y 2 9x mod 26
Checking, we see that 3 is the inverse of 9 modulo 26, as
Question 1:
1-a:
We have this equation from perfect secrecy:
Pr [ P=m C=c ] =Pr [ P=m ] H ( M C )=H ( M )
We should prove both direction of above formulation
1- Since we have
H ( M C )=
2-
m Pc C
Pr [ P=mC=c ]log Pr [ P=m C=c ]/ Pr [ P=m]= Pr [ M =m ]log
Question 1:
1-a:
We have this equation from p
erfect secrecy:
Pr [ P=m C=c ] =Pr [ P=m ] H ( M C )=H ( M )
We should prove both direction of above formulation
1- Since we have
H ( M C )=
2-
m Pc C
Pr [ P=mC=c ]log Pr [ P=m C=c ]/ Pr [ P=m]= Pr [ M =m ]log
Homework 3 - Due Monday November 2, by 5pm - in my mailbox
Problem 1
This problem gives an example of whats wrong with deterministic encryption. Suppose Bob and
David have two independent Rabin public keys nB and nD , respectively. Suppose Alice has a sin
CSC429
Cryptography
Assigment 2
Due at the beginning of class, Monday, February 20, 2017
(100 Marks total)
1. Let F be a pseudorandom function, and G a pseudorandom generator with expansion factor `(n) =
n + 1. For each of the following encryption schemes
CSC429/529
Midterm Topics Spring 2017
Classical and information theoretic crypto
Chapter 1 all sections
Kerchoffs principles
Shift, Affine and Vigenere ciphers
Frequency analysis, Kasiskis method
Chapter 2 all sections except 2.4
Basic principles of
Homework 1 - Comp150 - Due Friday October 2, by 5pm - in my
mailbox
Problem 1
a.) Compute 764 mod 23 (show work; do not use a calculator). (Hint: compute 72 , 74 , 78 , . . . mod
23 first.)
b.) Compute 771 mod 23 (show work; do not use a calculator). (Hin
Homework 2 - Due Thursday October 22, by 5pm - in my mailbox
Problem 1
Prove that if the discrete logarithm assumption holds, then it is hard to compute x given g xy and g y .
Formally, prove that if the discrete logarithm assumption holds, then for any p
CHAPTER 2
CIRCUITS WITH SWITCHES AND DIODES
We assume that all elements are ideal.
Switches: INFINITE or ZERO resistance to current, and INSTANTANEOUS TRANSITION from one state
to another. (However, we will also discuss non-ideal devices at a later stage
CHAPTER 5
[CHAPTER 3, EXPERIMENT 2 of LAB MANUAL]
SINGLE-PHASE FULL-WAVE CONTROLLED RECTIFIER
OBJECTIVE: To study the operation of a practical single-phase controlled rectifier and observe
the effect of a free-wheeling diode.
5.1 INTRODUCTION
Controlled r
Example 3.1: The circuit shown in Fig. E3.1 (Fig. 1.14(a) of Chapter-3 notes) is employed to
charge a bank of batteries of which the nominal terminal voltage is Vc = 72 V. Calculate the
average and rms line currents and the power factor at the source if
(
EXAMPLES Chapters 2-3
Example 2.1: In the circuit of Fig. E2.1 (fig. 1.18a of notes), the source voltage v =
110 2 [sin(120t)] V, R = 1 , and the load-circuit emf Vc = 100 V. If switch SW is closed
during the negative half-cycle of the source voltage, cal
CHAPTER 4: EXAMPLES
Example 4.1: A single-phase full-wave ac voltage controller (Fig. 4.1(a) is used to control the
power from a 2300-V ac source into a resistive load that can vary from 1.15 to 2.30 The
maximum output power desired is 2300 kW. Calculate
CHAPTER 6
(Lab. Manual: CHAPTER 4, EXPERIMENT 3)
ONE-QUADRANT CHOPPER OR
DC-TO-DC CONVERTER Part 1
Part - A
6.1 INTRODUCTION
In many applications, a dc source is available and the average value of a direct voltage applied to
the load has to be varied.
A d
Example 6.1 In the Type A chopper circuit of Fig. 6.2(a), V = 110 V, L = 1 mH, R = 0.25 , VC =
11 V, T = 2500 s, tON = 1000 s.
(a)
(b)
(c)
(d)
Calculate the average output current Io and the average output voltage Vo.
Calculate the maximum and minimum val
Example 5.1 For the single-phase bridge controlled rectifier shown in Fig. E5.1 L = 20 mH, R =
4.35 , VC = 0, and the delay angle = 75o. Calculate the following:
(a) The average output current.
(b) The rms output current.
(c) The average and rms thyristor
CHAPTER 1
INTRODUCTION
Any power semiconductor system employed for rectifying, inverting, or otherwise modulating
the power output of an ac or dc energy source is called a CONVERTER SYSTEM or POWER
CONDITIONING SYSTEM.
Objective: Adjustable ratio transfor
ELEC 410 Power Electronics (A.K.S. Bhat)
SOLUTIONS To ASSIGNMENT # 1
(1)
0 < t < 10 ms:
Equivalent circuit for 0 < t < 10 ms.
SW is closed at t = 0, i = 0, iD = 0.
KVL:
V = vL + vR = L
i.e.,
di
Ri
dt
V
(1)
A/s
(2)
di R
V 100
i
dt L
L
L
Forced (steady-s
ELEC 410 POWER ELECTRONICS
SOLUTIONS TO ASSIGNMENT # 2
PART-A
(1) In the circuits of Fig. P 1(a) to (c), L = 100 H, C = 25 F. Sketch to scale the time variations
of i, vL, and vC if the thyristor is turned on with the initial capacitor voltages as follows
ELEC 410. ASSIGNMENT#1. (Dr. A.K.S. Bhat)
lcfw_a:r 17 .2016:May 27 .2016
(1) In the circuit of Fig. Pl, switch SW is closed at t : and opened again at / : 10 ms. At / : 0,
iL: o. Sketch approximately to scale the time variations of i, iy, ip, and v, and d