South Asian Free Trade Area
The South Asian Free Trade Area or SAFTA is a pact signed in 6 January 2004 that
would gradually eliminate most tariffs and other trade barriers on products and services
passing between Bangladesh, Bhutan, India, Maldives, Nepa
Latin American Free Trade Association
The Latin American Free Trade Association (LAFTA) was created in the 1960 Treaty
of Montevideo by Argentina, Brazil, Chile, Mexico, Paraguay, Peru, and Uruguay. The
signatories hoped to create a common market in Latin
North American Free Trade Agreement
The North American Free Trade Agreement (NAFTA) is an agreement signed by the
governments of Canada, Mexico, and the United States, creating a trilateral trade bloc in
North America. The agreement came into force on Jan
Walton Hi-Tech Industries Ltd
Walton Hi-Tech Industries Limited, commonly referred to as Walton, is a private limited company of
Bangladesh. It is a sister concern of R.B. Group. Walton is one of the largest electrical, electronics and
automobiles manufac
QUESTIONNAIRE FOR FOOD AND GROCERY SHOPPING
Thank you for responding to this questionnaire. This document will be used only for
academic purposes.
Name: _ Address: _
Below is given a series of features found in most food and grocery stores. Keeping your
F
Chapter- 1
Introduction
1
1.1 Background of the Study
It has become essential for every person to have some idea on the bank and banking
procedure. As our educational system predominantly text based, inclusion of practical
orientation program is an except
Chapter One
Introduction
Page | 1
Janata Bank Limited, the 2nd largest State Owned Commercial Bank (SCB) in Bangladesh, has
an authorized capital of Tk. 30000 million, is playing pivotal role in overall financial activities
of the country. In todays world
The house of quality translates the voice of customers into design requirements that meets
specific target values and matches those how organization will meet those requirements.
Many managers and engineers consider the house of quality to be primary char
Group
INVINCIBLE
Group Members:
SL NO
NAME
ID
01
Md. Muddassir Uddin
19
02
Jouti Chowdhury
33
03
Shaha Alam
65
04
Md.Uzzal Mia
85
05
Kaniz Fatima Lima
96
Quality Function
Deployment of
higher education in
Bangladesh
Jouti Chowdhury
ID-33
Quality Function
How Business Operate
Assessor Name
:
Student Name
:
Student ID
:
Table of Contents
Introduction.2
1.1 Description of the types of organisations found in the public and private sectors in a named
country.3
1.2 Explanation of the different structures within
Executive summary
Mushroom made food distribution center processes the collected mushrooms and sells to the
customers. It is located at Shreepur in Gazipur. It has two primary distribution centers one in
Dhanmondi area and the other in Uttara area. Its vi
Abridged Version
Health Care Seeking
Behavior of Slum-Dwellers
in Dhaka City
Results of a Household Survey
Institute of Health Economics
University of Dhaka
JUNE, 2015
Report prepared for Health Economics Unit (HEU) of
MoHFW and World Health Organization
I
Letter of Transmittal
Date: February 28, 2016.
Dr. Shyam Sundar Karmaker
Professor
Department of Management
Faculty of Business Studies
University of Dhaka
Subject: Submission of Internship Report.
Dear Sir,
I have the pleasure to submit an Internship R
Student Declaration
First of all I would like to declare that this internship report isnt a copy another persons report.
The study is original in nature .I have tried my best to make this report informative as well as
descriptive. I also ensure that this
5.1. Elliptic curves
281
R !
Q
!
P!
L
E
P Q = R
!
Figure 5.2: The addition law on an elliptic curve
!
"2
7
1
X
= X 3 15X + 18,
3
3
1
49 2 14
X X + = X 3 15X + 18,
9
9
9
161
49
121
X+
.
0 = X3 X2
9
9
9
We need to find the roots of this cubic polynomial.
290
5. Elliptic Curves and Cryptography
Example 5.12. Let E be given by the equation
E : Y 2 = X 3 + 4X + 6.
We can think of E as an elliptic curve over Fp for dierent finite fields Fp and
count the number of points in E(Fp ). Table 5.2 lists the results
5.1. Elliptic curves
283
223
substitute X = 193
64 into the equation (5.3) for L to get Y = 512 , and then
we switch the sign on Y to get
!
"
193 223
,
P P =
.
64 512
A second potential problem with our addition law arises if we try to
add a point P = (a,
286
5. Elliptic Curves and Cryptography
(X + )2 = X 3 + AX + B,
so
X 3 2 X 2 + (A 2)X + (B 2 ) = 0.
We know that this cubic has x1 and x2 as two of its roots. If we call the third
root x3 , then it factors as
X 3 2 X 2 + (A 2)X + (B 2 ) = (X x1 )(X x2 )(X
292
5. Elliptic Curves and Cryptography
Notice the analogy with the ordinary logarithm log() = log() + log()
and the discrete logarithm for Fp (cf. Remark 2.2). The fact that the discrete
logarithm for E(Fp ) satisfies (5.4) means that it respects the add
5.8. Bilinear pairings on elliptic curves
5.8.3
319
The Weil pairing
The Weil pairing, which is denoted by em , takes as input a pair of points
P, Q E[m] and gives as output an mth root of unity em (P, Q). The bilinearity
of the Weil pairing is expressed
5.6. Lenstras elliptic curve factorization algorithm
303
in town meant that it automatically received extensive scrutiny from the
academic community, which helped to validate its security.
The invention and eventual commercial implementation of ECC follow
298
5. Elliptic Curves and Cryptography
Bob and Alice have exchanged the secret point (3347, 1242). As will be explained in Remark 5.20, they should discard the y-coordinate and treat only
the value x = 3347 as a secret shared value.
One way for Eve to di
5.4. Elliptic curve cryptography
Alice computes
Bob computes
299
QA = nA P = 2489(920, 303) = (593, 719) E(F3851 ),
QB = nB P = 2286(920, 303) = (3681, 612) E(F3851 ).
However, rather than sending both coordinates, Alice sends only xA = 593 to
Bob and Bob
296
5. Elliptic Curves and Cryptography
As we saw in Section 4.4, if r is somewhat larger than p, say r 3 p, then
there is a very good chance that there will be a collision.
This naive collision algorithm requires quite a lot of storage for the two
lists.
312
5. Elliptic Curves and Cryptography
(P + Q) = (P ) + (Q).
(5.11)
In other words, maps E(F2k ) to itself, and it respects the addition law.
(In mathematical terminology, the Frobenius map is a group homomorphism
of E(F2k ) to itself.)
It is easy to ch
324
5. Elliptic Curves and Cryptography
284
fQ (P S)
=
= 88 F631 .
fQ (S)
204
Finally, taking the ratio of these two values yields
e5 (P, Q) =
473
= 242 F631 .
88
We check that (242)5 = 1, so e5 (P, Q) is a fifth root of unity in F631 .
Continuing to work
5.9. The Weil pairing over fields of prime power order
327
5. Solve the DLP for and in Fpk , i.e., find an exponent n such that
= n . If pk is not too large, this can be done using the index calculus.
Note that the index calculus (Section 3.8) is a subex
5.4. Elliptic curve cryptography
297
Public Parameter Creation
A trusted party chooses and publishes a (large) prime p,
an elliptic curve E over Fp , and a point P in E(Fp ).
Private Computations
Alice
Bob
Chooses a secret integer nA .
Chooses a secret in