MATH 201
DB FORUM 1 INSTRUCTIONS AND RUBRIC
This week's Discussion Board forum is the only one in which you will work individually.
Submit an original thread answering the forum questions by Saturday at 11:59 p.m. (ET) and
then reply to two other students
Hypothesis a statement about a population parameter that can be tested
Null hypothesis (H0): no difference btw pop parameter and a given value
H1: there is a difference btw pop parameter and a given value
One-tailed test H1 specifies how pop parameter dif
MATH 201
PROJECT 1 INSTRUCTIONS
Based on Larson & Farber: section 2.1
Use the Project 1 Data Set to create the graphs and tables in Questions 14 and to answer both parts of
Question 5. If you cannot figure out how to make the graphs and tables in Excel, y
Temperature Frequency Distribution Data Analysis
After reviewing the data from the provided table I have come to a few
conclusions. Historically this appears to be from either early spring or early fall.
Although it is more consistent with the month of Ap
Data Set for Project 1
Maximum Temperatures by State
in the United States
for the month of August, 2013
State Name
AL
AK
AZ
AR
CA
CO
CT
DE
FL
Max Temps in August 2013
97
97
45
100
49
109
93
91
102
GA
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
N
MATH 201
Mini Project 1: Standard Deviation
Log into our course on www.coursecompass.com and then select the Multimedia Library button.
Next, check the Java Applets box and click Find Now. Then select the link for the Standard
Deviation Applet from Chapte
Question 1. The meaning being 50% of the date the Z score of that would be 0.50. O.50 would be found on the Z Chart at interseciton of = -0.00
Question 2. Mean (925.886) - the 800 divided by the Standard Deviation 112.14145 =918.732
Question 3. Mean (925.
Math 201 Web Assign Homework Guide
Chapter One Homework
Be careful with these questions: for questions 1 & 6, you will get three attempts to give the
correct response and for question 5, you get five attempts, but you only have two attempts on the
remaini
Mini Project 1: Standard Deviation
1. a) What is the impact of the new point on the standard deviation?
ANSWER: The new point will cause the deviation on the chart to move towards the new
point that was added to the line.
b) What did you do differently to
1.
Prophecy
Probability
Justification_
1
1/13 or .077
There was 13 fathers before Jesusbirth.
2
1/40,000 or .000025 The population of Jerusalem was about
40,000.
3
or 0.50
Like flipping a coin, any human pierced in
the side after death would have a flow
6.12. Lattice reduction algorithms
6.12.4
417
Generalizations of LLL
There have been many improvements to and generalizations of the LLL algorithm. Most of these methods involve trading increased running time for
improved output. We briefly describe two o
404
6. Lattices and Cryptography
solve apprCVP, and we conclude in Section 6.12.4 by briefly describing some
generalizations of LLL.
6.12.1
Gaussian lattice reduction in dimension 2
The algorithm for finding an optimal basis in a lattice of dimension 2 is
Chapter 7
Digital Signatures
7.1
What is a digital signature?
Encryption schemes, whether symmetric or asymmetric, solve the problem of
secure communications over an insecure network. Digital signatures solve a
dierent problem, analogous to the purpose of
428
Exercises
(a) Let f (x) Z[x]/(X N 1) be a polynomial, and suppose that we have already
found a polynomial F (x) such that
f (x) F (x) 1
(mod pi )
for some i 1. Prove that the polynomial
!
"
G(x) = F (x) 2 f (x) F (x)
satisfies
f (x) G(x) 1
(mod p2i ).
6.12. Lattice reduction algorithms
405
Loop
If v2 < v1 , swap v1 and v2 .
"
#
!
Compute m = v1 v2 v1 2 .
If m = 0, return the basis vectors v1 and v2 .
Replace v2 with v2 mv1 .
Continue Loop
More precisely, when the algorithm terminates, the vector v1 is
7.3. ElGamal digital signatures and DSA
445
Samantha, or some trusted third party, chooses two primes p and q with
p 1 (mod q).
(In practice, typical choices satisfy 21000 < p < 22000 and 2160 < q < 2320 .)
She also chooses an element g Fp of exact order
6.12. Lattice reduction algorithms
413
Proof (sketch) of Theorem 6.68. For simplicity, and because it is the case
that we need, we will assume that L Zn is a lattice whose vectors have
integral coordinates.
It is clear that if the LLL algorithm terminates
430
Exercises
6.34. Suppose that Bob and Alice are using NTRU to exchange messages and that
Eve intercepts a ciphertext e(x) for which she already knows part of the plaintext m(x). (This is not a ludicrous assumption; see Exercise 6.31, for example.)
More
440
7. Digital Signatures
The standard solution to this problem is to use a hash function, which is
an easily computable function
Hash : (arbitrary size documents) cfw_0, 1k
that is very hard to invert. (More generally, one wants it to be very dicult
to f
402
6. Lattices and Cryptography
"
!
!
(b) !(f , g)! 4d 4N/3 1.155 N .
(c) The Gaussian heuristic predicts that the shortest nonzero vector in the
NTRU lattice has length
$ "
#
N q/e 0.484N.
LNTRU
h
Hence if N is large, then there is a high probability
6.12. Lattice reduction algorithms
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Input a basis cfw_v1 , . . . , vn for a lattice L
Set k = 2
Set v1 = v1
Loop while k n
Loop j = 1, 2, 3, . . . , k 1
Set vk = vk k,j vj
End j Loop
"
!
2
If vk 2 34 2k,k1 vk1
[9]
Set k = k
418
6. Lattices and Cryptography
by vk1 and vk . In BKZ-LLL, one works instead with a block of vectors of
length , say
vk , vk+1 , . . . , vk+1 ,
and one replaces the vectors in this block with a KZ-reduced basis spanning
the same sublattice. If is large,
7.1. What is a digital signature?
439
create a digital signature scheme in which the owner of the private key K Pri is
able to create valid signatures, but knowledge of the public key K Pub does not
reveal the private key K Pri . Necessary general conditi
6.12. Lattice reduction algorithms
407
Suppose that we are given a basis cfw_v1 , v2 , . . . , vn for a lattice L. Our
object is to transform the given basis into better basis. But what do we
mean by a better basis? We would like the vectors in the bette
6.13. Applications of LLL to cryptanalysis
6.13.1
419
Congruential cryptosystems
Recall the congruential cipher described in Section 6.1. Alice chooses a modulus q and two small secret integers f and g, and her public key is the integer h f 1 g (mod q). E
The mean is the measure of central tendency affected by an extreme value (outlier)
Definition:
True
Study 1 - 2
12 terms
Vocabulary for Study 1 - 2. Find, create, and access Probability, flashcards with Course Hero.
10 terms
Term:
If a z-score if zero, which of the following must be true?
Definition:
The corresponding x-vale is equal to the mean, because the z-score is equal to the difference the x-value and the mean, divided by the standard deviation.
Study Notes Test 2 3.1-5.3
10 terms
Vocabulary for Study Notes Test 2 3.1-5.3. Find, create, and access Probability And Statistics, flashcards with Course Hero.