AN INTRODUCTION TO MATHEMATICAL CRYPTOGRAPHY
ERRATA FOR THE FIRST EDITION
JEFFREY HOFFSTEIN, JILL PIPHER, JOSEPH H. SILVERMAN
Acknowledgements
We would like to thank the following people who have sent us comments and corrections: Stefanos Aivazidis, Rober
Codes
Jonathan L.F. King
University of Florida, Gainesville FL 32611-2082, USA
squash@ufl.edu
Webpage http:/www.math.u.edu/squash/
26 April, 2011 (at 17:16 )
(Folks, help me proofread and correct this.)
Dene the Kleene star operator by
L
Formal languages
MAC 3473 Honors Calculus 2 Keesling Review Test #2 Test Date 3/3/08 1. 2. 3. 4. 5. 6. Show that
"n
n =1
!
1
3
converges.
Denote the limit by
1 " n 3 = L . What must N be so that n =1
!
"n
n =1
N
1
3
!L <
1 ? 10, 000
For what values of p does Show that
"n
Study Sheet for Test 2 MAC 3473, Honors Calculus 2 Keesling Test on 3/4/11 1. Determine the following integrals. (a) 2. ! ! sin ! !" (b)
! ! ! (! ! !)(!)
!"
Determine the following integrals. (a) ! sin ! ! !" (b) (e) (h) ! ! ! !" tan! ! !"
! ! !
(c) (f) (
MAC 3473 Honors Calculus 2 Keesling Review Test #3 Test Date 4/4/08 1. Determine a numerical estimate of the following integrals using Romberg Integration using 2 6 = 64 intervals. For each answer the following questions: (a) (b) (c) Give the numbers in t
Study Sheet for Test 3 MAC 3473, Honors Calculus 2 Keesling Test on 4/19/11 1. Determine the area of the circle using the polar coordinate parameterization ! ! = ! for 0 ! 2!. 2. Determine the arc length of the cardioid for the parameter range 0 ! 2!. The
MAC 3473 Honors Calculus 2 Keesling Review Test #4 Test Date 4/22/08 1. Consider a circle of radius R rolling along the xaxis with the speed of the center of the circle being R. Give a parametric representation of the motion of the point. Suppose that the
Study Sheet for Test 1 MAT 4930 Topics in Calculus Keesling Test on 9/19/12 1. Determine the centroids of the following figures. (a) [a,b] [c,d] (c) The graph of 2. (b) The area under the curve
R 2 - x 2 over [0, R] R 2 - x 2 over [0, R]
Determine which n
Study Sheet for Test 2 MAT 4930 Topics in Calculus Keesling Test on 10/29/12 1. Let f (x) be a continuous function on R . Let x0 be a point in the line. Consider the sequence of points cfw_ x0 , x1 , x2 ,. defined by f (xi ) = xi+1 for i = 0,1,2,. . Suppo
Study Sheet for Test 3 MAT 4930 Topics in Calculus Keesling Test on 12/5/12 1. Let f (x) be a continuous function on R . Let x0 be a point in the line. Consider the sequence of points cfw_ x0 , x1 , x2 ,. defined by f (xi ) = xi+1 for i = 0,1,2,. . Suppos
MAT 4930 Topics in Calculus Keesling Test 1 9/19/12 Name Work all problems. Show all work with an explanation for each answer. Each problem is worth 20 points. 1. Determine the centroid of the following figures. (a) The area under the curve R 2 - x 2 ove
Study Sheet for Test 1 MAC 3473, Honors Calculus 2 Keesling Test on 2/2/2011 1. 2. 3. 4. 5. 6. Show that
"n
n =1
!
1
3
converges.
Denote the limit by
1 " n 3 = L . What must N be so that n =1
!
!n
n =1
N
1
3
"L <
1 ? 10, 000
For what values of p does Show
MAC 3473 Honors Calculus 2 Keesling Review Test #1 Test Date 2/4/08 1. Find the surface area and the volume of the torus which is formed by rotating about the yaxis a disk of radius b whose center is located at the point (a,0) . Find these using Pappus' T
NT-Cryptography
MAT4930 7554
Q1: Wedn. N := (100)=
26 Jan
165
EFT says that 3
Q6: Wedn. Bits
23 Feb
29Sep2010
Quizzes Q
20 31 40 30 61 0 7
decode to
20 bits
.
N
. So (N )=
.
[3165 ]
EFT) last two digits of 7
are
.
.
[0 . N ). Hence (by
.
.
.
via Ziv-Lemp
NT-Cryptography
MAT4930 7554
Class-W
Prof. JLF King
23Feb2011
W1: Show no work. Please write DNE in a blank if the
described object does not exist or if the indicated operation
cannot be performed.
W2: Essay question, OYOSOP:
For a nite code C over alphab
NT-Cryptography
MAT4930 7554
Prof. JLF King
22Feb2011
Home-W
b
This take-home is due at the BoC of Wedn, 16Feb2011.
Please write DNE in a blank if the described object does not
exist or if the indicated operation cannot be performed. Fill-in
all blanks on
NT-Cryptography
MAT4930 7554
Prof. JLF King
23Mar2011
X4: Show no work. Please write DNE in a blank if the
described object does not exist or if the indicated operation
cannot be performed.
a
Modulo 35, the multiplicative-order of 3 is
. [Hint: (35) has v
NT-Cryptography
MAT4930 7554
Home-X
Prof. JLF King
21Mar2011
This take-home is due at the BoC of Mon, 21Mar2011.
Please write DNE in a blank if the described object does not
exist or if the indicated operation cannot be performed. Fill-in
all blanks on th
NT-Cryptography
MAT4930 7554
Prof. JLF King
6Apr2011
Class-Y
Y1: Show no work. Please write DNE in a blank if the
described object does not exist or if the indicated operation
cannot be performed.
z
Prof. King wears
bifocals, and cannot read small
Circle
NT-Cryptography
MAT4930 7554
Project-Z
Prof. JLF King
19Apr2011
This optional nal-project is due by noon, Friday,
22Apr2011, slid completely under my ofce door,
LIT402. Fill-in every blank on this sheet. Please write
.
DNE in a blank if the described obje
Topics in Calculus Quiz 10 1. Derive the steady-state probabilities for being in each state for the queue M / M /1 / FIFO . Use for the arrival rate and for the service rate. Assume that > . Assume that = 9 and = 10 . Give the probability that the system
MAT 4930 Topics in Calculus Keesling Test 3 12/5/12 Name Work all problems. Show all work with an explanation for each answer. Each problem is worth 20 points. 1. Consider the quadratic function f (x) = x (1- x) for x [0,1] . Suppose that 1 1 < < 3 . Sho