Page 1 (line 1) and Page 2 (line 6)
The 19th character in the ciphertext string should be a J instead of an I.
Page 7 - Section 1.1
Exercise 1 should read:
Does every subset of the negative integers have a smallest element?
Page 8 - Section 1.1
The definition should read:
An integer p greater than 1 is called a prime number if its only positive divisors are 1 and p. A positive integer other than 1 that is not prime is called a composite number. The integer 1 is neither prime nor composite.
Page 12 - Section 1.2
In line 13 replace b(qy1) with b(-qy1).
The seventh line from the bottom of the page should read:
relies on repeated application of the Division Algorithm and is described in Book VIII of Euclid's Elements.
The bold text on the sixth line from he bottom of the page should be replaced by:
The Euclidean Algorithm for Finding gcd(a,b).
Page 16 - Section 1.3
The paragraph sandwiched between the definition and Theorem 1.5 should read:
Examples of relatively prime integers are 5 and 3, and 7 and 11. 7469 and 2387 are not relatively prime as Example 1.9 demonstrates. 15 and 35 are not relatively prime because gcd(15, 35) = 5. The only positive factor two relatively prime integers have in common is 1.
Page 17 - Section 1.3
Delete the word "positive" from the statement of Theorem 1.7.
Also delete the word "positive" from the third line from the bottom of the page.
Page 41 - Section 1.6
In Exercise #6 the 26th letter of the ciphertext should be a "Q" and not an "O."
Page 50 Problem #3
This information should have been included in the statement of the problem: The number 7 can be associated with either P, Q, R, or S.
Page 65 - Section 2.3
In the text box, replace "sapce" with "space."
Page 66 - Section 2.3
The correct solution to Example 2.11(b) is 13/25.
Page 72 - Section 2.3
In Exercise #9, Part (b), the word "diamond" should be "diamonds."
Page 73 (line 23)
A "?" is missing at the end of the sentence.
Page 75 - Section 2.4
Exercise 4 should read:
Suppose that in a certain language, the probability of two characters selected at random from a text being the same is 0.03. If a document in this language contains 5713 characters,
Page 81 - Section 2.5
Append the following to the end of the first paragraph:
Notice that when the letter of the keyword is c (the third letter of the alphabet), the ciphertext letter is alphabetically two characters beyond the plaintext character (e.g., m -» O, w -» Y). When the letter of the keyword is h (the eighth letter of the alphabet), the ciphertext letter is alphabetically seven characters beyond the plaintext character (e.g., o -» V, i -» P). Do you see any pattern here? If so, Molly would like to talk with you.
Page 90 - Section 2.5
The table on this page should read:
| Column -» | 1 |
2 |
3 |
4 |
... |
r-1 |
r |
| Letters of keyword -» | k1 |
k2 |
k3 |
k4 |
... |
kr-1 |
kr |
| Alphabetic position of keyword letter -» | s1 |
s2 |
s3 |
s4 |
... |
sr-1 |
sr |
| Ciphertext -» | c1 |
c2 |
c3 |
c4 |
... |
cr-1 |
cr |
cr+1 |
cr+2 |
cr+3 |
cr+4 |
... |
c2r-1 |
c2r |
|
c2r+1 |
c2r+2 |
c2r+3 |
c2r+4 |
... |
c3r-1 |
c3r |
|
c3r+1 |
... |
... |
... |
... |
... |
... |
|
... |
... |
... |
... |
... |
... |
... |
Page 91 - Section 2.5
The text in the fourth row of the first column should read: Ciphertext -»
Page 91 - Section 2.5
The second and third sentences of the second full paragraph should read:
In the current example, another way of saying this is that the ciphertext letters in the first column are enciphered by using an additive cipher with key = 9. Similarly, the ciphertext letters in the second column are enciphered using an additive cipher with key = 14.
Page 93 – Section 2.5
The first four letters of the string of ciphertext are missing. Replace the text on this page beginning with the line under "Column 1:" with
JQCJQLJWRANJMACBCCJMVBJCXARQCJRJQRRRBVEBVMHQCUDXUWNANJNYNYRCBNYNNABWAWRNAWNAEBVMNUWNANJNYNNWBCNAORRNRRRBVNRRQNBVOWA
|
Letter |
Count |
Letter |
Count |
|
A |
11 |
N |
20 |
|
B |
10 |
O |
2 |
|
C |
9 |
P |
0 |
|
D |
1 |
Q |
6 |
|
E |
2 |
R |
15 |
|
F |
0 |
S |
0 |
|
G |
0 |
T |
0 |
|
H |
1 |
U |
3 |
|
I |
0 |
V |
6 |
|
J |
10 |
W |
8 |
|
K |
0 |
X |
2 |
|
L |
1 |
Y |
4 |
|
M |
4 |
Z |
0 |
Page 106 - Section 3.1
The fourth rule contains two errors in the font. It should read:
Should a double plaintext letter be required, replace the second occurrence of the plaintext letter with an agreed upon letter, say x. For example, the plaintext word better is first converted to betxer before it is enciphered IOKGXS.
Page 111 (line 17)
The entry in the first row, fourth column of the matrix A X B should be 6 · 8 + 2 · 6.
Page 115 - Section 3.2
The last equation in step 5 should read: -bch + adh = a.
Page 129 - Section 3.3
On line 13 "and so f = 24" should actually read "and so f = 8."
Similarly, on line 16, "f is either 12, 24 or 25." should be replaced by "f is either 8, 12 or 25."
Page 143 - Section 4.1
Delete the word "positive" from the statement of Lemma 4.1.
Page 144 - Section 4.1
On the third line from the bottom, replace "gcd(5,15)=3" with "gcd(5,15)=5."
Page 145 - Section 4.1
On the third line from the bottom, replace "(r,m)" with "gcd(r,m)."
Page 150
– Section 4.1
Exercise 2 should read "Prove: If n is an odd integer greater than 1, then ø(2n) = ø(n)."
Page 150 - Section 4.1
In
Exercise 6, p must be greater than 2. So the problem should begin:
"Assume p and 2p – 1 are both primes with p >
2".
Page 156 - Section 4.2
On line 4, change the word "private" to "public," and on line 5, change the word "public" to "private."
In Theorem 4.1, interchange the words "public" and "private."
Page 160 - Section 4.2
In the fourth line of Exercise 5, replace m2 . m2 . m2 with m2 . m2 . m2 . m2 .
Page 164 - Section 4.3
The Mathematica syntax in step 12 should read:
n={}
Do[n=Join[n,{Quotient [m'[[i]],1000], Mod[m'[[i]],1000]}], {i, 1, Length[m']}]
Page 166 - Section 4.3
Replace the second sentence of Step 3 with:
We do this by asking for a prime number less than ø(n) and checking to see if gcd (e,ø(n)) = 1.
Page 167 (Step 7)
Note that the space character appears between the letter Z and the number 1.
Page 169 - Section 4.3
In Step 15 of the algorithm, m_prime is initialized to ` ` (a space between the two backquotes). In the text it appears that no space is included between the quotes.
Page 170 Problem #1
The value of n should be 3365.
Page 175 - Section 4.4
In the ninth line, replace eS with eS.
Page 177 - Exercises 4.4
In Exercise #6, the word "encrypted" is misspelled as "ecrypted."
Page 182 - Appendix A
The ASCII character corresponding to 126 should be ~ .
Page 189 - Solutions
The answer to #4 should be preceded by a 1. That is, the correct answer is 188,956,800,000.
Page 190 - Solutions
The answer to Section 2.3, #4c should be 0.55.
Page 190 - Solutions
In Exercises 2.4, #2, replace "p(E(F)" with "p(E∩F)"
Page 190 - Solutions
In Exercises 2.4, #4, the solution that appears in the text is for part (b) of the problem. The solution for part (a) is C(5713,2) = 16,316,328.
Page 195 - Solutions
Replace the 24001 appearing in the table with 55585.
Page 197 - Index
Add the entry: Euclidean Algorithm, 12
Back Cover
On line 13, replace "Outsanding" with "Outstanding."
This page was last edited on Thursday, June 14, 2012 08:30 AM .
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