Cryptography Reference
In-Depth Information
2.14. 2
x
+1
≡
3 (mod 7)
2.15. 6
x
+5
≡
2 (mod 7)
2.16 17
x
≡
4 (mod 26)
≡
2.17. 23
x
+1
5 (mod 24)
2.18. 2
x
−
3
≡
6 (mod 13)
2.19. 2
x
−
5
≡
7 (mod 9)
2.20. 5
x
−
2
≡−
1 (mod 6)
In Exercises 2.21 and 2.22, find the values of
a
and
b
for which the congru-
ences hold.
Hint: Find the value of
a
in terms of
b
from one congruence
and plug it into the other.
2.21. 3
a
+
b
≡
10 (mod 29) and
a
+
b
≡
5 (mod 29)
2.22. 5
a
+2
b
≡
1 (mod 26) and 7
a
+9
b
≡
2 (mod 26)
In Exercises 2.23-2.25, find the plaintext given that the cipehrtext is produced
via the congruence
c
3
m
+ 10 (mod 26)
where the values of
m
in the
plaintext are given in Table 1.3 on page 11.
≡
2.23.
3
,
9
,
0
,
3
,
22
,
9
,
15
,
4
,
2
,
8
,
21
,
22
,
23
,
10
,
24
,
10
,
4
,
15
,
0
,
25
,
9
,
8
,
22
,
23
,
19
,
12
,
8
,
12
,
15
,
5
,
9
,
0
,
23
,
17
,
4
,
14
,
8
,
23
,
19
,
24
,
8
,
17
,
17
,
25
,
0
,
9
,
22
,
21
,
22
,
9
,
13
,
0
,
18
,
9
,
12
This is a quote from
Martial (Marcus Valerius Martialis) (circa 40-104
AD).
taken from
“Epigrammata”
. Martial was an Iberian-born Roman
poet.
2.24.
24
,
5
,
22
,
23
,
24
,
10
,
9
,
8
,
12
,
19
,
22
,
16
,
17
,
10
,
22
,
19
,
15
,
9
,
18
,
15
,
5
,
8
,
12
,
15
,
5
,
22
,
25
,
8
,
9
,
12
,
15
This is a quote from
Arthur Ponsonby (1871-1946)
taken from
“Falsehood
in Wartime” (1928)
. Ponsonby was an English diplomat and writer.
2.25.
5
,
10
,
8
,
17
,
22
,
20
,
3
,
22
,
9
,
22
,
9
,
24
,
22
,
24
,
5
,
0
,
10
,
9
,
22
,
10
,
13
,
0
,
18
,
15
,
15
,
0
,
3
,
22
,
9
,
8
,
17
,
0
,
18
,
9
,
17
,
8
,
21
,
22
,
12
,
12
,
10
,
17
,
18
,
15
,
22
,
4
,
0
,
18
This is a quote from
Suetonius (Gaius Suetonius Tranquillus) (circa 70-
140 AD)
taken from
[276, p. 320]. Suetonius was a Roman historian (also
see page 10).
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