1
Name:
Radford University
MA 195 Cryptography - Test # 1
Department of Mathematics
Makeup Test
On all of the following problems, please show all work. Write all your work
including answers on your test paper.
1. Find the quotient q and remainder r such that b  qm  r according to the division algorithm.
Use the answer to compute b MOD m. (4 pts each)
a. b  831, m  29 .
b. b  57, m  17
2. Name three of the most highly occurring letters in the English language (include at least one
consonant). What three letter word (trigraph) is the most frequently occurring in the English
language? (4 pts)
3. Make a list of five solutions to the following congruence. (7 pts)
x  7  5 (mod 10)
2
4. Suppose a 23-shift shift cipher is used to encrypt and decrypt messages. Use it to (7 pts each)
a. Encipher “GOOD”
b. Decipher “YVB”
5. Given the affine cipher y  (21x  16) MOD 26 .
a. Encipher the message “MARS”. (7 pts)
b. Find the decipherment formula. (7 pts)
3
4
c. Use the decipherment formula to decipher "PWDUE". (7 pts)
d
Suppose someone wanted you to send them a message using the affine cipher
y  (13x  15) MOD 26. What is wrong with this cipher? (2 pts)
5
6. Suppose that an affine cipher y  (ax  b) MOD 26 was used to encipher a plaintext. If Eve
knows that the plaintext V enciphers as L and the plaintext M enciphers as O, we can determine
the coefficients a and b in the encipherment formula. Find the values of a and b for her. (12 pts)
6
7. Suppose you are asked to use the keyword “THEBATMAN” to create a mixed
substitution cipher alphabet.
a. Obtain the cipher alphabet using a simple substitution cipher. (9 pts)
b. Obtain the cipher alphabet using a keyword columnar substitution cipher. (9 pts)
c. Use it to encipher your name (first and last) using the two cipher alphabets you found in
part a or part b. (7 pts)
d. Decipher “FLGAQ” using the cipher alphabet you obtained in part a and “SWK RQ
RHIEQMR” using the cipher alphabet you obtained in part b. (7 pts)
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Alphabet to number assignment for a MOD 26 cryptosystem
A0
K  10
U  20
B1
L  11
C2
D3
M  12
N  13
V  21
W  22
E4
F 5
G6
H7
I 8
J9
O  14
P  15
Q  16
R  17
S  18
T  19
X  23
Y  24
Z  25
Multiplicative Inverses MOD 26
a
1
a MOD 26
1
1
3
9
5
21
7
15
9
3
11
19
15
7
17
23
19
11
21
5
23
17
25
25