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Discrete Mathematics Exercises For Homework 8

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discrete mathematics

Exercises for Homework 8


8.1. Encrypt the message STOP POLLUTION by translating the letters into numbers, applying the
given encryption function, and then translating the numbers back into letters.
STOP POLLUTION
18,14,19,15 15,14,11,11,20,19,8,14,13

a) f(p)= (p+4) mod 26


WXST TSPPYXMSR
18,19,14,15 15,14,11,11,20,19,8,14,13

b) f(p)= (p+21) mod 26


NOJK KJGGPODJI
13,14,9,10 10,9,6,6,15,14,3,9,8

c) f(p)= (17p+22) mod 26


17*18+22
QAHR RABBYHCAJ
16,26,7,17 17,26,1,1,24,7,2,26,9

8.2. Decrypt these messages that were encrypted using the Caesar cipher.
a) EOXH MHDQV

f(p)=(p+3) mod 26
BLUE JEANS
1,11,20,4 9,4,0,13,18

b) WHVW WRGDB

f(p)=(p+3) mod 26
TEST TODAY
19,4,18,19 19,14,3,0,24

c) HDW GLP VXP

f(p)=(p+3) mod 26
EAT DIM SUM
4,0,19 3,8,12 18,20,12

8.3. Suppose that the ciphertext ERC WYJJMGMIRXPC EHZERGIH XIGLRSPSKC MW


MRHMWXMRKYMWLEFPI JVSQ QEKMG was produced by encrypting a plaintext message
using a shift cipher. What is the original plaintext?
ANY SUFFICIENTLY ADVANCED TECHNOLOGY IS INDISTINGUISHABLE FROM MAGIC

8.4. Decrypt the message EABW EFRO ATMR ASIN which is the ciphertext produced by
encrypting a plaintext message using the transposition cipher with blocks of four letters and the
permutation σ of {1,2,3,4} defined by σ(1) = 3, σ(2) = 1, σ(3) = 4, and σ(4) = 2.

EABW EFRO ATMR ASIN


3142 3142 3142 3142

BEWA REOF MART IANS

8.5. The ciphertext OIKYWVHBX was produced by encrypting a plaintext message using the
Vigenère cipher with key HOT. What is the plaintext message?
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HURRICANE key: HOT
8.6. Encrypt the message MATH using the RSA system with n = 43·59 and e = 5, translating each
letter into integers and grouping together pairs of integers.
MATH
12,00,19,07

Key (44*59,5) 2537=43*59 p=43, q=59


gcd (e, (p-1) (q-1)) = gcd (5, 43*58)= 1

8.7. What is the original message encrypted using the RSA system with n = 43·59 and e = 13 if the
encrypted message is 0667 1947 0671 (d=937)?

S I L V E R
18 08 11 21 04 17

Key (43*59, 13) 2537=43*59, p=43, q-59


Gcd(e, (p-1) (q-1)) = gcd(13, 43*58) = 1

This study source was downloaded by 100000816070467 from CourseHero.com on 04-16-2022 02:02:41 GMT -05:00

https://www.coursehero.com/file/74733317/Home-work-8-1docx/
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