Solve Two Mathematical Questions Showing the Steps Clearly

FratBro23
Category:
Other
Price: $15 USD

Question description

1. Here is a message to you in which I am using RSA system with pulic key n = 2773 and encryption key e = 157.

0245  2040  1698  1439  1364  1758  0946  0881

1979  1130

I have broken my original message into pairs of characters and converted these pairs to numbers as we did in the text. For example, the word "MATH" would be broken into "MA" and "TH" that would be converted to the numbers 1301 and 2008, respectively, and encrypted. Figure out the decryption key d, decrypt the message and answer the question that it asks.

RSA Cryptosystem table.

A

B

C

D

E

F

G

H

I

J

K

L

M

01

02

03

04

05

06

07

08

09

10

11

12

13

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

14

15

16

17

18

19

20

21

22

23

24

25

26

Euler's theorem

C(pq) = (p-1)(q-1)

n = pq = 2773*157 = 435,361

C(n) = c(pq) = (p-1)(q-1) = 2772*156 = 432,432

encryption E(M) = M^e mod n

M^157 mod 435,361

decryption D(N) = N^d mod n

N^d mod 435,361

d = e^-1 mod c(n)



2. Use mathematical induction to prove that for every n >= 1, if a set has n elements, then

its power set has 2^n elements.



Must Show all Works and proper steps and signs. these two questions are seperated and not related to each other.


Studypool has helped 1,244,100 students
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1831 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors