Question

it is a question of discrete math

RSA is the most widely used public key cryptosystem. In this discussion, you will apply RSA to post and read messages. For this reflection discussion, use the prime numbers p = 3 and q = 11.
Using the public key e = 3, post a phrase about something that you found interesting or relevant in this course. Include only letters and spaces in your phrase. Represent the letters A through Z by using the numbers 01 through 26, and represent a space by the number 32. Treat upper case and lower case letters as the same.
Optional: If you want to include punctuation characters, you can use the numbers 27 through 31 for that, but you must inform your classmates that you did.
How did you calculate your value for d? As a check, the phrase “A CAB” would be represented by “01 32 03 01 02” and would be encrypted as “01 32 27 01 08”.

Answer 1

Hi,

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Cipher Text C = (M)^emodN

Message M = (C)^dmodN

ϕ(N)=(p-1)(q-1)

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How to calculate d ??

dxe=1modϕ(N) or  d=e^-1modϕ(N)

Solution:

given p = 3 , q = 11 and public key e = 3

then ϕ(N) = (p-1)(q-1) = (3-1)(11-1) = 20

then d = e^-1modϕ(N) = 3^-1mod20 = 7 (Answer)

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given p = 3 and q = 11

public key e = 3

M= “A CAB” would be represented by “01 32 03 01 02”

C = “01 32 27 01 08”.

Solution:

Cipher Text C = (M)^emodN

01→(01)³mod33→(01)mod33 = 01 (Cipher Text)

32→(32)³mod33→(32768)mod33 = 32

03→(03)³mod33→(27)mod33 = 27

01→(01)³mod33 →(01)mod33= 01

02→(02)³mod33→(08)mod33 = 08

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