(a) Using RSA choose p = 3 and q = 11 and

Authors:

James F. Kurose, Keith W. Ross

Chapter:

Security In Computer Networks

Exercise:

Problems

Question:7 | ISBN:9780132856201 | Edition: 6

Question

(a) Using RSA, choose p = 3 and q = 11, and encode the word “dog” by encrypting each letter separately. Apply the decryption algorithm to the encrypted version to recover the original plaintext message.

(b) Repeat part (a) but now encrypt “dog” as one message m.

Answer

Consider the data: p = 3 and q = 11

Consider the endcode word: “dog”

Using RSA,

$\large n= p\times q$

$\large n= 3\times 11$

$\large n= 33$

$\large z= (p-1)\times (q-1)$

$\large z= (3-1)\times (11-1)$

$\large z= (2)\times (10)$

$\large z= 20$

Take e=9, since 9 and 20 have no common factors and d=29, since 9.29-1(that is, e.d-1) is exactly divisible by 20.

So, the encrypting the each letter “dog” by RSA encryption, e=9, n=33.

The following table encrypted version to recover the original plaintext message

word	m	m^e	c=m^e mod n
d	4	26214425	25
o	15	38443359375	3
g	7	40353607	19

So, the encrypted message is 25,3,19.

The following table decryption algorithm to the encrypted version to recover the original plaintext message by using RSA:

c	c^d	m=c^d mod n	plaintext
25	25²⁹	4	d
3	68630377364883	15	o
19	19²⁹	7	g

Consider the above part (a), now have to encrypt “dog” as one message m:

Consider p = 43 and q = 107.

$\large n=p\times q$

$\large n=43\times 107$

$\large n=4601$

$\large z=(p-1)\times (q-1)$

$\large z=(43-1)\times (107-1)$

$\large z=(42)\times (106)$

$\large z=4452$

Ciphertext c = m^emod n

= 4452⁶¹ mod 4601

= 402

So, the encrypted message “dog” as one message m is 402

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