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In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.
Note: This questions appeared as Numerical Answer Type.
Note: This questions appeared as Numerical Answer Type.
- a)11
- b)13
- c)16
- d)17
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a RSA cryptosystem a particular A uses two prime numbers p = 13 and...
n an RSA cryptosystem, for public key:
GCD( ϕ(n) , e) = 1
And, for private key:
(e * d) mod ϕ(n) = 1
Where,
ϕ(n) = (p -1)*(q - 1) = (13 - 1)(17 - 1) =12*16 = 192
Such that 1 < e, d < ϕ(n)
Therefore, the private key is:
(35 * d) mod ϕ(n) = 1
d = 11
GCD( ϕ(n) , e) = 1
And, for private key:
(e * d) mod ϕ(n) = 1
Where,
ϕ(n) = (p -1)*(q - 1) = (13 - 1)(17 - 1) =12*16 = 192
Such that 1 < e, d < ϕ(n)
Therefore, the private key is:
(35 * d) mod ϕ(n) = 1
d = 11
Most Upvoted Answer
In a RSA cryptosystem a particular A uses two prime numbers p = 13 and...
Given:
In RSA cryptosystem, A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. The public key of A is 35.
To find:
The private key of A.
Solution:
Step 1: Calculate n:
n = p * q
n = 13 * 17
n = 221
Step 2: Calculate phi(n):
phi(n) = (p - 1) * (q - 1)
phi(n) = (13 - 1) * (17 - 1)
phi(n) = 12 * 16
phi(n) = 192
Step 3: Find a number e such that 1 < e="" />< phi(n)="" and="" gcd(e,="" phi(n))="" />
Given, the public key of A is 35. Therefore, e = 35.
Step 4: Calculate d using the equation:
d * e ≡ 1 mod phi(n)
To calculate d, we need to find the modular multiplicative inverse of e with respect to phi(n).
Using Extended Euclidean Algorithm:
phi(n) = 192, e = 35
phi(n) = e * q + r
192 = 35 * 5 + 7
e = r * q1 + r1
35 = 7 * 5 + 0
The gcd of e and phi(n) is 1. So, d = q1 = 5.
Step 5: The private key of A is d = 5.
Therefore, the correct answer is option A) 5.
In RSA cryptosystem, A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. The public key of A is 35.
To find:
The private key of A.
Solution:
Step 1: Calculate n:
n = p * q
n = 13 * 17
n = 221
Step 2: Calculate phi(n):
phi(n) = (p - 1) * (q - 1)
phi(n) = (13 - 1) * (17 - 1)
phi(n) = 12 * 16
phi(n) = 192
Step 3: Find a number e such that 1 < e="" />< phi(n)="" and="" gcd(e,="" phi(n))="" />
Given, the public key of A is 35. Therefore, e = 35.
Step 4: Calculate d using the equation:
d * e ≡ 1 mod phi(n)
To calculate d, we need to find the modular multiplicative inverse of e with respect to phi(n).
Using Extended Euclidean Algorithm:
phi(n) = 192, e = 35
phi(n) = e * q + r
192 = 35 * 5 + 7
e = r * q1 + r1
35 = 7 * 5 + 0
The gcd of e and phi(n) is 1. So, d = q1 = 5.
Step 5: The private key of A is d = 5.
Therefore, the correct answer is option A) 5.
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In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer?
Question Description
In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer?.
In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.Note:This questions appeared as Numerical Answer Type.a)11b)13c)16d)17Correct answer is option 'A'. Can you explain this answer?.
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