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In a RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______
Correct answer is '97'. Can you explain this answer?
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Verified Answer
In a RSA cryptosystem, the value of the public modulus parameter n is ...
Given that n = 3007
φ( n )= 2880
As per RSA algorithm,
n = p * q = 3007 (97*31)
φ (n) = (p-1) (q-1) =2880 (96*30)
For P = 97 and q = 31 only satisfies the given n & φ ( n )
Since, the question is asking for a prime number which greater than 50, So 97 is correct answer.
φ( n )= 2880
As per RSA algorithm,
n = p * q = 3007 (97*31)
φ (n) = (p-1) (q-1) =2880 (96*30)
For P = 97 and q = 31 only satisfies the given n & φ ( n )
Since, the question is asking for a prime number which greater than 50, So 97 is correct answer.
Most Upvoted Answer
In a RSA cryptosystem, the value of the public modulus parameter n is ...
N is the product of two prime numbers p and q, we can find the values of p and q by factorizing n.
To factorize 3007, we can start by checking for prime factors up to the square root of 3007 (approximately 54.8).
Checking for prime factors:
2 is not a factor of 3007.
3 is not a factor of 3007.
5 is not a factor of 3007.
7 is not a factor of 3007.
11 is not a factor of 3007.
13 is not a factor of 3007.
17 is not a factor of 3007.
19 is not a factor of 3007.
23 is not a factor of 3007.
29 is not a factor of 3007.
31 is not a factor of 3007.
37 is not a factor of 3007.
41 is not a factor of 3007.
43 is not a factor of 3007.
47 is not a factor of 3007.
53 is not a factor of 3007.
There are no prime factors between 2 and 54.8, so we can conclude that 3007 is a prime number and cannot be factorized into two primes p and q.
However, if there was a mistake in the given value of n (3007), and it is not a prime number, we would need to find its prime factorization by using more advanced factorization methods, such as Pollard's rho algorithm or the quadratic sieve algorithm.
To factorize 3007, we can start by checking for prime factors up to the square root of 3007 (approximately 54.8).
Checking for prime factors:
2 is not a factor of 3007.
3 is not a factor of 3007.
5 is not a factor of 3007.
7 is not a factor of 3007.
11 is not a factor of 3007.
13 is not a factor of 3007.
17 is not a factor of 3007.
19 is not a factor of 3007.
23 is not a factor of 3007.
29 is not a factor of 3007.
31 is not a factor of 3007.
37 is not a factor of 3007.
41 is not a factor of 3007.
43 is not a factor of 3007.
47 is not a factor of 3007.
53 is not a factor of 3007.
There are no prime factors between 2 and 54.8, so we can conclude that 3007 is a prime number and cannot be factorized into two primes p and q.
However, if there was a mistake in the given value of n (3007), and it is not a prime number, we would need to find its prime factorization by using more advanced factorization methods, such as Pollard's rho algorithm or the quadratic sieve algorithm.
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In a RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. Can you explain this answer?
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In a RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. 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, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. 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, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. Can you explain this answer?.
In a RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. 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, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. 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, the value of the public modulus parameter n is 3007. If it is also known that φ( n )= 2880, where φ () denotes Euler's Totient function, then the prime factor of n which is greater than 50 is_______Correct answer is '97'. Can you explain this answer?.
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