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In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .
Correct answer is 'Efficient for bigger values'. Can you explain this answer?
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In a RSA cryptosystem, a participant A uses two prime numbers P = 13 a...
Efficient for bigger values
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In a RSA cryptosystem, a participant A uses two prime numbers P = 13 a...
Understanding RSA Key Generation
RSA (Rivest–Shamir–Adleman) is a widely used encryption algorithm that relies on the mathematical properties of prime numbers for secure communication. In this case, participant A uses two prime numbers, P and Q, to generate their public and private keys.
Step 1: Calculate N
- N is calculated as the product of P and Q:
- N = P * Q = 13 * 17 = 221
Step 2: Calculate Euler's Totient (φ(N))
- Euler's totient function φ(N) is given by:
- φ(N) = (P-1)(Q-1) = (13-1)(17-1) = 12 * 16 = 192
Step 3: Determine the Public Key
- The public key consists of the pair (e, N), where e is the encryption exponent.
- In this scenario, the public key of A is given as 35 (e = 35).
Step 4: Calculate the Private Key (d)
- The private key d is derived from the equation:
- d * e ≡ 1 (mod φ(N))
- To find d, we need to calculate the modular multiplicative inverse of 35 modulo 192.
Conclusion on Efficiency
- The phrase "Efficient for bigger values" refers to the scalability of RSA.
- RSA's security increases with larger prime numbers, making it difficult for an attacker to factor N.
- For practical purposes, larger primes are used to ensure robust encryption, making RSA secure for widespread applications in digital communication.
In summary, while the specific private key for smaller primes can be calculated, the real strength of RSA lies in its efficiency and security when using larger prime numbers.
RSA (Rivest–Shamir–Adleman) is a widely used encryption algorithm that relies on the mathematical properties of prime numbers for secure communication. In this case, participant A uses two prime numbers, P and Q, to generate their public and private keys.
Step 1: Calculate N
- N is calculated as the product of P and Q:
- N = P * Q = 13 * 17 = 221
Step 2: Calculate Euler's Totient (φ(N))
- Euler's totient function φ(N) is given by:
- φ(N) = (P-1)(Q-1) = (13-1)(17-1) = 12 * 16 = 192
Step 3: Determine the Public Key
- The public key consists of the pair (e, N), where e is the encryption exponent.
- In this scenario, the public key of A is given as 35 (e = 35).
Step 4: Calculate the Private Key (d)
- The private key d is derived from the equation:
- d * e ≡ 1 (mod φ(N))
- To find d, we need to calculate the modular multiplicative inverse of 35 modulo 192.
Conclusion on Efficiency
- The phrase "Efficient for bigger values" refers to the scalability of RSA.
- RSA's security increases with larger prime numbers, making it difficult for an attacker to factor N.
- For practical purposes, larger primes are used to ensure robust encryption, making RSA secure for widespread applications in digital communication.
In summary, while the specific private key for smaller primes can be calculated, the real strength of RSA lies in its efficiency and security when using larger prime numbers.
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In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer?.
In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer?.
Solutions for In a RSA cryptosystem, a participant A uses two prime numbers P = 13 and q = 17 to generate here public and private keys. If the public key of A is 35 , then the private key of A is __________ .Correct answer is 'Efficient for bigger values'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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