GATE CS 2017 Set 1 — Question 44
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Computer Networks → Application Layer → Symmetric & Asymmetric Encryption
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Question
In a RSA cryptosystem, a participant A uses two prime numbers and to generate her public and private keys. If the public key of A is 35, then the private key of A is _______.
Correct answer
11 to 11
Solution
In RSA, we have:
,
Euler's totient function Public key .
Private key must satisfy , i.e., .Using the Extended Euclidean Algorithm to find the multiplicative inverse of 35 modulo 192:
Substitute :
Thus, .
So, .
,
Euler's totient function Public key .
Private key must satisfy , i.e., .Using the Extended Euclidean Algorithm to find the multiplicative inverse of 35 modulo 192:
Substitute :
Thus, .
So, .
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