**RSA Problem**Given: \[ n = p \times q = 726067 \]\[ e = 17 \]\[ \phi = 724360 \]Tasks: (a) Find the decryption exponent $ d $ (b) Find the prime numbers $ p $ and $ q $

Answered: (RSA) Given n = = 17 e = P* 1 4 १ 11 =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**RSA Problem**

Given:
\[ n = p \times q = 726067 \]

\[ e = 17 \]

\[ \phi = 724360 \]

Tasks:
(a) Find the decryption exponent $ d $
(b) Find the prime numbers $ p $ and $ q $

Expert Solution

Step 1

Here, in the question given the RSA. Asymmetric cryptography uses the RSA algorithm. Asymmetric really implies that it utilizes both the public and private keys, which are two separate keys. As implied by the name, the private key is kept secret while the public key is distributed to everyone.

Asymmetric cryptography illustration:

When requesting data from the server, a client (for instance, a browser) transmits the server its public key.
Using the client's public key, the server encrypts the data before sending it.
This data is delivered to the client, who decrypts it.

The given events are decrypting events and also the calculation of events is done based on it. Also, the prime numbers $p & a$ are to be calculated.