Choose e such that 1 e \u03c6n and e and n are coprime Let e 7 Compute a value for d

Choose e such that 1 e φn and e and n are coprime

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Choose e such that 1 < e < φ(n) and e and n are coprime. Let e = 7 Compute a value for d such that (d * e) % φ(n) = 1.
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24 KEY MANAGEMENT There are two distinct aspects to the use of public-key cryptography: I) The distribution of public keys II) The use of public-key encryption to distribute secret keys I) Distribution of Public Keys There are four different schemes i. Public announcement ii. Publicly available directory iii. Public-key authority iv. Public-key certificates (i) Public announcement Any participant can send his or her public key to any other participant or broadcast the key to the community. Limitation Anyone can forge such a public announcement. That is, some user could pretend to be user A and send a public key to another participant or broadcast such a public key. Authentication is needed to avoid this problem. (ii) Publicly Available Directory A greater degree of security can be achieved by maintaining a publicly available dynamic directory of public keys. Maintenance and distribution of the public directory would have to be the responsibility of some trusted entity or organization. The authority maintains a directory with a {name, public key} entry for each participant. Each participant registers a public key with the directory authority. Participants could also access the directory electronically. Participant may replace the existing key with new one at any time to avoid the attack on that key. Periodically, the authority publishes the entire directory or updates of the directory to all participants in the form of telephone index.
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25 Advantage More secure than individual public announcement. Limitation Problem arises if the opponent captures the private key of the directory authority. (iii) Public-key authority Stronger security for public-key distribution can be achieved by providing tighter control over the distribution of public keys from the directory. The central authority maintains all public keys of participants in its dynamic directory. Each participant knows the public key of the authority, but the private key of the authority is kept secret. 1. A sends a timestamped request to public-key authority for the public key of B. 2. The authority replies with a message that is encrypted using the authority's private key, PRauth. A is know the public key of authority. Therefore, A decrypts the message. The message includes the following: B's public key, PUb Request already sent by A (for verification)
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26 )
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