Public-Key Cryptosystem | Lesson Summary | Alison
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Public-Key Cryptosystem - Lesson Summary

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The key points from this module are:
Differences between COA security in PUblic-Key setting and Private-Key setting are:

In the Public-Key setting, the adversary is explicitly given the Public-Key PK, while in the Private-Key world the adversary is not given the Private-Key PK.
There is free access to the encryption-oracle service in the Public-key world; there is no encryption-oracle service in the COA experiment, in the symmetric-Key world.


In the Public-Key setting, the adversary is explicitly given the Public-Key PK, while in the Private-Key world the adversary is not given the Private-Key PK.
There is free access to the encryption-oracle service in the Public-key world; there is no encryption-oracle service in the COA experiment, in the symmetric-Key world.

The idea behind the Padded RSA Public-Key Cryptosystem is to append random strings to the plain tex bits before encrypting as per the RSA function.
The Hybrid El Gamal Encryption Scheme used a two-staged approach where you choose a random Symmetric-Key K, and encrypt K using a Public-Key Encryption. For the Hybrid-Encryption using the Key-encapsulation Mechanism(KEM) - both tasks can be done in a single shot, and conceptually it is simpler and more efficient. The Symmetric-Key Encryption Scheme used for encrypting the plain text is called a Data-encapsulation Mechanism (DEM).
The Hybrid El Gamal Encryption Scheme used a two-staged approach where you choose a random Symmetric-Key K, and encrypt K using a Public-Key Encryption. For the Hybrid-Encryption using the Key-encapsulation Mechanism(KEM) - both tasks can be done in a single shot, and conceptually it is simpler and more efficient. The Symmetric-Key Encryption Scheme used for encrypting the plain text is called a Data-encapsulation Mechanism (DEM).
In the Public-Key Encryption process, the COA-Security, the Single-Message CPA-Security and the Multi-message CPA-Security are all equivalent.
Comparison between the Public-Key Encryption Scheme and the Private-Key Encryption Scheme:


In the Private-Key Encryption Scheme, the key agreement is not a challenge, but in the Private-Key setting, it is a big challenge.


In the Public-Key Encryption Scheme, the message space has to be a finite group, but the message space in the Private-Key setting are binary strings.


In the Public-Key setting, the Ciphertext expansion is huge. In the Symmetric-key world, the Ciphertext expansion is minimal.

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