ElGamal Partially Homomorphic Encryption in Python 🔐

In this video, we'll explore the concepts of ElGamal encryption and partially homomorphic encryption, with a focus on multiplicatively homomorphic ElGamal and additively homomorphic exponential ElGamal encryption. We'll take a closer look at how ElGamal encryption works, and how it's used in modern cryptographic systems to secure communications and transactions. We'll also dive into partially homomorphic encryption, which allows computations to be performed on encrypted data with some restrictions. Specifically, we'll focus on the properties of multiplicatively homomorphic ElGamal encryption, which enables complex computations on encrypted data to be performed efficiently as long as they involve multiplication only, and additively homomorphic exponential ElGamal encryption, which enables some computations on the ciphertexts with addition operation. Finally, we'll demonstrate a Python implementation of partially homomorphic ElGamal encryption. By the end of this video, you'll have a better understanding of these powerful encryption techniques and their practical applications, particularly for scenarios where data privacy is crucial.

Homomorphic encryption has the potential to enable secure computation on sensitive data without requiring decryption, which makes it a powerful tool for protecting privacy in various applications. Homomorphic encryption can also be used in cloud computing, where it enables secure computation on encrypted data stored in the cloud without exposing the data to the cloud provider. Additionally, e-voting is another potential use case for homomorphic encryption. With homomorphic encryption, votes can be encrypted and counted without the need to decrypt them, which ensures the privacy and integrity of the voting process. Homomorphic encryption also enables vote auditing by allowing voters to verify that their votes were correctly counted without revealing their actual vote. This has the potential to improve the security and transparency of e-voting systems, making them more trustworthy and reliable.

Tutorial: https://sefiks.com/2023/03/27/a-step-by-step-partially-homomorphic-encryption-example-with-elgamal-in-python/

Want to do partially homomorphic ElGamal encryption with a few lines of code in Python? Check out LightPHE: https://youtu.be/fh1Dgir5FXM

If you like this video, you may like these videos:
- Partially Homomorphic RSA in Python: https://youtu.be/PzKch8UQAmQ
- Partially Homomorphic Paillier in Python: https://youtu.be/Yerhc9B2zjQ
- Partially Homomorphic Elliptic Curve ElGamal: https://youtu.be/6yN00ttpjSE
- Fully Homomorphic Encryption in Python: https://youtu.be/2qkCLaeD7pA

Contents of this video:
00:00 - Introduction
00:30 - Key Genertion
02:45 - Encryption and Decryption
05:36 - Proof of ElGamal Encryption
06:40 - Proof of Multiplicative Homomorphic ElGamal
08:41 - Multiplicative Homomorphic ElGamal in Python
10:29 - Proof of Additive Homomorphic ElGamal
11:40 - Additive Homomorphic ElGamal in Python

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