Partially Homomorphic Encryption with ElGamal in Python From Scratch

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.

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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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[BulentSiyah]

it's great that you share new information every week

[zaursamedov]

thank you for this kinda precious tutorial

[nurhakkarakaya]

thanks for sharing. can you also share the codes of videos

[HayaFayaz]

How do we make division when the the data is entirely encrypted? Multiplying with inverse involves decrypting, and multiplying with power of -1 doesn't work since tenseal library does not accept power of -1. I want to try it when the data is entirely encrypted.

[saisiddharth]

When u modify the encryption function to E' there u used g^m if we use same decrypting function the result will not be same as m it would be g^m can u tell how to get m as plaintext back?