Homomorphic Encryption In Python

Slides of my talk given at PyData London's 86th meet-up

Transcript

1. Sefik Serengil Homomorphic Encryption In Python software engineer @ vorboss London 2024, Jul 02
2. Sefik Serengil Software Engineer About Me sefiks.com @serengil @sefiks serengil UK Global Talent
3. sefiks.com @serengil @sefiks LightPHE serengil RetinaFace About Me 11K 1K 500 50 101 TensorFlow 1K
4. PyData London ‘24 PyData London’s 74th Meetup 2023, May 2 2024, June 16 Billion-Scale Facial Recognition The Art and Science of Deep Face Recognition in Python
5. sefiks.com @serengil @sefiks serengil
6. sefiks.com @serengil @sefiks serengil
7. sefiks.com @serengil @sefiks serengil
8. sefiks.com @serengil @sefiks serengil On-Prem Cloud salary, key Key can be stolen in this design!
9. sefiks.com @serengil @sefiks serengil On-Prem Cloud encrypted_salary
10. sefiks.com @serengil @sefiks serengil On-Prem Cloud encrypted_salary encrypted_salary We cannot use the computation power of cloud in this design! encrypted_salary
11. sefiks.com @serengil @sefiks serengil Can Update Be Done In The Cloud Without Key?
12. RSA sefiks.com @serengil @sefiks serengil 𝜀(𝑚) = 𝑚𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚1 ) = (𝑚1 )𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚2 ) = (𝑚2 )𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚1 ) × 𝜀(𝑚2 ) = (𝑚1 )𝑒 × (𝑚2 )𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚1 ) × 𝜀(𝑚2 ) = (𝑚1 × 𝑚2 )𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚1 × 𝑚2 ) = (𝑚1 × 𝑚2 )𝑒𝑚𝑜𝑑𝑛 𝜀(𝑚1 × 𝑚2 ) = 𝜀(𝑚1 ) × 𝜀(𝑚2 ) RSA is multiplicatively homomorphic! https://sefiks.com/2018/05/21/the-math-behind-rsa-algorithm/
13. Paillier sefiks.com @serengil @sefiks serengil 𝜀(𝑚, 𝑟) = 𝑔𝑚 × 𝑟𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚1 , 𝑟1 ) = 𝑔𝑚1 × (𝑟1 )𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚2 , 𝑟2 ) = 𝑔𝑚2 × (𝑟2 )𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚1 , 𝑟1 ) × 𝜀(𝑚2 , 𝑟2 ) = 𝑔𝑚1 × (𝑟1 )𝑛 × 𝑔𝑚2 × (𝑟2 )𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚1 , 𝑟1 ) × 𝜀(𝑚2 , 𝑟2 ) = 𝑔𝑚1+𝑚2 × (𝑟1 × 𝑟2 )𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚1 + 𝑚2 , 𝑟1 × 𝑟2 ) = 𝑔𝑚1+𝑚2 × (𝑟1 × 𝑟2 )𝑛𝑚𝑜𝑑𝑛2 𝜀(𝑚1 + 𝑚2 , 𝑟1 × 𝑟2 ) = 𝜀(𝑚1 , 𝑟1 ) × 𝜀(𝑚2 , 𝑟2 ) Paillier is additively homomorphic sefiks.com/2023/04/03/a-step-by-step-partially-homomorphic-encryption-example-with-paillier-in-python/
14. sefiks.com @serengil @sefiks serengil PHE Algorithms
15. LightPHE A Hybrid Partially Homomorphic Encryption Library for Python • Open sourced at github.com/serengil/LightPHE under MIT license • Can be installed with command `pip install lightphe` • Wrapping RSA, ElGamal, Exponential ElGamal, Elliptic Curve ElGamal, Paillier, Damgard-Jurik, Okamoto–Uchiyama, Benaloh, Naccache–Stern, Goldwasser–Micali • Stars are welcome! sefiks.com @serengil @sefiks serengil LightPHE
16. sefiks.com @serengil @sefiks serengil Building a Cryptosystem This generates random private - public key pair
17. sefiks.com @serengil @sefiks serengil Encryption and Decryption
18. sefiks.com @serengil @sefiks serengil Homomorphic Addition
19. sefiks.com @serengil @sefiks serengil Scalar Multiplication
20. sefiks.com @serengil @sefiks serengil Unsupported Operations
21. sefiks.com @serengil @sefiks serengil Homomorphic Multiplication
22. PHE vs FHE • Notably faster • Demands fewer computational resources • Generating much smaller ciphertexts • Distributing much smaller keys • Well-suited for memory-constrained environments • Strikes a favorable balance for practical use cases sefiks.com @serengil @sefiks serengil
23. Thank you for your attention! sefiks.com @serengil @sefiks serengil