# FHE Meeting #3: Paillier encryption

**URL:** <https://forum.anoma.net/t/fhe-meeting-3-paillier-encryption/236>\
**Category:** FHE kindergarten\
**Created:** [September 12, 2023, 1:58pm UTC](https://forum.anoma.net/t/fhe-meeting-3-paillier-encryption/236 "2023-09-12T13:58:40Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![vveiln](https://dub1.discourse-cdn.com/flex013/user_avatar/forum.anoma.net/vveiln/32/60_2.png) [@vveiln](https://forum.anoma.net/u/vveiln)\
**Post date:** [September 12, 2023, 1:58pm UTC](https://forum.anoma.net/t/fhe-meeting-3-paillier-encryption/236/1 "2023-09-12T13:58:40Z")

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**Date:** 28.09.23  
**Time:** 4pm CEST  
**Reading materials:**

- [Public-Key Cryptosystems Based on Composite Degree Residuosity Classes](https://link.springer.com/chapter/10.1007/3-540-48910-X_16)
- [CryptDB: Protecting Confidentiality with Encrypted Query Processing](https://people.csail.mit.edu/nickolai/papers/raluca-cryptdb.pdf)

**Optional:**

- [A Generalisation, a Simplification and some Applications of Paillier’s Probabilistic Public-Key System](https://www.brics.dk/RS/00/45/BRICS-RS-00-45.pdf)

Please read the papers in advance!

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<div class="post-metadata">

**Author:** ![vveiln](https://dub1.discourse-cdn.com/flex013/user_avatar/forum.anoma.net/vveiln/32/60_2.png) [@vveiln](https://forum.anoma.net/u/vveiln)\
**Post date:** [September 27, 2023, 6:24am UTC](https://forum.anoma.net/t/fhe-meeting-3-paillier-encryption/236/2 "2023-09-27T06:24:31Z")

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Meeting moved to **19.10.23, 4pm CEST**

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<div class="post-metadata">

**Author:** ![vveiln](https://dub1.discourse-cdn.com/flex013/user_avatar/forum.anoma.net/vveiln/32/60_2.png) [@vveiln](https://forum.anoma.net/u/vveiln)\
**Post date:** [October 23, 2023, 2:25pm UTC](https://forum.anoma.net/t/fhe-meeting-3-paillier-encryption/236/3 "2023-10-23T14:25:52Z")

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A short summary:

- Paillier encryption is based on some fancy [residuosity math assumption](https://en.wikipedia.org/wiki/Decisional_composite_residuosity_assumption) and is additively homomorphic: E(m\_1) \* E(m\_2) = E(m\_1 + m\_2). Provides more or less the same homomorphic functionality as [ElGamal encryption](https://forum.anoma.net/t/fhe-meeting-2-elgamal-encryption/205/3) but is based on a different assumption which might be handy for diversifying security
- CryptDB allows performing computations on encrypted data and uses Paillier encryption as one of the encryption types to support homomorphic queries. CryptDB’s _onion encryption_ that uses multiple types of encryption providing different guarantees allows to find a compromise between:
  - privacy (more operations on encrypted data → less privacy),
  - customizability (does the query require the operation, e.g., ordering of the entries or addition, to be performed at all?),
  - and performance (is it fast enough to be used in real world systems?)