# Homomorphic Encryption Vocabulary

## posted July 2015

As I'm doing some research on Homomorphic Encryption, and trying to watch everything from Gentry (lots of videos available and he has a soothing voice), and possibly read everything from him (which I didn't do so don't take my word). Here's a vocab list I did for reference:

- HE: Homomorphic Encryption
- leveled: no bootstrapping, only compute circuits up to a degree (public key grows with the depth of the circuit for f )
- LWE: Learning With Error (a problem hard to solve)
- R-LWE: Ring-Learning With Error
- Craig Gentry: the one who found the holy grail
- holy grail: Fully Homomomorphic Encryption
- FHE: another name for the holy grail
- SHE/SWHE: somewhat homomorphic encryption
- BGV: the first Leveled FHE (without bootstraping), from
**B**rakerski,**G**entry and**V**aikuntanathan - GSW: a FHE scheme from
**G**entry,**S**ahai and**W**aters, that takes ideas from BGV and like BGV has its security based on LWE - NTRU: N-th degree truncated polynomial ring, the base of a lattice-based cryptosystem
- modulus switching: (some messy operation that they got rid of in bra12)
- bootstrapping: to make a bootstrappable somwehat homomorphic encryption scheme into a fully homomorphic encryption scheme (Gentry recommends not to use this, although it was the original way of building FHE)
- IBE: Identity Based Encryption scheme (introduced by the famous Boneh paper)
- IBFHE: Identity Based Fully Homomoprhic Encryption scheme (introduced by GSW)
- SIMD: Single Instruction, Multiple Data

... more to come