Hey! I'm David, a security consultant at Cryptography Services, the crypto team of NCC Group . This is my blog about cryptography and security and other related topics that I find interesting.

# 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 Brakerski, Gentry and Vaikuntanathan
• GSW: a FHE scheme from Gentry, Sahai and Waters, 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

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