Fully homomorphic encryption (FHE)
全同态加密 Fully homomorphic encryption (FHE)
What’s is FHE
第一种形式:同时使用secret key加密和解密,public key用于第三方加密进行同态计算
第二种形式:asymmetric FHE,只使用public key进行加密,secret key用于解密
Efficient FHE is a giant leap towards httpz://
? what’s httpz?
History
Major task: find a new scheme to combine both addition and multiplication together.
1. First generation
Plain text: single bit
这个方法的主要问题是noise,随着计算的叠加,there is a notion of noise in ciphertexts,noise accumulates
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Defining noise budget thourgh defining parameters
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noise growth is exponential
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bootstrapping to rescure (decrease the noise)
Somewhat homomorphic encyption (SHE)
初代的FHE目标是每一步同态计算,都进行一次bootstrapping,来抑制噪音增加。但是bootstrapping的计算消耗太大,所以SHE的目标是控制在output时的噪音水平,保证是可以接受的。
2. Second generation
targeting the exponential growing noise
3. Third generation: GSW
只是概念上的简化,但是无法实用。
4. 4th generation: Torus FHE, TFHE
Open-source FHE librabies
FV-NFLlib
SEAL
HEAAN
TFHE
HElib
nuFHE
Palisade
Two encryption
Plaintext encoding
但是在计算的时候,noise会在右侧累积。
通过bootstrapping,可以减少右侧的noise
LWE ciphertexts are homomorphic
Ref
Complete talk: Introduction to Homomorphic Encryption (by Pascal Paillier) - YouTube