Exciting Facts about Homomorphic Encryption

Homomorphic encryption (HE) is a process that allows computations to be performed on encrypted data without requiring the secret key.

2. The most widely used schemes are

A. BFV
B. BGV
C. CKKS
D. TFHE

SIMD means single instruction multiple data.


3. Hey, can BGV/BFV perform the evaluation of trigonometric functions?. Ans: No (It's difficult) 😭 

4. Hey, can  CKKS can perform the evaluation of trigonometric functions? Ans: YES 😆

5. Homomorphic multiplication is costly, as it rapidly increases noise growth.

6. In homomorphic encryption ciphertext can be defined as
        C = C0 + C1.s
Thus, during multiplication
C*C' = (C0+C1.s)*(C0'+C1'.s)
C*C' = C0C0' + [C0C1' + C0'C1].s +C1C1'.s^2
oops!!! C*C' is quadratic 😭
Introduce the concept of re-linearization here (re-linearization means converting degree 2 ciphertext into degree 1 ciphertext).
Thus,
C*C' = C0C0' + C.S 
In another way, re-linearization is a technique that makes your process comfortable. 😉

7. Below is a snippet explaining how Gentry's bootstrapping works.



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