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update math expression in eliza-with-fhe.md
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georgesheth committed Jan 28, 2025
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18 changes: 9 additions & 9 deletions docs/docs/advanced/eliza-with-fhe.md
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Expand Up @@ -38,28 +38,28 @@ The main idea of FHE is that operations performed on the encrypted data produce
#### Core Components

1. **Encryption**: Transform plaintext data into ciphertext using an encryption key.
```math
c = E_k(m)
```

$$c = E_k(m)$$

Where:
- $m$: plaintext message
- $k$: encryption key
- $E_k$: encryption function
- $c$: ciphertext

3. **Computation on Encrypted Data**: Perform operations directly on the ciphertext, such as addition or multiplication, to produce a new ciphertext.
```math
c' = F(c_1, c_2)
```

$$c' = F(c_1, c_2)$$

Where:
- $c_1, c_2$: input ciphertexts
- $F$: homomorphic function (e.g., addition, multiplication)
- $c'$: resulting ciphertext after computation

4. **Decryption**: Decrypt the result to reveal the final output, which matches the result of performing the operation on the plaintext.
```math
m' = D_k(c')
```

$$m' = D_k(c')$$

Where:
- $D_k$: decryption function
- $m'$: result of computation in plaintext form
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