Blindfolded Evaluation of Random Forests with Multi-Key Homomorphic Encryption

https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8827928

“bib
@article{aloufi_blindfolded_2021,
title = {Blindfolded {Evaluation} of {Random} {Forests} with {Multi}-{Key} {Homomorphic} {Encryption}},
volume = {18},
issn = {1941-0018},
doi = {10.1109/TDSC.2019.2940020},
number = {4},
journal = {IEEE Transactions on Dependable and Secure Computing},
author = {Aloufi, Asma and Hu, Peizhao and Wong, Harry W. H. and Chow, Sherman S. M.},
month = jul,
year = {2021},
note = {Conference Name: IEEE Transactions on Dependable and Secure Computing},
keywords = {Applied cryptography, Collaboration, Computational modeling, decision tree, Decision trees, Encryption, homomorphic encryption, machine learning, Protocols, random forest},
pages = {1821—1835},
file = {IEEE Xplore Full Text PDF:/Users/kamata/Zotero/storage/XLKQKYNU/Aloufi et al. - 2021 - Blindfolded Evaluation of Random Forests with Mult.pdf:application/pdf;IEEE Xplore Abstract Record:/Users/kamata/Zotero/storage/9FJ3WF5I/8827928.html:text/html},
}

## 5.5 Evaluationg Ecrypted Decision Trees
流れ

- Setup phrase
	- **Model owner**
	- **Client**
- Phrase1: Outsourcing computations
	- **Model owner**
	- **Client**
	- **Evalator**
- Phrase 2&3: Evaluating decision trees and random forest
	- **Evaluator**
- Phrase4: Decrypting result
	- **Model owner**
	- **Client**
	- **Evalator**

### Secure Comparison

^993b85

暗号化された特徴量ベクトル $X$, 
特徴量 $x \in X$としきい値 $y \in Y$ をブール関数を評価することで安全に比較するアルゴリズム.  $\mathrm{SecComp}(x, y)$. $b = 1(x < y)$.

$$
\begin{aligned}
b =& (x_{\ell - 1} < y_{\ell - 1}) \lor \\
  &  (x_{\ell - 1} = y_{\ell - 1}) \land (x_{\ell - 2} < y_{\ell - 2}) \lor \\
  & \vdots \\
  
\mathrm{where} \\
& (x_j < y_j) := (\lnot x_j \land y_j) \\
& (x_j = y_j) := (x_j \oplus y_j + 1)
\end{aligned}
$$