Vertical federated logistic regression via homomorphic encryption and secret sharing

doi:10.12267/j.issn.2096-5931.2022.05.005

Abstract

Abstract:

This paper presents a novel vertical federated logistic regression algorithm with provable security guarantees of both model training and inference under the semi-honest security model. The proposed algorithm is privacy-preserving, lossless, and efficient. Firstly, by combining the homomorphic encryption and secret sharing mechanisms, data protection is provably ensured, including the protection of both features and labels. Secondly, the algorithm is lossless since it does not require any approximations for the non-linear functions.

Key words: vertical federated learning, logistic regression, homomorphic encryption, secret sharing

CLC Number:

TP309.2

FU Fangcheng, LIU Shu, CHENG Yong, TAO Yangyu. Vertical federated logistic regression via homomorphic encryption and secret sharing[J]. Information and Communications Technology and Policy, 2022, 48(5): 34-44.

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URL:

http://ictp.caict.ac.cn/EN/10.12267/j.issn.2096-5931.2022.05.005

http://ictp.caict.ac.cn/EN/Y2022/V48/I5/34

Figures/Tables 10

输入	参与方A密钥sk_A
输入	参与方B输入密文$\left[\!\left[ \text{x} \right]\!\right]$和密钥pk_A
输出	参与方A输出x_A
输出	参与方B输出x_B,并满足明文空间里 x_A+x_B=x

	参与方A不应获得	参与方B不应获得
模型参数	W_A,W_B	W_A,W_B
前向计算	X_AW_A,X_BW_B,Z	X_AW_A,X_BW_B
反向计算	▽Z,▽W_A,▽W_B	▽W_A

输入	参与方A输入特征X_A,模型${{\left[\!\left[ {{W}_{A}} \right]\!\right]}_{B}}$,和密钥sk_A,pk_A,pk_B
输入	参与方B输入特征X_B,模型U_B,${{\left[\!\left[ {{V}_{B}} \right]\!\right]}_{A}}$,和密钥sk_B,pk_A,pk_B
输出	参与方A无输出
输出	参与方B输出Z=X_AW_A+X_BW_B, $y ︿$ =Sigmoid(Z),其中W_B=U_B+V_B

输入	参与方A输入特征X_A,模型${{\left[\!\left[ {{W}_{A}} \right]\!\right]}_{B}}$,和密钥sk_A,pk_A,pk_B
输入	参与方B输入特征X_B,模型U_B,${{\left[\!\left[ {{V}_{B}} \right]\!\right]}_{A}}$,和密钥sk_B,pk_A,pk_B
输出	参与方A无输出
输出	参与方B输出Z=X_AW_A+X_BW_B, $y ︿$ =Sigmoid(Z),其中W_B=U_B+V_B

输入	参与方A输入特征X_A,模型${{\left[\!\left[ {{W}_{A}} \right]\!\right]}_{B}}$,和密钥sk_A,pk_A,pk_B
输入	参与方B输入特征X_B,标签y,预测值,模型U_B, ${{\left[\!\left[ {{V}_{B}} \right]\!\right]}_{A}}$,和密钥sk_B,pk_A,pk_B
输出	参与方A输出${{\left[\!\left[ \nabla {{W}_{A}} \right]\!\right]}_{B}}$
输出	参与方B输出$\nabla W_{B}$

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