A Privacy Preserving and Verifiable Federated Learning Scheme Based on Homomorphic Encryption

doi:10.3969/j.issn.1671-1122.2024.01.009

Abstract

Abstract:

Cross-silo federated learning enables clients to collaboratively train a machine learning model by aggregating local model updates without sharing raw data. However, studies have shown that intermediate parameters transmitted during training can also leak the privacy of raw data. A curious central server may falsify or tamper with aggregation results for its own benefit. To address these issues, an anti-collusion privacy preserving and verifiable cross-silo federated learning scheme was proposed. Specifically, the intermediate parameters of each client were encrypted to protect data privacy, and key management and collaborative decryption were achieved by combining secret sharing schemes to enhance system security. Furthermore, data integrity and authentication were achieved through aggregate signatures, and the verifiability of central server aggregation gradients was ensured using polynomial commitments. Security analysis shows that the proposed scheme not only protects the privacy of intermediate parameters and verifies data integrity, but also ensures the correctness of aggregation gradients. Performance analysis shows that compared to the existing schemes, the proposed scheme can significantly reduce the communication overhead.

Key words: federated learning, privacy preserving, homomorphic encryption, polynomial commitment, aggregate signature

CLC Number:

TP309

LAI Chengzhe, ZHAO Yining, ZHENG Dong. A Privacy Preserving and Verifiable Federated Learning Scheme Based on Homomorphic Encryption[J]. Netinfo Security, 2024, 24(1): 93-105.

Figures/Tables 8

References 35

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符号	含义
CS	中央服务器
TA	可信中心
C_i	第i个客户端
e:G₁?G₁→G_T	双线性映射
(PK^Enc, SK^Enc)	C_i用于加密的公私钥对
$SK_{i}^{ES}$	C_i获得的加密私钥份额
$PK_{i}^{Enc}$	C_i用于验证解密份额的公钥
$PK_{i}^{Sig}$	C_i用于验证签名的公钥
(pk, sk)	C_i用于计算承诺的公私钥对
H:{0,1}*→G₁	哈希函数
N	客户端数量

方案	完整性和认证	抵御合谋攻击	抵御其他客户端的攻击	可验证性	抵御好奇中央服务器攻击
文献[17]方案	?	?	?	?	√
文献[18]方案	?	?	√	√	√
文献[24]方案	?	?	?	√	√
本文方案	√	√	√	√	√

符号	描述	运行时间/ms
T_p	双线性对操作	7.52
T_m_{_}_b_p	双线性对中的指数	13.867
T_pa_{_}_bp	双线性对中的乘法	0.145
T_{m_ecc}	椭圆曲线上的标量乘法	4.355
T_pa_{_}_ecc	椭圆曲线上的点加法	0.016
T_exp	模指数运算	2.571
T_mul	模乘运算	0.006
T_enc	Paillier加密	6.781
T_dec	Paillier解密	12.982
T_c_{_}_mul	Paillier密文乘法	0.021