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Due to digitization, handling big data safely is a big concern nowadays. Cryptography plays a crucial role in protecting sensitive data. Encrypting the data before sending it to the cloud server is a better practice to secure data and perform analysis on encrypted data without revealing raw data. Machine learning is used to make inferences from this encrypted data. The fully homomorphic encryption (FHE) scheme CKKS enables us to perform operations like training, testing, and inference on encrypted data. We have used the TenSEAL library in Python to encrypt our datasets using the CKKS fully homomorphic encryption scheme. As the traditional sigmoid activation function ( \(\sigma (x) \) ) used in logistic regression is not FHE-friendly, we have designed the logistic regression model to train this encrypted data using various polynomial approximations of the sigmoid. This model is secure, as it has been trained on encrypted data. We have experimented on binary classification datasets and observed diabetes, statlog, titanic, and heart datasets for polynomial approximation ( \(0.500781 +0.14670403x +0.001198 x^2 - 0.001006 x^3 \) ), which gives better accuracy than the traditional sigmoid activation function.

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Encrypted Training Using Logistic Regression with Different Polynomial Approximations of the Sigmoid Function

  • 会议论文

  • 发表日期：

    2026年

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  • Anushka Seth,
  • Shubhangi Gawali,
  • Amy Corman,
  • Neena Goveas,
  • Asha Rao

摘要

Due to digitization, handling big data safely is a big concern nowadays. Cryptography plays a crucial role in protecting sensitive data. Encrypting the data before sending it to the cloud server is a better practice to secure data and perform analysis on encrypted data without revealing raw data. Machine learning is used to make inferences from this encrypted data. The fully homomorphic encryption (FHE) scheme CKKS enables us to perform operations like training, testing, and inference on encrypted data. We have used the TenSEAL library in Python to encrypt our datasets using the CKKS fully homomorphic encryption scheme. As the traditional sigmoid activation function ( \(\sigma (x) \) ) used in logistic regression is not FHE-friendly, we have designed the logistic regression model to train this encrypted data using various polynomial approximations of the sigmoid. This model is secure, as it has been trained on encrypted data. We have experimented on binary classification datasets and observed diabetes, statlog, titanic, and heart datasets for polynomial approximation ( \(0.500781 +0.14670403x +0.001198 x^2 - 0.001006 x^3 \) ), which gives better accuracy than the traditional sigmoid activation function.