Table 3 Example CML methods that replace the expensive algorithmic components with their crypto-friendly versions

Mohassel and Zhang (2017)

Logistic Regression, Neural Networks

Sigmoid, Softmax

ReLu

Avoids inversion and limits expensive confidential divisions to one.

Graepel et al. (2012)

LMC, Fisher’s LDA

Divisions

Multiplications with incorporated division factors

Avoids division costs and simplifies the protocol.

Nikolaenko et al. (2013)

Ridge Linear Regression

LU decomposition

Cholesky’s decomposition

Reduces the cost complexity by half.

Nikolaenko et al. (2013)

Matrix Factorization

Cholesky’s Decomposition

Sorting based matrix factorization

Reduces the overall complexity from quadratic to within a polylogarithmic factor of the complexity in the plaintext

Sharma and Chen (2019)

Boosting

Decision Stumps

Random Linear Classifiers

Reduced number of comparisons and simplicity in learning.

Naehrig et al. (2011)

Logistic Regression

Exponentiation

Taylor Expansion

Avoids costs involved in multiple levels of multiplications.

Sharma et al. (2019)

Spectral Clustering

Eigen decomposition

Eigen-approximation by Lanczos and Nystrom

Reduces complexity of the problem from O(N³) to O(N²).