Authors:
Devharsh Trivedi
1
;
Nesrine Kaaniche
2
;
Aymen Boudguiga
3
and
Nikos Triandopoulos
1
Affiliations:
1
Department of Computer Science, Stevens Institute of Technology, Hoboken, NJ 07030, U.S.A.
;
2
Télécom SudParis, Institut Polytechnique de Paris, 91000, France
;
3
Université Paris-Saclay, CEA-List, 91191 Gif-sur-Yvette, France
Keyword(s):
Python Library, Comparison Approximation, Private Machine Learning, Fully Homomorphic Encryption.
Abstract:
Fully Homomorphic Encryption (FHE) is a prime candidate to design privacy-preserving schemes due to its cryptographic security guarantees. Bit-wise FHE (e.g., FHEW , T FHE) provides basic operations in logic gates, thus supporting arbitrary functions presented as boolean circuits. While word-wise FHE (e.g., BFV , CKKS) schemes offer additions and multiplications in the ciphertext (encrypted) domain, complex functions (e.g., Sin, Sigmoid, TanH) must be approximated as polynomials. Existing approximation techniques (e.g., Taylor, Pade, Chebyshev) are deterministic, and this paper presents an Artificial Neural Networks (ANN) based probabilistic polynomial approximation approach using a Perceptron with linear activation in our publicly available Python library chiku. As ANNs are known for their ability to approximate arbitrary functions, our approach can be used to generate a polynomial with desired degree terms. We further provide third and seventh-degree approximations for univariate S
ign(x) ∈ {−1, 0, 1} and Compare(a − b) ∈ {0, 12 , 1} functions in the intervals [−1, 1] and [−5, −5]. Finally, we empirically prove that our probabilistic ANN polynomials can improve up to 15% accuracy over deterministic Chebyshev’s.
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