Polynomial function approximations with leading integer coefficients for efficient encrypted implementations

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dc.contributor.authorTeichrib, Dieter
dc.contributor.authorAdamek, Janis
dc.contributor.authorBinfet, Philipp
dc.contributor.authorSchulze Darup, Moritz
dc.date.accessioned2025-10-06T09:18:39Z
dc.date.available2025-10-06T09:18:39Z
dc.date.issued2025-09-04
dc.description.abstractComputations on encrypted data can, in principle, be performed using homomorphic encryption. However, due to certain limitations, only algorithms based on polynomial functions can be efficiently implemented in an encrypted setting. Consequently, polynomial approximations of non-polynomial functions are essential for efficient encrypted computations. In particular, low- to moderate-degree polynomial approximations of activation functions in neural networks are of special interest.We show that the accuracy of encryption-friendly approximations can be improved through a simple yet effective extension of state-of-the-art methods. Specifically, we show that enforcing a leading integer coefficient enables the use of polynomials of one degree higher than all existing approaches. Incorporating this novel integer constraint into classical regression problems initially leads to mixed-integer programs (MIPs). However, we develop tailored solution schemes that avoid MIP solving. Using these schemes, we compute new polynomial approximations for various test cases and demonstrate the effectiveness of our method compared to existing approaches.en
dc.identifier.urihttp://hdl.handle.net/2003/44020
dc.language.isoen
dc.relation.ispartofseriesIEEE Access; 13
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectPolynomial regressionen
dc.subjectOptimizationen
dc.subjectHomomorphic encryptionen
dc.subjectChebyshev regressionen
dc.subjectPrivacy-preserved machine learningen
dc.subject.ddc620
dc.subject.rswkPolynomiale Regression
dc.subject.rswkOptimierung
dc.subject.rswkHomomorphismus
dc.subject.rswkChiffrierung
dc.subject.rswkČebyšev-Polynome
dc.subject.rswkMaschinelles Lernen
dc.subject.rswkDatenschutz
dc.titlePolynomial function approximations with leading integer coefficients for efficient encrypted implementationsen
dc.typeText
dc.type.publicationtypeArticle
dcterms.accessRightsopen access
eldorado.doi.registerfalse
eldorado.secondarypublicationtrue
eldorado.secondarypublication.primarycitationD. Teichrib, J. Adamek, P. Binfet and M. S. Darup, "Polynomial Function Approximations With Leading Integer Coefficients for Efficient Encrypted Implementations," in IEEE Access, vol. 13, pp. 157455-157462, 2025, doi: 10.1109/ACCESS.2025.3606013
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1109/access.2025.3606013

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