Arithmetisation of the Floor Function and Its Applications to Homomorphic Cryptography
Arithmétisation de la fonction Floor et application à la cryptographie homomorphe
Résumé
Cryptography has historically been based on integer arithmetic. Thus, there was no need to investigate functions related to real numbers or analysis, such as the fractional part or the floor function. The floor function has several applications in modern cryptography. Its arithmetisation can allow for the application of generic side-channel countermeasures, like masking, without being limited by the chosen representation of rationnal or real numbers. It has also some applications in Fully Homomorphic Encryption (FHE), either directly in CKKS, or indirectly, as an arithmetised floor function can be computed with FHE. A consequence is the possibility of protecting normalisation or discretisation operations in Machine Learning or Deep Learning. In this work, we perform the arithmetisation by adapting a Fourier series and speeding up its convergence by composing partial series with themselves.
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