Ring-Learning with Errors problem

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Table of contents

Introduction (français)
1 Contexte historique et motivations
2 But et organisation de la thèse
Introduction
1 Historical context and motivations
1 Preliminarie
1.1 Ring-Learning with Errors problem
1.2 Somewhat Homomorphic Encryption based on Ring-LWE
1.3 Classical arithmetic in cyclotomic rings
2 Full RNS scaled-invariant schemes
2.1 Towards a full RNS decryption
2.2 Towards a full RNS homomorphic multiplication
2.3 Last step: the relinearization
2.4 Software implementation
2.5 Conclusion
3 Polynomial arithmetic in general cyclotomic rings
3.1 Preliminaries
3.2 Improving polynomial reduction modulo m
3.3 Adaptation of BGV and FV to the Montgomery representation
3.4 Experimental results
3.5 Conclusion
4 Homomorphic evaluation of support vector machine
4.1 Preliminaries
4.2 Novel homomorphic techniques for SVM classification
4.3 Implementation details
4.4 Experimental results
4.5 Conclusion