The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Cryptography and Machine Learning
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Can homomorphic encryption be practical?
Proceedings of the 3rd ACM workshop on Cloud computing security workshop
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
On ideal lattices and learning with errors over rings
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Better bootstrapping in fully homomorphic encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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We demonstrate that, by using a recently proposed leveled homomorphic encryption scheme, it is possible to delegate the execution of a machine learning algorithm to a computing service while retaining confidentiality of the training and test data. Since the computational complexity of the homomorphic encryption scheme depends primarily on the number of levels of multiplications to be carried out on the encrypted data, we define a new class of machine learning algorithms in which the algorithm's predictions, viewed as functions of the input data, can be expressed as polynomials of bounded degree. We propose confidential algorithms for binary classification based on polynomial approximations to least-squares solutions obtained by a small number of gradient descent steps. We present experimental validation of the confidential machine learning pipeline and discuss the trade-offs regarding computational complexity, prediction accuracy and cryptographic security.