A journey towards practical fully homomorphic encryption

Guillaume Bonnoron 1, 2
1 Lab-STICC_IMTA_CID_IRIS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : Craig Gentry presented in 2009 the first fully homomorphic encryption scheme. Since then, a tremendous effort has been, and still is, dedicated by the cryptographic community to make practical this new kind of cryptography. It is revolutionnary because it enables direct computation on encrypted data (without the need for the computing entity to decrypt them). Several trends have been developed in parallel, exploring on one side fully homomorphic encryption schemes, more versatile for applications but more costly in terms of time and memory. On the other side, the somewhat homomorphic encryption schemes are less flexible but more efficient. This thesis, achieved within the Chair of Naval Cyber Defence, contributes to these trends. We have endorsed different roles. First, an attacker position to assess the hardness of the security assumptions of the proposals. Then, we conducted a state-of-the-art of the most promising schemes in order to identify the best(s) depending on the use-cases and to give precise advice to appropriately set the parameters that drive security level, ciphertext sizes and computation costs. Last, we endorsed a designer role. We proposed a new powerful fully homomorphic encryption scheme together with its open-source implementation, available on github.
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Guillaume Bonnoron. A journey towards practical fully homomorphic encryption. Cryptography and Security [cs.CR]. Ecole nationale supérieure Mines-Télécom Atlantique, 2018. English. ⟨NNT : 2018IMTA0073⟩. ⟨tel-02011668⟩

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