Fully Homomorphic Encryption: A Case Study

Abstract

Fully Homomorphic Encryption (FHE) has been dubbed as cryptography’s holy grail. It opens the door to many new capabilities with the goal to solve the IT world’s problems of security and trust. After 2009, when Craig Gentry showed that FHE can be realised, research in the area exploded and substantial progress has been made in finding more practical and more efficient schemes. FHE is a cryptographic primitive that allows one to compute arbitrary functions over encrypted data. Such schemes have numerous applications since it allows users to encrypt their private data locally but still outsource the computation of the encrypted data without risking exposing the actual data. In 2012, LTV12 published the first multi-key FHE scheme and proved that any Somewhat Homomorphic Encryption (SHE) scheme could be made multi-key. As in the single key setting, a lot of progress been made in the area but no work has been done in implementing the multi-key schemes. This thesis is survey on FHE and MKFHE, with special attention to the state of the art implementations available as well as three implementations including the first implementation in the multi-key settings to the best of our knowledge.