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2017

Optimizing relinearization in circuits for homomorphic encryption

Chen, Hao

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Fully homomorphic encryption (FHE) allows an untrusted party to evaluate arithmetic cir- cuits, i.e., perform additions and multiplications on encrypted data, without having the decryp- tion key.

One of the most efficient class of FHE schemes include BGV and FV schemes, which are based on the hardness of the RLWE problem.
They share some common features: ciphertext sizes grow after each homomorphic multiplication; multiplication is much more costly than addition, and the cost of homomorphic multiplication scales linearly with the input ciphertext sizes.
Furthermore, there is a special relinearization operation that reduce the size of a ciphertext, and the cost of relinearization is on the same order of magnitude as homomorpic multiplication.

Optimizing relinearization in circuits for homomorphic encryption · Around

Built on

Somewhat practical fully homomorphic encryption
Junfeng Fan and Frederik Vercauteren · 2012
Earlier work this paper cites.
On the minimal number of bootstrappings in homomorphic circuits
Tancrède Lepoint and Pascal Paillier · 2013
Earlier work this paper cites.
(Leveled) fully homomorphic encryption without bootstrapping
Zvika Brakerski, Craig Gentry, and Vinod Vaikuntanathan · 2014
Earlier work this paper cites.
Algorithms in helib
Shai Halevi and Victor Shoup · 2014
Earlier work this paper cites.

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