HELib homomorphic encryption library

IBM has released the free HElib cryptographic library with support for homomorphic encryption (HE). This is the first implementation of such a cryptosystem in history and an important stage in the development of cryptography as a science and mathematical methods of protecting information. Development has special practical value in our days, with the spread of cloud services.

Homomorphic encryption is a cryptographic system that allows you to perform mathematical operations on encrypted data without first decrypting it. The idea was formed 30 years ago by the famous cryptographer Ronald Rivest, but for a long period of time the existence of completely homomorphic systems has not been proved. Rivest himself decided that the idea was not to be realized.

Nevertheless, IBM researchers were able to implement not partially, but completely homomorphic encryption. The scheme was called BGV (Brakerski-Gentry-Vaikuntanathan, Brakerski-Gentry-Vaikuntanathan).

Stanford graduate student Craig Gentry proposed this model in 2009 for his Ph.D.“Fully homomorphic encryption using ideal lattices”. The model was very favorably received by the community of cryptographers, who immediately realized a number of improvements for it. Gentry himself had already received support from the National Science Society and the research division of IBM Research.

In the HElib library, the BGV scheme is implemented with optimizations for speed, including the use of the Smart-Verkauteren ciphertext packaging technique and Gentry-Halevy-Smart optimizations .

HElib is written in C ++ using the NTL math library . Source code is distributed under the GPL.

Unfortunately, homomorphic encryption greatly increases the computing requirements of a computer. According to Gentry himself, in 2009, for example, processing a search query in Google if the text is encrypted will require about a trillion times more calculations . Nevertheless, the optimization made it possible to significantly increase the performance of the library, so that in a few years or decades, if Moore’s law continues, the library can be widely used in web applications. Perhaps even earlier than we think.