Library for homomorphic encryption HELib

IBM has released the free HElib cryptographic library with support for homomorphic encryption (homomorphic encryption, HE). This is the first in the history of the implementation of such a cryptosystem and an important stage in the development of cryptography as a science and mathematical methods for protecting information. The development has a special practical value precisely today, 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 proven. Rivest himself decided that the idea could not be implemented.

Nevertheless, IBM researchers managed to implement not partially, but completely homomorphic encryption. The scheme is called BGV (Brakerski-Gentry-Vaikuntanatan, Brakerski-Gentry-Vaikuntanathan).

Stanford graduate student Craig Gentry offered this model in 2009 for his Ph.D. thesis “Fully homomorphic encryption using ideal lattices”. Fully homomorphic encryption. The model was very favorably accepted by the community of cryptographers, who immediately implemented a number of improvements for it. Gentry himself even before that received support from the National Research Society and the IBM Research research unit.
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In the HElib library, the BGV scheme is implemented with optimizations for speed, including using the Smart-Vercauteren ciphertext packing technique and Gentry-Halevi-Smart optimizations.

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

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