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https://github.com/bogdan-kulynych/libshe

Symmetric somewhat homomorphic encryption library based on DGHV
https://github.com/bogdan-kulynych/libshe

c-plus-plus ciphertext-compression cryptography homomorphic-encryption homomorphic-encryption-library

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Symmetric somewhat homomorphic encryption library based on DGHV

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README 

        
# libshe



[![Build Status](https://travis-ci.org/bogdan-kulynych/libshe.svg?branch=master)](https://travis-ci.org/bogdan-kulynych/libshe) [![Coverage Status](https://coveralls.io/repos/bogdan-kulynych/libshe/badge.svg?branch=master)](https://coveralls.io/r/bogdan-kulynych/libshe?branch=master)



Symmetric somewhat homomorphic encryption library based on DGHV scheme.



## Introduction



Homomorphic encryption is a kind of encryption that allows to execute functions over the ciphertexts without decrypting them. This library implements a symmetric variant of originally asymmetric somewhat homomorphic encryption scheme over the integers by van Dijk et al. [DGHV10][DGHV10] using ciphertext compression techniques from [CNT11][CNT11]. The symmetricity of the scheme means that only the private key is used to encrypt and decrypt ciphertexts. A relatively small public element, however, is used in homomorphic operations, but it is not a real public key.



Such scheme is useful in secure function evaluation setting, where a client encrypts an input to an algorithm using their private key, sends it to a server which executes an algorithm homorphically, and sends the output back to the client. The client then obtains the output of the algorithm by decrypting server response using the private key.



See the following diagram for visual explanation.



- Let _f_ be an algorithm to be evaluated on a server.

- Let _a[1], a[2], ... a[n]_ be inputs of _f_ that client provides to the server.

- Let _b[1], b[2], ... b[n]_ be inputs of _f_ that server possesses.

- Let _p_ be the client's private key, and _x[0]_ be the corresponding public element



![SFE](misc/sfe.png)



## Status



_Warning_. This is experimental software. **It is not to be used in mission-critical applications.** Since the time this software was written, parameters of the underlying scheme were broken many times.



## Installation



You can consult the `.travis.yml` for concrete installation commands on Debian-based systems.



### Requirements



- gcc >= 4.8

- [boost](http://www.boost.org/) >= 1.55

- [GMP](https://gmplib.org/) >= 6.0.0

- [lcov](http://ltp.sourceforge.net/coverage/lcov/readme.php) >= 1.11 (optional)



### Building and installation



Build and install `libshe.so` library and headers:



```

make

sudo make install

```



You can also uninstall with



```

sudo make uninstall

```



## Usage



### Tests and benchmarks



Run tests:



```

make tests

```



_Note_. Running tests will compile sources with debug options. Do `make clean` before installing if tests were run previously.



Run benchmarks:



```

make benchmarks

```



### Building your program



Use C++11 and link against _GMP_ and _Boost Serialization_ when building your program:



```

-std=c++11 -lgmp -lboost_serialization -lshe

```



Include libshe in your sources:



```cpp

#include 



using she::ParameterSet;

using she::PrivateKey;

// ...

```



### Example



The following example assumes a client and a server that are engaged in a two-party secure function evaluation protocol.



Client generates a parameter set:



```cpp

const ParameterSet params = ParameterSet::generate_parameter_set(62, 1, 42);

```



Given these parameters, the encryption scheme exhibits following properties:



   - Security level is **(62-bit)**

   - At least 1 multiplication can be evaluated on every bit in the ciphertext

   - The non-secure random number generator used in ciphertext compression is seeded with number 42



Client then constructs a private key object from generated parameters:



```cpp

const PrivateKey sk(params);

```



Encrypts the plaintext:



```cpp

const vector plaintext = {1, 0, 1, 0, 1, 0, 1, 0};

const auto compressed_ciphertext = sk.encrypt(plaintext);

```



Serializes and sends compressed ciphertext to server.



Upon obtaining the compressed ciphertext, Server expands it to perform operations:



```cpp

const auto ciphertext = compressed_ciphertext.expand();

```



Executes the algorithm (here negation of an 8-bit input)



```cpp

const vector another_plaintext = {1, 1, 1, 1, 1, 1, 1, 1};

const auto response = ciphertext ^ another_plaintext;

```



Serializes the output and sends it back to the client.



Client decrypts the response and obtains the algorithm output in plaintext:



```cpp

const auto decrypted_response = sk.decrypt(response);

const vector expected_result = {0, 1, 0, 1, 0, 1, 0, 1};

assert(decrypted_response == expected_result);

```



Note that ciphertext can be compressed only during encryption on the client side, so cost for Server → Client communication is significantly higher than that of Client → Server communication.



### Available homomorphic operations



- Bitwise addition (XOR): `c1 ^ c2`

- Bitwise multiplication (AND): `c1 & c2`

- Equality comparison: `c0.equal({c1, c2, ..., cn})`..

- Selection of _i_-th ciphertext: `c0.select({c1, c2, ..., cn})`.



## License



The code is released under the [GNU General Public License v3.0](https://www.gnu.org/licenses/gpl-3.0.html).



Copyright © 2015 Bogdan Kulynych. `hello [at] bogdankulynych.me`



[DGHV10]: http://eprint.iacr.org/2009/616.pdf

[CNT11]: http://eprint.iacr.org/2011/440.pdf