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HEAAN is software library that implements homomorphic encryption (HE) that supports fixed point arithmetics. This library supports approximate operations between rational numbers. The approximate error depends on some parameters and almost same with floating point operation errors. The scheme in this library is on the paper "Homomorphic Encryption for Arithmetic of Approximate Numbers" (


In "Params.h", 'pbnd' value is 59.0 by default. If you are using NTL with "NTL_ENABLE_AVX_FFT=on", This option reduces that small-prime size bound from 60 bits to 50 bits (see For this reason, you need to change the setting to 49.0.


v1.0 Implementation of Original HEAAN scheme

V1.1 Implementation of Original HEAAN scheme with bootstrapping (

V2.1 Faster Implementation of HEAAN scheme


This library is written by c++ and using NTL library (

How to use this library?

1. Build a static library/Running test functions

You can make a static library by typing "make all" in the /lib directory. After successful compilation you can find a static library libHEAAN.a in the /lib directory.

After you build libHEAAN.a, you can run a test program in the /run directory. In run.cpp, you need uncomment tests you need and type "make" in the /run directory. This command will run exe file "HEAAN".

We checked the program was working well on Ubuntu 16.04.2 LTS. You need to install NTL (with GMP), pThread, libraries.


Copyright (c) by CryptoLab inc. This program is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. You should have received a copy of the license along with this work. If not, see


In /test folder, we have test.cpp. You can compile this code using "make". After that, ./TestHEAAN TEST_NAME will test HEAAN library. TEST_NAME can be one of followings: Encrypt, EncryptSingle, Add, Mult, iMult, RotateFast, Conjugate


#include "HEAAN.h"

using namespace std;
using namespace NTL;

int main() {
  * Basic Parameters are in src/Params.h
  * If you want to use another parameter, you need to change src/Params.h file and re-complie this library.

  // Parameters //
  long logq = 300; ///< Ciphertext modulus (this value should be <= logQ in "scr/Params.h")
  long logp = 30; ///< Scaling Factor (larger logp will give you more accurate value)
  long logn = 10; ///< number of slot is 1024 (this value should be < logN in "src/Params.h")
  long n = 1 << logn;
  long slots = n;
  long numThread = 8;
  // Construct and Generate Public Keys //
  TimeUtils timeutils;
  Ring ring;
  SecretKey secretKey(ring);
  Scheme scheme(secretKey, ring);
  scheme.addLeftRotKeys(secretKey); ///< When you need left rotation for the vectorized message
  scheme.addRightRotKeys(secretKey); ///< When you need right rotation for the vectorized message
  // Make Random Array of Complex //
  complex<double>* mvec1 = EvaluatorUtils::randomComplexArray(slots);
  complex<double>* mvec2 = EvaluatorUtils::randomComplexArray(slots);
  // Encrypt Two Arry of Complex //
  Ciphertext cipher1;
  scheme.encrypt(cipher1, mvec1, n, logp, logq);
  Ciphertext cipher2;
  scheme.encrypt(cipher2, mvec2, n, logp, logq);
  // Addition //
  Ciphertext cipherAdd;
  scheme.add(cipherAdd, cipher1, cipher2);
  // Multiplication And Rescale //
  Ciphertext cipherMult;
  scheme.mult(cipherMult, cipher1, cipher2);
  Ciphertext cipherMultAfterReScale;
  scheme.reScaleBy(cipherMultAfterReScale, cipherMult, logp);
  // Rotation //
  long idx = 1;
  Ciphertext cipherRot;
  scheme.leftRotateFast(cipherRot, cipher1, idx);
  // Decrypt //
  complex<double>* dvec1 = scheme.decrypt(secretKey, cipher1);
  complex<double>* dvec2 = scheme.decrypt(secretKey, cipher2);
  return 0;

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