BCPalgorithmForPython
The BCP Algorithm For Python2.7
A brief overview about BCP algorithm
Firstly we should know the concept of Additive Homomorphic Cryptosystem
Suppose [M1]pk and [M2]pk are two additive homomorphic ciphertexts under the same public key pk. The additive homomorphic cryptosystem (AHC) has the additive homomorphic property:
Dsk ([M1]pk * [M2]pk) = M1 + M2
BCP is an Additive Homomorphic Cryptosystem. besides, it has a special property which offers two independent decryption mechanisms, The second decryption mechanism decrypts given ciphertext successfully if and only if a certain master secret key is known.
The BCP algorithm and its properties
To know more about the BCP algorithm and its properties, I highly recommend you to read the original paper
- Bresson, E., Catalano, D., Pointcheval, D.: A simple public key cryptosystem with a double trapdoor decryption mechanism and its applications. In: ASIACRYPT. LNCS, vol.2894, pp. 37–54. Springer (2003).
- Peter, A., Tews, E., & Katzenbeisser, S. (2013). Efficiently outsourcing multiparty computation under multiple keys.IEEE Transactions on Information Forensics & Security, 8(12), 2046-2058.
And also my paper (IEEE DSC on workshop PBD 2017)
Time series discord discovery under Multi-party Privacy Preserving
How to install
OS (only available for Linux)
I was developed this project on Ubuntu 17.04， and I used three encrypted library， gmp，pbc，and charm.
Ubuntu has their own python environment, but I don't recommend to use the default Python，there are too many package you need to install in the following steps，so I recommend the anaconda, it already installed many useful packages. link: https://www.continuum.io/downloads/ For Chinese mainland developer, you can download anaconda from "tuna" https://mirrors.tuna.tsinghua.edu.cn/anaconda/
Environment
sudo apt-get install m4
sudo apt-get install pyparing (unnecessary)
sudo apt-get install openssl-dev
sudo apt-get install python-dev (necessary)
GMP library
For Ubuntu, you can directly install the gmp library with command “ sudo apt-get install libgmp-dev”
For other linux system，you need to download the gmp source code and make. I have provided the source code in the folder “gmp-6.1.1”
cd gmp-6.1.1 excute
./configure
make
make install
PBC library
./configure
make
make install
ln -s /usr/local/lib/libpbc.so.1 /usr/lib
Charm Library (must installed openssl-dev,python-dev)
./configure.sh (notice that if you use anaconda, you need to change the python path in configure.sh line 134, change it to your anaconda's python path)
make build
make install
ldconfig
How To Use
BCP SetUP
For BCP algorithm, the first thing we should to do is setup -- generate the public key and master key.
keyGen() Function, def keyGen(secparam = 1024,paramPath = 'param',mkPath = 'mk') it will generate:
>>>1. public parameters: N2,N,k,g (write in to paramPath )
>>>2. master key (write into paramPath)
After generated the public parameters, you can instantiate a BCP context by using parameters bcp = genBCPcontext(paramPath = 'param')
Generate KEYS
And the pk and sk will be generated when you got the BCP context pk,sk = genKeyPair(bcp, keyPairPath = 'keyPair')
generate pk and sk ( write into keyPairPath)
When you get the key pair, you don't need to generate them again the next time, you can directly read it from file
pk,sk = readKeyPairFromFile(keyPairPath = 'keyPair')
Encrypt
You got pk, and BCP context now, so you can encrypt the number now, >> ciphertext1 = bcp.Encrypt(pk,12) >> ciphertext2 = bcp.Encrypt(pk,18) >> print ciphertext1 >>#it will show two line ciphertext
Decrypt
there are two types decypt, decrypted by sk and decrypted by mk
with sk
m = bcp.Decrypt(ciphertext1,sk) print m
#m = 12with MK
m = DecryptMK(ciphertext2,pk) print m #m = 18
Computation
Multiply
ciphertext3 = bcp.multiply(ciphertext1,ciphertext2) print Decrypt(ciphertext3,sk) #30
Exponentiate
ciphertext3 = bcp.exponentiate(ciphertext3, 2) print Decrypt(ciphertext3,sk) #60 (30*2)