The main idea of this repo is to boost paillier encryption function to support degree-2 homomorphic encryption.(somewhat full homomorphic even though it's only 2-d XD)
- GNU MP Library, download and install instruction can be found on its official website.
- Simply copy the code to your cmomputer (preferred Debian-based), this program has not been tested on other platforms.
- Run binary file or compile from source file.
gcc test.c paillier.c paillier_mh.c -o test -lgmp
./test
.
├── include
│ ├── paillier.h
│ └── paillier_mh.h
├── README.md
├── src
│ ├── paillier.c
│ ├── paillier_mh.c
│ ├── test
│ └── test.c
└── test
Catalano, D., & Fiore. (2015). Using linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data. Proceedings of the ACM Conference on Computer and Communications Security, 2015, 1518-1529. #Avaliable Online#
The linerly-homomorphic encryption cryptosystem we chose is Pallier Cryptosystem. As an addictive homomorphic cryptosystem, when given public key and Enc(m1), Enc(m2), it is possible (in PPT) to calculate Enc(m1+m1). The listed paper presents a method to convert 1-d (linear) homomorphic encryption to 2-d homomorphic encryption. That is to say, we intend to calculate Enc(m1*m2) without any prior knowledage about m1 and m2. A more concrete formal representation is shown below:
Enc(m1*m2-b1*b2) = Enc((m1-b1)*(m2-b2))*Enc(b1)^(m2-b2) * Enc(b2)^(m1-b1)
Paillier functions including encryption and decryption function are from paillier-libraries-benchmarks repository.
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