user404d/Paillier-GMP

Implementation of the Paillier homomorphic cryptosystem using GMP

Secure Dot Product

Authors

Akshatha Bhat | Quincy Conduff | Sai Sruti

Description

Secure dot product protocol using Paillier homomorphic encryption. Paillier homomorphic encryption was implemented using GMP.

Requirements

• C++ 17 compliant compiler
• make >=3.81
• cmake >=3.2
• gmp >= 6.1.2
  • Requires both gmp.h and gmpxx.h for C++ compatibility

Installation

git clone https://github.com/user404d/Paillier-GMP.git
cd Paillier-GMP
make

Usage

$ ./bin/secure_dot_product --help
Secure dot product using Paillier homomorphic encryption
Usage:
  secure_dot_product [OPTION...]

  -h, --help     Print help message
      --pk FILE  Public key (required)
      --sk FILE  Private key (required)

 key generation options:
      --seed FILE     Seed key generation with k,p,q,g
  -k, --kbits uint64  Generate keys using k bits

 input options:
  -u, FILE  Vector u (default: u.vec)
  -v, FILE  Vector v (default: v.vec)

 output options:
      --eu FILE      Encrypted vector u (default: u.vec.enc)
      --ev FILE      Encrypted vector v (default: v.vec.enc)
  -o, --output FILE  Dot product of u and v (default: res.out)

Usage Notes

• Using --seed arg has precedence over --keygen arg.
• The size of k for key generation should be at least 2*s where s is the number of bits needed to represent the dot product. This will allow the computation to be performed safely.
• If public and private keys are already known or generated, then simply remove the --keygen arg flag and provide the path to each file.

Seed File Format

<k bits>
<p>
<q>
<g>

If g = 0 then g will be set to p*q + 1.

Seed Example

File seed.in.

8
7
11
78

Key File Format

All values are integers separated by whitespace (newlines by default).

Public Key

<k bits>
<n>
<g>

Public Key Example

File pub.key.

8
143
0

The above implies that g = n + 1.

Private Key

<k bits>
<lambda>
<mu>
<n>
<p^2>
<(p^2)^-1 mod (q^2)>
<q^2>

Private Key Example

File priv.key.

8
60
31
143
121
88
169

Vector File Format

A vector file contains white space delimited positive integers.

<int><space|tab|newline><int><space|tab|newline>...<int>

Examples

File u.vec.

0 1 2 3 4 5

File v.vec.

5
4
3
2
1
0

Demo Usage

Taken from test/functional_test.sh.

#!/bin/bash -e

TMP=tmp
U_VEC=u.vec
V_VEC=v.vec
RESULT=u_dot_v.out

test_result()
{
    if [ "$1" -eq "$2" ]; then
        echo "[+] -> $1 == $2"
    else
        echo "[-] -> $1 != $2"
        if [ `head -n 2 $3 | tail -1` -le $2 ]; then
            echo "output was larger than modulo n found in $3"
        fi
    fi
}

test -d ${TMP} || mkdir tmp
echo "1 3 5 2 3 1 4" > ${TMP}/${U_VEC}
echo "2 2 2 2 2 2 2" > ${TMP}/${V_VEC}

./../bin/secure_dot_product -k 4096 \
    --pk ${TMP}/pub.key \
    --sk ${TMP}/priv.key \
    -u  ${TMP}/${U_VEC} \
    -v ${TMP}/${V_VEC} \
    --eu ${TMP}/u.vec.enc \
    --ev ${TMP}/v.vec.enc \
    -o ${TMP}/${RESULT}

test_result `tail -1 ${TMP}/${RESULT}` "38" ${TMP}/pub.key