Overview

bls48 is an Optimal Ate Pairing(OAP) on BLS Curve implementation in C++.
This implementation is based on the drafts below;

• Y. Kiyomura, et al. “Secure and Eifficient Pairing at 256-Bit Secure Level” (2017)
• C. Costello, K. Lauter, M. Naehrig, “Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings.” (2011)
• draft-by-Kato(not submitted)

Furthermore, this implementation uses libsnark library.

• https://github.com/scipr-lab/libsnark/tree/deprecated-master (branch : deprecated-master)

We are motivated by the security consideration for pairing on any curve give by T. Kim.

• T. Kim et al. “The extended tower number field sieve: A new complexity for the medium prime case. In Advances in Cryptology”, (2016).

Kim’s attack made us to update the security parameters or to use alternative curves in OAP.
BLS-48 cuerve is one of the pairing friendly curves, and recommended parameters for realizing 256-bit security is written in [Kiyomura].

Build instructions

This implementation relies on the following:

• C++ build environment
• GMP for certain bit-integer arithmetic
• libprocps for reporting memory usage
• GTest for some of the unit tests

We have tested these only Linux so far(Ubuntu14.04).
For example, on a fresh install of Ubuntu 14.04, install the following packages:

$ sudo apt-get install build-essential git libgmp3-dev libprocps3-dev libgtest-dev python-markdown libboost-all-dev libssl-dev

In the case of Ubuntu 16.04, install the following packages:

$ sudo apt-get install build-essential git libgmp3-dev libprocps4-dev libgtest-dev python-markdown libboost-all-dev libssl-dev

Then, to compile, run:

$ make

Timing Test

• Ubuntu14.04　　
  Intel(R) Core(TM) i5-4210M CPU @ 2.60GHz, 4 cores RAM 8GB

• Ubuntu16.04　　
  Intel(R) Core(TM) i7 CPU 950 @ 3.07GHz, 8 cores RAM 24GB

• Raspberry Pi 3 model B
  Linux devuan 4.6.3-gb48d47a(64bit OS) CPU Cortex-A53 ARMv8 64bit @ 1.2GHz, 4 cores RAM 1GB

• Raspberry Pi model B
  Ubuntu16.04.2 LTS xenial(32bit OS) CPU Cortex-A53 ARMv8 64bit @ 1.2GHz, 4 cores RAM 1GB

• Mac
  Mac OS Sierra Intel Core i7 @ 3.5 GHz, 2 cores RAM 16 GB

• Windows (Using MSYS2)
  Windows10 Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz, 4 cores RAM 16 GB