ssscomp

Secret Sharing & Secure Computation Library for Go

Package ssscomp is a High Performance, Pure Go Secret Sharing & Secure Computation Library including support for several HE (Homomorphic Encryption) algorithms. It provides a Development Kit for Python too!

Install

Copyright (C) 2019 Sergio Anguita
See Contributors.md for a complete list of contributors.  
Licensed under the MIT License.  

go get github.com/zerjioang/ssscomp

Install for Python

Copyright (C) 2019 Sergio Anguita
See Contributors.md for a complete list of contributors.  
Licensed under the MIT License.  

This package is designed to be compatible with current Machine Learning frameworks such as: pandas, keras or tensorflow Use pip install ssscomp to download the package to you environment. Development Python SDK is provided with examples at sdk/python/example

Features

Secret Sharing

Description

The most common examples of finite fields are given by the integers mod p when p is a prime number.

Packed sharing

If many secrets are to be secret shared, it may be beneficial to use the packed scheme where several secrets are packed into each share. While still very computational efficient, one downside is that the parameters are somewhat restricted.

Specifically, the parameters are split in scheme parameters and implementation parameters:

• the former, like in Shamir sharing, determines the abstract properties of the scheme, yet now also with a secret_count specifying how many secrets are to be packed into each share; the reconstruction limit is implicitly defined as secret_count + threshold + 1
• the latter is related to the implementation (currently based on the Fast Fourier Transform) and requires not only a prime specifying the field, but also two principal roots of unity within that field, which must be respectively a power of 2 and a power of 3

Due to this increased complexity, providing helper functions for finding suitable parameters are in progress. For now, a few fixed fields are included in the packed module as illustrated in the example below:

• PSS_4_8_3, PSS_4_26_3, PSS_155_728_100, PSS_155_19682_100

with format PSS_T_N_D for sharing D secrets into N shares with a threshold of T.

Homomorphic properties

Both the Shamir and the packed scheme enjoy certain homomorphic properties: shared secrets can be transformed by manipulating the shares. Both addition and multiplications work, yet notice that the reconstruction limit in the case of multiplication goes up by a factor of two for each application.

Other SSS Implementations

• https://github.com/itslab-kyushu/sss
• https://github.com/amousa11/sss
• https://github.com/sam701/secret-sharing

Homomorphic Encryption Algorithms

This library has support for current homomorphic algorithms:

• Unpadded RSA
• ElGamal
• Paillier
• DGHV

References

• Efficient Integer Vector Homomorphic Encryption. Angel Yu, Wai Lok Lai, James Payor. (https://courses.csail.mit.edu/6.857/2015/files/yu-lai-payor.pdf)

• Homomorphic Encryption and the BGN Cryptosystem. David Mandell Freeman (http://theory.stanford.edu/~dfreeman/cs259c-f11/lectures/bgn)

• Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups. David Mandell Freeman. (http://theory.stanford.edu/~dfreeman/papers/subgroups.pdf, http://theory.stanford.edu/~dfreeman/talks/eurocrypt10.pdf)

• Public Key Compression and Modulus Switching for FullyHomomorphic Encryption over the Integers. Jean-S ́ebastien Coron, David Naccache, and Mehdi Tibouchi (https://eprint.iacr.org/2011/440.pdf)

• Fully Homomorphic Encryption over the Integers. Marten van Dijk and Craig Gentry and Shai Halevi and Vinod Vaikuntanathan (https://eprint.iacr.org/2009/616.pdf)

• Somewhat Homomorphic Encryption Scheme for Arithmetic Operations on Large Integers. (https://www.gta.ufrj.br/ftp/gta/TechReports/PAD12.pdf)

• Fully Homomorphic Encryption from Ring-LWEand Security for Key Dependent Messages. Zvika Brakerski and Vinod Vaikuntanathan (http://www.wisdom.weizmann.ac.il/~zvikab/localpapers/IdealHom.pdf)

• Secure Computation for Machine Learning With SPDZ (https://arxiv.org/pdf/1901.00329.pdf)

• Protocols for Secure Computations (https://research.cs.wisc.edu/areas/sec/yao1982-ocr.pdf)

• A Pragmatic Introduction toSecure Multi-Party Computation. (https://www.cs.virginia.edu/~evans/pragmaticmpc/pragmaticmpc.pdf)

• Secure Multiparty Computation. (https://www.cs.tau.ac.il/~iftachh/Courses/Seminars/MPC/Intro.pdf)

• https://hal.archives-ouvertes.fr/tel-01918263/document

• https://www.di.ens.fr/~minelli/docs/phd-thesis.pdf

• https://petsymposium.org/2019/files/papers/issue2/popets-2019-0026.pdf

• https://eprint.iacr.org/2015/472.pdf

Other references

• http://cryptowiki.net/index.php?title=Fully_homomorphic_encryption_schemes
• https://asecuritysite.com/encryption
• https://medium.com/@apogiatzis/shamirs-secret-sharing-a-numeric-example-walkthrough-a59b288c34c4
• https://towardsdatascience.com/understanding-differential-privacy-85ce191e198a
• https://blog.quarkslab.com/a-brief-survey-of-fully-homomorphic-encryption-computing-on-encrypted-data.html

License

Copyright (c) 2019 Sergio Anguita

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
• Uses GPL license described below

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.