Shamir secret sharing library

sss is a library that exposes an API to split secret data buffers into a number of different shares. With the possession of some or all of these shares, the original secret can be restored. It is the schoolbook example of a cryptographic threshold scheme. This library has a command line interface. (web demo)

Table of contents

1. Introduction
2. Download
3. Usage
   1. Example
   2. How to Run Program (above)
4. Bindings
5. Technical details
6. Comparison of secret sharing libraries
7. Questions

Introduction

An example use case is a beer brewery which has a vault which contains their precious super secret recipe. The 5 board members of this brewery do not trust all the others well enough that they won't secretly break into the vault and sell the recipe to a competitor. So they split the code into 5 shares, and allow 4 shares to restore the original code. Now they are sure that the majority of the staff will know when the vault is opened, but they can still open the vault when one of the staff members is abroad or sick at home.

As often with crypto libraries, there is a lot of Shamir secret sharing code around that does not meet cryptographic standards (a.k.a. is insecure). Some details—like integrity checks and side-channel resistance—are often forgotten. But these slip-ups can often fully compromise the security of the scheme. With this in mind, I have made this library to:

• Be side channel resistant (timing, branch, cache)
• Secure the shared secret with a MAC
• Use the platform (OS) randomness source

It should be safe to use this library in "the real world". I currently regard the API as being stable. Should there be any breaking changes, then I will update the version number conforming to the semantic versioning spec.

Download

I have released version 0.1.0 of this library, which can be downloaded from the releases page. However, I actually recommend cloning the library with git, to also get the necesarry submodules:

git clone --recursive https://github.com/dsprenkels/sss.git

The current version is version 0.1.0, which should be stable enough for now. The functionality may still change before version 1.0.0, although I will still fix any security issues before that.

Usage

Secrets are provided as arrays of 64 bytes long. This should be big enough to store generally small secrets. If you wish to split larger chunks of data, you can use symmetric encryption and split the key instead. Shares are generated from secret data using sss_create_shares and shares can be combined again using the sss_combine_shares functions. The shares are octet strings of 113 bytes each.

This library is implemented in such a way that the maximum number of shares is 255.

Moreover, every share includes an ID, which is implemented as a counter. This ID is not considered a secret by the library, and an participants may be able to infer the amount of shares from these ids (for example, if I have a share with ID=3, I expect that ID∈{1,2} will also exist. If you require random share IDs, then you should generate 255 different shares, and randomly throw away the excess shares.

Example

#include "sss.h"
#include "randombytes.h"
#include <assert.h>
#include <string.h>

int main()
{
	uint8_t data[sss_MLEN], restored[sss_MLEN];
	sss_Share shares[5];
	size_t idx;
	int tmp;

	// Read a message to be shared
	strncpy(data, "Tyler Durden isn't real.", sizeof(data));

	// Split the secret into 5 shares (with a recombination theshold of 4)
	sss_create_shares(shares, data, 5, 4);

	// Combine some of the shares to restore the original secret
	tmp = sss_combine_shares(restored, shares, 4);
	assert(tmp == 0);
	assert(memcmp(restored, data, sss_MLEN) == 0);
}

How to Run program (above)

1. clone from git by bellow command. (As It is recommended. If you clone make sure that file under subdirectory also came with it)

git clone --recursive https://github.com/dsprenkels/sss.git

2. go inside sss directory and run make command

make

3. copy the example provided in readme as above and save it as demo.c

4. compile demo.c by running bellow commnad

gcc demo.c -o demo randombytes.o sss.o hazmat.o tweetnacl.o

5. execute program by bellow command

./demo

Bindings

I have currently written bindings for the following languages:

• Node.js (currently outdated, see sss-node/#11)
• Go
• Rust
• WASM
• Android¹
• Haskell¹
• Swift¹

¹ No releases yet.

There are also contributed bindings:

• Nim
• Erlang

Technical details

Shamir secret sharing works by generating a polynomial (e.g. 33x³ + 8x² + 29x + 42). The lowest term is the secret and is just filled in. All the other terms are generated randomly. Then we can pick points on the polynomial by filling in values for x. Each point is put in a share. Afterwards, with k points we can use interpolation to restore a k-degree polynomial.

In practice there is a wrapper around the secret-sharing part (this is done because of crypto-technical reasons). This wrapper uses the XSalsa20/Poly1305 authenticated encryption scheme. Because of this, the shares are always a little bit larger than the original data.

This library uses a custom randombytes function to generate a random encapsulation key, which talks directly to the operating system. When using the high level API, you are not allowed to choose your own key. It must be uniformly random, because regularities in shared secrets can be exploited.

With the low level API (hazmat.h) you can choose to secret-share a piece of data of exactly 32 bytes. This produces a set of shares that are much shorter than the high-level shares (namely 33 bytes each). However, keep in mind that this module is called hazmat.h (for "hazardous materials") for a reason. Please only use this if you really know what you are doing. Raw "textbook" Shamir secret sharing is only safe when using a uniformly random secret (with 128 bits of entropy). Note also that it is entirely insecure for integrity. Please do not use the low-level API unless you really have no other choice.

Comparison of secret-sharing libraries

If you would like your library to be added here, please open a pull request. :)

Notes

It is important to note that a limited secret length does not mean that it is impossible to share longer secrets. The way this is done is by secret sharing a random key and using this key to encrypt the real secret. This is a lot faster and the security is not reduced. (This is actually how sss-cli produces variable-length shares.)

1. Uses the GNU gmp library.
2. Uses lookup tables for GF(256) multiplication.
3. This library is implemented in a high level scripting library which does not guarantee that its basic operators execute in constant-time.
4. Uses randomized x-coordinates.
5. Uses randomized y-coordinates.
6. When using the snipsco library you will have to specify your own prime. Computation time is O(p²), so on a normal computer you will be limited to a secret size of ~1024 bytes.
7. As mentioned by the documentation.
8. Uses Java BigInteger class.
9. Basic usage of this tool does not protect the integrity of the secrets. However, the project's readme file advises the user to use a hybrid encryption scheme and secret share the key. Through destroying the ephemeral key, the example that is listed in the readme file protects prevents an attacker from arbitrarily inserting a secret. However, inserting a garbled secret is still possible. To prevent this the user should use a AEAD scheme (like AES-GCM or ChaCha20-Poly1305) instead of AES-CBC.

Questions

I do not know a lot about secret sharing. Is Shamir secret sharing useful for me?

It depends. In the case of threshold schemes (that's what this is) there are two types:

1. The share-holders cannot verify that their shares are valid.
2. The share-holders can verify that their shares are valid.

Shamir's scheme is of the first type. This immediately implies that the dealer could cheat. Indeed, they can distribute a number of shares which are just random strings. The only way the participants could know is by banding together and trying to restore the secret. This would show the secret, which would make the scheme totally pointless.

Use Shamir secret sharing only if the dealer and the participants have no reason to corrupt any shares.

Examples where this is not the case:

• When the secret hides something that is embarrasing for one of the participants.
• When the shared secret is something like a testament, and the participants are the heirs. If one of the heirs inherits more wealth when the secret is not disclosed, they can corrupt their share (and it would be impossible to check this from the share alone).

In these cases, you will need a scheme of the second type. See the next question.

Wait, I need verifiable shares! What should I use instead?

There are two straightforward options:

1. When the secret is fully random—for example, a cryptographic key—use Feldman verifiable secret sharing.
2. When the secret is not fully random—it could be a message, a number, etc.—use Pedersen verifiable secret sharing.

Other

For other questions, feel free to open an issue or send me an email on my Github associated e-mail address.