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https://github.com/dsprenkels/sss

Library for the Shamir secret sharing scheme
https://github.com/dsprenkels/sss

cryptography shamir-secret-sharing

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Library for the Shamir secret sharing scheme

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README 

        
# Shamir secret sharing library



[![Build Status](https://travis-ci.org/dsprenkels/sss.svg?branch=master)](https://travis-ci.org/dsprenkels/sss)



`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][sss-cli]. ([web demo])



[sss-cli]: https://github.com/dsprenkels/sss-cli



## Table of contents



1. [Introduction](#introduction)

2. [Download](#download)

3. [Usage](#usage)

	1. [Example](#example)

  	2. [How to Run Program (above)](#How-to-Run-program-(above))

4. [Bindings](#bindings)

5. [Technical details](#technical-details)

6. [Comparison of secret sharing libraries](#comparison-of-secret-sharing-libraries)

7. [Questions](#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][semver].



[semver]: http://semver.org/



## Download



I have released version 0.1.0 of this library, which can be downloaded from

the [releases](https://github.com/dsprenkels/sss/releases) page. However, I

actually recommend cloning the library with git, to also get the necesarry

submodules:



```shell

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



```c

#include "sss.h"

#include "randombytes.h"

#include 

#include 



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)

```shell

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

```



2. go inside sss directory and run make command

```shell

make

```



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



4. compile demo.c by running bellow commnad

```shell

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

```



5. execute program by bellow command

```shell

./demo

```



## Bindings



I have currently written bindings for the following languages:



- [Node.js](https://github.com/dsprenkels/sss-node)

- [Go](https://github.com/dsprenkels/sss-go)

- [Rust](https://github.com/dsprenkels/sss-rs)

- [WASM](https://github.com/3box/sss-wasm)

- [Android](https://github.com/dsprenkels/sss-android)¹

- [Haskell](https://github.com/dsprenkels/sss-hs)¹

- [Swift](https://github.com/dsprenkels/sss-swift)¹

> ¹ No releases yet.



There are also contributed bindings:



- [Nim](https://github.com/markspanbroek/sss.nim)

- [Erlang](https://github.com/arekinath/esss)



## 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`][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. :)



| Library         | Side-channels | Tamper-resistant | Secret length |

|-----------------|---------------|------------------|---------------|

| [B. Poettering] | Insecure¹     | Insecure         | 128 bytes     |

| [libgfshare]    | Insecure²     | Insecure         | ∞             |

| [blockstack]    | ??³           | Insecure         | 160 bytes     |

| [sssa-golang]   | Secure        | Secure⁴          | ∞             |

| [sssa-ruby]     | ??³           | Secure⁴          | ∞             |

| [snipsco]       | Secure        | Insecure         | Note⁶         |

| [c-sss]         | Insecure⁷     | Insecure         | ∞             |

| [timtiemens]    | Insecure⁸     | Note⁹            | 512 bytes     |

| [dsprenkels]    | Secure        | Secure⁵          | 64 bytes      |



### 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](https://github.com/fletcher/c-sss#security-issues).

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.



[B. Poettering]: http://point-at-infinity.org/ssss/

[libgfshare]: https://github.com/jcushman/libgfshare

[blockstack]: https://github.com/blockstack/secret-sharing

[sssa-golang]: https://github.com/SSSaaS/sssa-golang

[sssa-ruby]: https://github.com/SSSaaS/sssa-ruby

[snipsco]: https://github.com/snipsco/rust-threshold-secret-sharing

[c-sss]: https://github.com/fletcher/c-sss

[timtiemens]: https://github.com/timtiemens/secretshare

[dsprenkels]: https://github.com/dsprenkels/sss



## 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.



[web demo]: http://bakaoh.com/sss-wasm/

[randombytes]: https://github.com/dsprenkels/randombytes