shamir

README

Shamir Secret Sharing

This is a practical example of Shamir's secret sharing.

This tool allows you to divide up a secret string S into n shares where any k of the shares will allow you to reconstruct the original secret S. If you have fewer than k of the shares, you will have no information (other than the length of the secret) about what that secret is.

Usage

To distribute the secrets, use the command

shamir distribute -S "<secret>" -n <number of shares to produce> -k <minimum number of shares to reconstruct the secret> -d "<output directory>"

The shares will be saved as text files in the specified output directory. The default directory is the current directory.

Way we run shamir distribute -S="This is a super secret secret." -n=5 -k=3. Five text files will be saved in the current directory, each containing a share of the secret. The first file might be called shamir-IW6CPGV5COQ6FHMI-11d-1.txt, and it contains the text

shamir-IW6CPGV5COQ6FHMI-11d-1-IyJneCEokIwf319Sl+sqeuLtBLwqWMxyd/m5Hj/U

The prefix shamir- indicates that this is a share in Shamir's secret sharing scheme. IW6CPGV5COQ6FHMI is a randomly generated ID that allows you to correlate secrets and shares. 11d is the primitive polynomial used to construct the underlying Galois field. 1 is the x coordinate of the share. The remaining text is base64-encoded data. Each byte corresponds to the value of a polynomial evaulated at the corresponding x-coordinate of the share. (Note that each byte is encoded separately, each with a randomly-generated polynomial.)

To reconstruct the message, simply run shamir reconstruct in the same directory you ran shamir distribute command. This will check any text files with the .txt file extension for shares.

Say we have the following text files:

shamir-IW6CPGV5COQ6FHMI-11d-1-IyJneCEokIwf319Sl+sqeuLtBLwqWMxyd/m5Hj/U
shamir-IW6CPGV5COQ6FHMI-11d-4-lKF0rNRgjQGXKJ0gbfKDMompvM6KGtAPw5TGAUGc
shamir-IW6CPGV5COQ6FHMI-11d-5-4+t6p9Uhbq3p17EHinzbaBgh2wDFNjwO0Q4Negpm

We then run the command shamir reconstruct, and we see that the secret is successfully reconstructed and printed to the console:

IW6CPGV5COQ6FHMI: This is a super secret secret.

If we try to only use shares 4 and 5, we cannot reconstruct the message, and we get gibberish:

IW6CPGV5COQ6FHMI: U�L��y&�r�-����G��=ѫ�G
����pS

Note that the file names themselves do not matter. All of the information needed to reconstruct them is provided in the file itself.

Documentation

Overview

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