# Shamira #

Implements Shamir's secret sharing algorithm. Splits a string or a byte sequence byte-per-byte into _n_<255 shares, with any _k_ of them sufficient for reconstruction of the original input.

Outputs the shares as hexadecimal, Base32 or Base64 encoded strings.

Can be used on its own from the command line by invoking `shamira.py` or as a library by importing `shamira.py`.

## Performance ##

As it is, the code is not very fast. Splitting takes _n_ evaluations of a polynomial of order _k_ over Galois field 256, leading to _O(n*k)_ finite field multiplications. Reconstruction of the constant parameters during joining similarly takes _O(k*k)_ multiplications.

Benchmark results, all values mean _seconds per byte_ of the secret length:
<table>
    <tr>
        <th>k / n parameters</th>
        <th>Split</th>
        <th>Join</th>
    </tr>
    <tr>
        <td>2 / 3 (a Raspberry Pi 3)</td>
        <td>7.99e-05</td>
        <td>0.000428</td>
    </tr>
    <tr>
        <td>2 / 3 (a laptop)</td>
        <td>1e-05</td>
        <td>6.7e-05</td>
    </tr>
    <tr>
        <td>254 / 254 (a Raspberry Pi 3)</td>
        <td>0.417</td>
        <td>0.471</td>
    </tr>
    <tr>
        <td>254 / 254 (a laptop)</td>
        <td>0.0431</td>
        <td>0.0542</td>
    </tr>
</table>

While the speeds are not awful, for longer secrets I recommend encrypting them with a random key of your choice and splitting only the key. Anyway, you can run your own benchmark with `benchmark.py`