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.

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`

from argparse import ArgumentParser

import cProfile

import timeit

from shamira import generate, reconstruct

from tests.test_shamira import TestShamira

def measure(args):

	secret = "1234567890123456"

	shares = generate(secret, args.k, args.n)

	symbols = globals()

	symbols.update(locals())

	time = timeit.timeit("""generate(secret, args.k, args.n)""", number=1, globals=symbols)

	print("The generation took {0:.3}s, {1:.3} per byte.".format(time, time/16))

	time = timeit.timeit("""reconstruct(*shares)""", number=1, globals=symbols)

	print("The reconstruction took {0:.3}s, {1:.3} per byte.".format(time, time/16))

def profile(args):

	t = TestShamira()

	cProfile.runctx(r"""t.test_generate_reconstruct()""", globals=globals(), locals=locals())

parser = ArgumentParser()

parser.set_defaults(func=lambda _: parser.error("missing command"))

subparsers = parser.add_subparsers()

profile_parser = subparsers.add_parser("profile")

profile_parser.set_defaults(func=profile)

measure_parser = subparsers.add_parser("measure")

measure_parser.add_argument("-k", type=int, required=True)

measure_parser.add_argument("-n", type=int, required=True)

measure_parser.set_defaults(func=measure)

args = parser.parse_args()

args.func(args)