From ce2b670511b1f526b29b549f38c8eceaed2c777d Mon Sep 17 00:00:00 2001
From: John-Mark Gurney <jmg@funkthat.com>
Date: Tue, 30 May 2023 01:31:25 -0700
Subject: [PATCH] add/improve docs, more exhaustive testing of combinations.

---
 shamirss.py | 42 +++++++++++++++++++++++++++++++++++++-----
 1 file changed, 37 insertions(+), 5 deletions(-)

diff --git a/shamirss.py b/shamirss.py
index a6e1901..076b681 100644
--- a/shamirss.py
+++ b/shamirss.py
@@ -26,7 +26,27 @@
 # ls shamirss.py | entr sh -c ' date; python -m coverage run -m unittest shamirss && coverage report -m'
 #
 
+'''
+An implementation of Shamir's Secret Sharing.
+
+This is over GF(2^256), so unlike some other implementations that are
+over primes, it is valid for ALL values, and the output will be exactly
+the same size as the secret.  This also limits the number of shared to
+255.
+
+Sample usage:
+```
+import random
+from shamirss import *
+data = random.SystemRandom().randbytes(32)
+shares = create_shares(data, 3, 5)
+rdata = recover_data([ shares[1], shares[2], shares[4] ], 3)
+print(rdata == data)
+```
+'''
+
 import functools
+import itertools
 import operator
 import secrets
 import unittest.mock
@@ -63,10 +83,11 @@ def create_shares(data, k, nshares):
 	'''Given data, create nshares, such that given any k shares,
 	data can be recovered.
 
-	data must be bytes, or able to be converted to bytes.
+	data must be bytes, or able to be converted to bytes, e.g. a list
+	of ints in the range [ 0, 255 ].
 
 	The return value will be a list of length nshares.  Each element
-	will be a tuple of (<int in range [1, nshares + 1)>, <bytes>).'''
+	will be a tuple of (<int in range [ 1, nshares ]>, <bytes>).'''
 
 	data = bytes(data)
 
@@ -83,9 +104,13 @@ def create_shares(data, k, nshares):
 	    range(1, nshares + 1) ]
 
 def recover_data(shares, k):
-	'''Recover the value given shares, where k is needed.
+	'''Recover the value given shares, where k is the number of
+	shares needed.
+
+	shares must be as least length of k.
 
-	shares must be as least length of k.'''
+	Each element of shares is from one returned by create_shares,
+	that is a tuple of an int and bytes.'''
 
 	if len(shares) < k:
 		raise ValueError('not enough shares to recover')
@@ -234,7 +259,14 @@ class TestShamirSS(unittest.TestCase):
 		# that one share isn't enough
 		self.assertRaises(ValueError, recover_data, [ a[0] ], 2)
 
-		self.assertEqual(val, recover_data(a[:2], 2))
+		for i, j in itertools.combinations(range(3), 2):
+			self.assertEqual(val, recover_data([ a[i], a[j] ], 2))
+			self.assertEqual(val, recover_data([ a[j], a[i] ], 2))
+
+		a = create_shares(val, 15, 30)
+
+		for i in range(5):
+			self.assertEqual(val, recover_data([ a[j] for j in random.sample(range(30), 15) ], 15))
 
 	def test_gf2p8_inv(self):