From 5aaa3e7361c17cad0ce3887422ceb7df7ade9d64 Mon Sep 17 00:00:00 2001
From: "Ethan L. Miller" <elm@ucsc.edu>
Date: Wed, 2 Sep 2020 16:29:38 -0700
Subject: [PATCH] gfalg generates and recovers a secret via Shamir Secret
 Sharing!

---
 gfalg.py | 85 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)

diff --git a/gfalg.py b/gfalg.py
index e69de29..d741ca8 100644
--- a/gfalg.py
+++ b/gfalg.py
@@ -0,0 +1,85 @@
+#!/usr/bin/env python3
+
+import sys
+import secrets
+from galois import GaloisNumber as GN
+import galois
+from collections import namedtuple
+
+gf = galois.GaloisFieldLog (8)
+
+def _gf_unpack (v):
+    return tuple(GN(b, gf) for b in v)
+def _gf_pack (v):
+    return b''.join ([b.to_bytes() for b in v])
+
+class Secret:
+    value_len = 32
+    def __init__ (self, value = None):
+        if not value:
+            self.value = secrets.token_bytes (Secret.value_len)
+        elif type(value) == str:
+            self.value = bytes.fromhex (value)
+        elif type(value) == bytes:
+            self.value = value
+        else:
+            raise ValueError("Secret must be bytes or hex string")
+        if len (self.value) != Secret.value_len:
+            raise ValueError("Secret must be exactly {0} bytes long".format (Secret.value_len))
+    def __str__ (self):
+        return self.value.hex ()
+    def __repr__ (self):
+        return str(self)
+    def __len__ (self):
+        return len (self.value)
+
+class SSS_Share:
+    def __init__ (self, share_id, secret):
+        if not 0 < share_id < 254:
+            raise ValueError("Invalid share ID")
+        if type(secret) != Secret:
+            raise ValueError ("Invalid secret")
+        self.share_id = share_id
+        self.secret = secret
+    def __str__ (self):
+        return 'ID {0:2}: {1}'.format (self.share_id, self.secret)
+    def __repr__ (self):
+        return str(self)
+
+def _lagrange_interpolate (x, shares):
+    pass
+
+def sss_generate_shares (secret, min_shares, share_ids):
+    if any ([not 1 <= x <= 254 for x in share_ids]):
+        raise ValueError ("Share IDs must be between 1-254")
+    coeff = list()
+    coeff.append (_gf_unpack (secret.value))
+    for i in range (0, min_shares-1):
+        coeff.append (_gf_unpack (Secret().value))
+    shares = list()
+    for i in share_ids:
+        v = GN(i, gf)
+        m = GN(1, gf)
+        accum = [GN(0, gf)] * len (secret)
+        for a in coeff:
+            accum = m.mul_region (a, accum)
+            m *= v
+        shares.append (SSS_Share(i, Secret (_gf_pack(accum))))
+    return shares
+
+
+def sss_recover_secret (shares):
+    shrs = tuple (_gf_unpack (s.secret.value) for s in shares)
+    ids = tuple (GN(x.share_id, gf) for x in shares)
+    accum = [GN(0, gf)] * len(shares[0].secret)
+    for (x, shr) in zip (ids, shrs):
+        prod = GN(1, gf)
+        for i in ids:
+            if i != x:
+                prod *= i / (i - x)
+        accum = prod.mul_region (shr, accum)
+    return Secret (_gf_pack (accum))
+
+def sss_generate_new_share (shares, share_id):
+    pass
+