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tss.py
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tss.py
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"""
Threshold Secret Sharing (Shamir's secret sharing scheme)
http://tools.ietf.org/html/draft-mcgrew-tss-03
Example:
import tss
# Create 8 shares of the secret recoverable from at least 5
# differents shares. Use secretid42 as identifier and hash the
# secret with sha256.
shares = tss.share_secret(5, 8, 'my shared secret', 'secretid42',
tss.Hash.SHA256)
try:
# Recover the secret value
secret = tss.reconstruct_secret(shares)
except tss.TSSError:
pass # Handling error
Notes:
- Operations are _not_ constant-time, and are quite verbose too
- This implementation doesn't provide ECC encoding/decoding
"""
import hashlib
import itertools
import os
import struct
import sys
__author__ = 'Sebastien Martini ([email protected])'
__version__ = '0.1'
__license__ = 'MIT'
__all__ = ['share_secret', 'reconstruct_secret', 'Hash', 'TSSError']
# Compatibility
if sys.version_info < (3, 0):
b = lambda x: x
byte_to_chr = lambda x: x
byte_to_ord = lambda x: ord(x)
basestring = basestring
unicode = unicode
bytes = str
digest_size = lambda d: d.digestsize
else:
b = lambda x: x.encode('iso8859-1')
byte_to_chr = lambda x: chr(x)
byte_to_ord = lambda x: x
basestring = str
unicode = str
bytes = bytes
digest_size = lambda d: d.digest_size
def encode(value, encoding='utf-8', encoding_errors='strict'):
"""
Return a bytestring representation of the value.
"""
if isinstance(value, bytes):
return value
if not isinstance(value, basestring):
value = str(value)
if isinstance(value, unicode):
value = value.encode(encoding, encoding_errors)
return value
# GF(256) arithmetic
EXP = [0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff,
0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35,
0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4,
0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa,
0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26,
0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31,
0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc,
0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd,
0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7,
0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88,
0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f,
0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a,
0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0,
0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3,
0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec,
0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0,
0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2,
0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41,
0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0,
0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75,
0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e,
0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80,
0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf,
0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54,
0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09,
0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca,
0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91,
0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e,
0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c,
0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17,
0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd,
0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6, 0x00]
LOG = [ 0, 0, 25, 1, 50, 2, 26, 198,
75, 199, 27, 104, 51, 238, 223, 3,
100, 4, 224, 14, 52, 141, 129, 239,
76, 113, 8, 200, 248, 105, 28, 193,
125, 194, 29, 181, 249, 185, 39, 106,
77, 228, 166, 114, 154, 201, 9, 120,
101, 47, 138, 5, 33, 15, 225, 36,
18, 240, 130, 69, 53, 147, 218, 142,
150, 143, 219, 189, 54, 208, 206, 148,
19, 92, 210, 241, 64, 70, 131, 56,
102, 221, 253, 48, 191, 6, 139, 98,
179, 37, 226, 152, 34, 136, 145, 16,
126, 110, 72, 195, 163, 182, 30, 66,
58, 107, 40, 84, 250, 133, 61, 186,
43, 121, 10, 21, 155, 159, 94, 202,
78, 212, 172, 229, 243, 115, 167, 87,
175, 88, 168, 80, 244, 234, 214, 116,
79, 174, 233, 213, 231, 230, 173, 232,
44, 215, 117, 122, 235, 22, 11, 245,
89, 203, 95, 176, 156, 169, 81, 160,
127, 12, 246, 111, 23, 196, 73, 236,
216, 67, 31, 45, 164, 118, 123, 183,
204, 187, 62, 90, 251, 96, 177, 134,
59, 82, 161, 108, 170, 85, 41, 157,
151, 178, 135, 144, 97, 190, 220, 252,
188, 149, 207, 205, 55, 63, 91, 209,
83, 57, 132, 60, 65, 162, 109, 71,
20, 42, 158, 93, 86, 242, 211, 171,
68, 17, 146, 217, 35, 32, 46, 137,
180, 124, 184, 38, 119, 153, 227, 165,
103, 74, 237, 222, 197, 49, 254, 24,
13, 99, 140, 128, 192, 247, 112, 7]
def gf256_add(a, b):
return a ^ b
def gf256_sub(a, b):
return gf256_add(a, b)
def gf256_mul(a, b):
if a == 0 or b == 0:
return 0
return EXP[(LOG[a] + LOG[b]) % 255]
def gf256_div(a, b):
if a == 0:
return 0
if b == 0:
raise ZeroDivisionError
return EXP[(LOG[a] - LOG[b]) % 255]
# TSS error
class TSSError(Exception):
pass
# Hash
class Hash(object):
NONE = 0
SHA1 = 1
SHA256 = 2
@staticmethod
def to_func(hash_id):
if hash_id == 1:
return hashlib.sha1
if hash_id == 2:
return hashlib.sha256
raise TSSError('invalid hash algorithm %d' % hash_id)
@staticmethod
def is_valid(hash_id):
return 0 <= hash_id <= 2
# Share generation
def f(x, coefs_bytes):
if x == 0:
raise TSSError('invalid share index value, cannot be 0')
y = 0
x_i = 1
for c in coefs_bytes:
y = gf256_add(y, gf256_mul(byte_to_ord(c), x_i))
x_i = gf256_mul(x_i, x)
return y
def generate_shares(m, n, secret):
if len(secret) > (2**16 - 2) or m < 1 or m > 254 or n < m or n > 254:
raise TSSError('invalid share parameter')
shares = []
for i in range(1, n + 1):
share = bytearray()
share.append(i)
shares.append(share)
for secret_byte in secret:
r = os.urandom(m - 1)
for i in range(n):
shares[i].append(f(shares[i][0],
b(byte_to_chr(secret_byte)) + r))
return [bytes(share) for share in shares]
def format_header(identifier, hash_id, threshold, share_len):
return struct.pack('>16sBBH', identifier, hash_id, threshold, share_len)
def format_share(header, share):
return header[:] + share
def share_secret(threshold, nshares, secret, identifier, hash_id=Hash.SHA256):
"""
Create nshares of the secret. threshold specifies the number of shares
needed for reconstructing the secret value. A 0-16 bytes identifier must
be provided. Optionally the secret is hashed with the algorithm specified
by hash_id, a class attribute of Hash.
This function must return a list of formatted shares or raises a TSSError
exception if anything went wrong.
"""
if identifier is None:
raise TSSError('an identifier must be provided')
if not Hash.is_valid(hash_id):
raise TSSError('invalid hash algorithm %s' % hash_id)
secret = encode(secret)
identifier = encode(identifier)
if hash_id != Hash.NONE:
secret += Hash.to_func(hash_id)(secret).digest()
shares = generate_shares(threshold, nshares, secret)
header = format_header(identifier, hash_id, threshold, len(secret) + 1)
return [format_share(header, share) for share in shares]
# Secret reconstruction
def basis_poly(i, u):
prod = 1
for j in range(len(u)):
if i == j:
continue
prod = gf256_mul(prod, gf256_div(u[j], gf256_add(u[j], u[i])))
return prod
def lagrange_interpolation(u, v):
sum = 0
for i in range(len(v)):
sum = gf256_add(sum, gf256_mul(basis_poly(i, u), v[i]))
return sum
def parse_header(share):
return struct.unpack('>16sBBH', share)
def reconstruct_secret(shares, strict_mode=True):
"""
shares must be a container with a sufficient number of well-formatted
shares used to reconstruct the secret value. If any share format is
invalid a TSSError exception is raised.
If strict_mode is False all combinations of shares are tried in order
to reconstruct the secret. Otherwise this function raises an exception
TSSError on the first error encountered (either a duplicate share was
detected or the provided hash value didn't match the one computed from
the recovered secret).
This function must return the secret value or raise TSSError.
"""
ref_header = None
data_shares = []
for share in shares:
share = encode(share)
if len(share) < 20:
raise TSSError('share format invalid')
header = parse_header(share[:20])
if ref_header is None:
ref_header = header
if header[2] > len(shares):
raise TSSError('not enough shares for reconstructing secret')
if ref_header != header:
raise TSSError('invalid share headers %s' % header)
data_share = share[20:]
if len(data_share) != header[3]:
raise TSSError('invalid share data size %d (expected %d)' % \
(len(data_share), header[3]))
data_shares.append(data_share)
for combination in itertools.combinations(data_shares, ref_header[2]):
secret = bytearray()
u = [byte_to_ord(share[0]) for share in combination]
if len(dict().fromkeys(u)) != len(u):
if strict_mode:
raise TSSError('invalid share with duplicate index')
else:
continue
for i in range(1, ref_header[3]):
v = [byte_to_ord(share[i]) for share in combination]
secret.append(lagrange_interpolation(u, v))
secret = bytes(secret)
if ref_header[1] != Hash.NONE:
d = Hash.to_func(ref_header[1])()
digestsize = digest_size(d)
d.update(secret[:-digestsize])
if len(secret) < digestsize or d.digest() != secret[-digestsize:]:
if strict_mode:
raise TSSError('hash values mismatch')
else:
continue
return secret[:-digestsize]
return secret
raise TSSError('not enough valid shares for reconstructing the secret')