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A Merkle tree that pairs an odd last node with itself gives the same root for a list and that list with its last leaf duplicated: commit the leaf count or promote the odd node · id PC-227
· checked_on 2026-11-12
· license CC-BY-4.0
1) Commit the leaf count into the root or the signed manifest, or 2) do not pair an odd node with itself: RFC 6962 splits at the largest power of two smaller than n (and uses distinct 0x00 / 0x01 prefixes for leaf and inner hashes), so the two lists no longer share a root. 3) Check: compute the root for N leaves (N odd), then for the same N leaves plus a copy of the last leaf; the two roots must differ.
#!/usr/bin/env python3
"""merkle_odd.py — do not pair an odd last node with itself; commit the leaf count or promote.
usage: python3 -I merkle_odd.py --selftest
hash(x||x) on an odd last node gives the same root for [a,b,c] and [a,b,c,c].
RFC 6962 splits at the largest power of two instead, so the roots differ, as they
do when the leaf count is committed. This selftest uses fixture leaves (no network).
Exit 0: pass. Exit 1: unexpected result. Exit 2: usage.
"""
from __future__ import annotations
import hashlib
import sys
def sha(b: bytes) -> bytes:
return hashlib.sha256(b).digest()
def naive(leaves):
nodes = [sha(b"\x00" + x) for x in leaves]
while len(nodes) > 1:
if len(nodes) % 2 == 1:
nodes.append(nodes[-1])
nxt = []
for i in range(0, len(nodes), 2):
nxt.append(sha(b"\x01" + nodes[i] + nodes[i + 1]))
nodes = nxt
return nodes[0]
def rfc6962(leaves):
def mth(items):
n = len(items)
if n == 1:
return sha(b"\x00" + items[0])
k = 1
while k * 2 < n:
k *= 2
return sha(b"\x01" + mth(items[:k]) + mth(items[k:]))
return mth(leaves)
def with_count(leaves):
return sha(rfc6962(leaves) + str(len(leaves)).encode())
def selftest() -> None:
abc = [b"a", b"b", b"c"]
abcc = [b"a", b"b", b"c", b"c"]
assert naive(abc) == naive(abcc)
assert rfc6962(abc) != rfc6962(abcc)
assert with_count(abc) != with_count(abcc)
def main(argv=None) -> int:
argv = sys.argv[1:] if argv is None else argv
if argv == ["--selftest"]:
try:
selftest()
except AssertionError as e:
print("unexpected result", e)
return 1
print("pass")
return 0
print(__doc__.strip(), file=sys.stderr)
return 2
if __name__ == "__main__":
sys.exit(main())
Merkle rootCVE-2012-2459A manifest or batch is attested by a Merkle root; a verifier checks leaves against the root and accepts a list that contains one artifact twice, because both lists hash to the same root.
The roots of [a,b,c] and [a,b,c,c] are identical, so a duplicated last leaf still verifies.
On a level with an odd number of nodes the implementation duplicates the last node (hash(x||x)). Known from Bitcoin CVE-2012-2459.
Save the snippet as merkle_odd.py and run `python3 -I merkle_odd.py --selftest` (fixture leaves, no network). Pass: last line is `pass` and the exit code is 0. The naive hash(x||x) tree gives the same root for [a,b,c] and [a,b,c,c]; the RFC 6962 split and a root that commits the leaf count both differ. Without arguments the script prints usage and exits 2. Checked 2026-11-12 with Python 3.13.5: selftest pass, usage exit 2. The leaves are fixtures, not a live manifest.
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