From 9b1b32f9d5b87a69cb00283500884521f66d6626 Mon Sep 17 00:00:00 2001
From: kaxxa123 <axzammit@hotmail.com>
Date: Wed, 11 Sep 2024 15:02:43 +0200
Subject: [PATCH] research: sparse merkle tree optimizations proposed by
 vitalik

---
 vitalik_merkle_optimizations/.gitignore       | 162 ++++++++++++++++++
 vitalik_merkle_optimizations/bintrie_test.py  |  45 +++++
 vitalik_merkle_optimizations/new_bintrie.py   | 125 ++++++++++++++
 .../new_bintrie_hex.py                        | 125 ++++++++++++++
 .../new_bintrie_optimized.py                  | 126 ++++++++++++++
 .../new_bintrie_test.py                       |  27 +++
 6 files changed, 610 insertions(+)
 create mode 100644 vitalik_merkle_optimizations/.gitignore
 create mode 100644 vitalik_merkle_optimizations/bintrie_test.py
 create mode 100644 vitalik_merkle_optimizations/new_bintrie.py
 create mode 100644 vitalik_merkle_optimizations/new_bintrie_hex.py
 create mode 100644 vitalik_merkle_optimizations/new_bintrie_optimized.py
 create mode 100644 vitalik_merkle_optimizations/new_bintrie_test.py

diff --git a/vitalik_merkle_optimizations/.gitignore b/vitalik_merkle_optimizations/.gitignore
new file mode 100644
index 0000000..efa407c
--- /dev/null
+++ b/vitalik_merkle_optimizations/.gitignore
@@ -0,0 +1,162 @@
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+.pybuilder/
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# poetry
+#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
+#   This is especially recommended for binary packages to ensure reproducibility, and is more
+#   commonly ignored for libraries.
+#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
+#poetry.lock
+
+# pdm
+#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
+#pdm.lock
+#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
+#   in version control.
+#   https://pdm.fming.dev/latest/usage/project/#working-with-version-control
+.pdm.toml
+.pdm-python
+.pdm-build/
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+
+# PyCharm
+#  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
+#  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
+#  and can be added to the global gitignore or merged into this file.  For a more nuclear
+#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
+#.idea/
\ No newline at end of file
diff --git a/vitalik_merkle_optimizations/bintrie_test.py b/vitalik_merkle_optimizations/bintrie_test.py
new file mode 100644
index 0000000..e0c2460
--- /dev/null
+++ b/vitalik_merkle_optimizations/bintrie_test.py
@@ -0,0 +1,45 @@
+import new_bintrie as t1
+import new_bintrie_optimized as t2
+import new_bintrie_hex as t3
+import time
+import binascii
+
+keys = [t1.sha3(bytes([i // 256, i % 256])) for i in range(10000)]
+
+d = t1.EphemDB()
+r = t1.new_tree(d)
+a = time.time()
+for k in keys[:1000]:
+    r = t1.update(d, r, k, k)
+print("Naive bintree time to update: %.4f" % (time.time() - a))
+print("Root: %s" % binascii.hexlify(r))
+
+d = t2.EphemDB()
+r = t2.new_tree(d)
+a = time.time()
+for k in keys[:1000]:
+    r = t2.update(d, r, k, k)
+print("DB-optimized bintree time to update: %.4f" % (time.time() - a))
+print("Root: %s" % binascii.hexlify(r))
+print("Writes: %d, reads: %d" % (d.writes, d.reads))
+d.reads = 0
+for k in keys[:500]:
+    assert t2.get(d, r, k) == k
+for k in keys[-500:]:
+    assert t2.get(d, r, k) == b'\x00' * 32
+print("Reads: %d" % d.reads)
+
+d = t3.EphemDB()
+r = t3.new_tree(d)
+a = time.time()
+for k in keys[:1000]:
+    r = t3.update(d, r, k, k)
+print("DB-optimized bintree time to update: %.4f" % (time.time() - a))
+print("Root: %s" % binascii.hexlify(r))
+print("Writes: %d, reads: %d" % (d.writes, d.reads))
+d.reads = 0
+for k in keys[:500]:
+    assert t3.get(d, r, k) == k
+for k in keys[-500:]:
+    assert t3.get(d, r, k) == b'\x00' * 32
+print("Reads: %d" % d.reads)
diff --git a/vitalik_merkle_optimizations/new_bintrie.py b/vitalik_merkle_optimizations/new_bintrie.py
new file mode 100644
index 0000000..a12c4c5
--- /dev/null
+++ b/vitalik_merkle_optimizations/new_bintrie.py
@@ -0,0 +1,125 @@
+from ethereum.utils import sha3, encode_hex
+
+class EphemDB():
+    def __init__(self, kv=None):
+        self.kv = kv or {}
+
+    def get(self, k):
+        return self.kv.get(k, None)
+
+    def put(self, k, v):
+        self.kv[k] = v
+
+    def delete(self, k):
+        del self.kv[k]
+
+zerohashes = [b'\x00' * 32]
+for i in range(256):
+    zerohashes.insert(0, sha3(zerohashes[0] + zerohashes[0]))
+
+def new_tree(db):
+    h = b'\x00' * 32
+    for i in range(256):
+        newh = sha3(h + h)
+        db.put(newh, h + h)
+        h = newh
+    return h
+
+def key_to_path(k):
+    o = 0
+    for c in k:
+        o = (o << 8) + c
+    return o
+
+def descend(db, root, *path):
+    v = root
+    for p in path:
+        if p:
+            v = db.get(v)[32:]
+        else:
+            v = db.get(v)[:32]
+    return v
+
+def get(db, root, key):
+    v = root
+    path = key_to_path(key)
+    for i in range(256):
+        if (path >> 255) & 1:
+            v = db.get(v)[32:]
+        else:
+            v = db.get(v)[:32]
+        path <<= 1
+    return v
+
+def update(db, root, key, value):
+    v = root
+    path = path2 = key_to_path(key)
+    sidenodes = []
+    for i in range(256):
+        if (path >> 255) & 1:
+            sidenodes.append(db.get(v)[:32])
+            v = db.get(v)[32:]
+        else:
+            sidenodes.append(db.get(v)[32:])
+            v = db.get(v)[:32]
+        path <<= 1
+    v = value
+    for i in range(256):
+        if (path2 & 1):
+            newv = sha3(sidenodes[-1] + v)
+            db.put(newv, sidenodes[-1] + v)
+        else:
+            newv = sha3(v + sidenodes[-1])
+            db.put(newv, v + sidenodes[-1])
+        path2 >>= 1
+        v = newv
+        sidenodes.pop()
+    return v
+
+def make_merkle_proof(db, root, key):
+    v = root
+    path = key_to_path(key)
+    sidenodes = []
+    for i in range(256):
+        if (path >> 255) & 1:
+            sidenodes.append(db.get(v)[:32])
+            v = db.get(v)[32:]
+        else:
+            sidenodes.append(db.get(v)[32:])
+            v = db.get(v)[:32]
+        path <<= 1
+    return sidenodes
+
+def verify_proof(proof, root, key, value):
+    path = key_to_path(key)
+    v = value
+    for i in range(256):
+        if (path & 1):
+            newv = sha3(proof[-1-i] + v)
+        else:
+            newv = sha3(v + proof[-1-i])
+        path >>= 1
+        v = newv
+    return root == v
+
+def compress_proof(proof):
+    bits = bytearray(32)
+    oproof = b''
+    for i, p in enumerate(proof):
+        if p == zerohashes[i+1]:
+            bits[i // 8] ^= 1 << i % 8
+        else:
+            oproof += p
+    return bytes(bits) + oproof
+
+def decompress_proof(oproof):
+    proof = []
+    bits = bytearray(oproof[:32])
+    pos = 32
+    for i in range(256):
+        if bits[i // 8] & (1 << (i % 8)):
+            proof.append(zerohashes[i+1])
+        else:
+            proof.append(oproof[pos: pos + 32])
+            pos += 32
+    return proof
diff --git a/vitalik_merkle_optimizations/new_bintrie_hex.py b/vitalik_merkle_optimizations/new_bintrie_hex.py
new file mode 100644
index 0000000..354e0cb
--- /dev/null
+++ b/vitalik_merkle_optimizations/new_bintrie_hex.py
@@ -0,0 +1,125 @@
+from ethereum.utils import sha3, encode_hex
+
+class EphemDB():
+    def __init__(self, kv=None):
+        self.reads = 0
+        self.writes = 0
+        self.kv = kv or {}
+
+    def get(self, k):
+        self.reads += 1
+        return self.kv.get(k, None)
+
+    def put(self, k, v):
+        self.writes += 1
+        self.kv[k] = v
+
+    def delete(self, k):
+        del self.kv[k]
+
+# Hashes of empty subtrees
+zerohashes = [b'\x00' * 32]
+for i in range(256):
+    zerohashes.insert(0, sha3(zerohashes[0] + zerohashes[0]))
+
+# Create a new empty tree
+def new_tree(db):
+    return zerohashes[0]
+
+# Convert a binary key into an integer path value
+def key_to_path(k):
+    return int.from_bytes(k, 'big')
+
+tt256m1 = 2**256 - 1
+
+# And convert back
+def path_to_key(k):
+    return (k & tt256m1).to_bytes(32, 'big')
+
+# Read a key from a given tree
+def get(db, root, key):
+    v = root
+    path = key_to_path(key)
+    for i in range(0, 256, 4):
+        if v == zerohashes[i]:
+            return b'\x00' * 32
+        child = db.get(v)
+        if len(child) == 65:
+            if (path % 2**256) == key_to_path(child[1:33]):
+                return child[33:]
+            else:
+                return b'\x00' * 32
+        else:
+            index = (path >> 252) & 15
+            v = child[32*index: 32*index+32]
+        path <<= 4
+    return v
+
+# Make a root hash of a (sub)tree with a single key/value pair
+def make_single_key_hash(path, depth, value):
+    if depth == 256:
+        return value
+    elif (path >> 255) & 1:
+        return sha3(zerohashes[depth+1] + make_single_key_hash(path << 1, depth + 1, value))
+    else:
+        return sha3(make_single_key_hash(path << 1, depth + 1, value) + zerohashes[depth+1])
+
+# Hash together 16 elements
+def hash_16_els(vals):
+    assert len(vals) == 16
+    for _ in range(4):
+        vals = [sha3(vals[i] + vals[i+1]) for i in range(0, len(vals), 2)]
+    return vals[0]
+
+# Make a root hash of a (sub)tree with two key/value pairs, and save intermediate nodes in the DB
+def make_double_key_hash(db, path1, path2, depth, value1, value2):
+    if depth == 256:
+        raise Exception("Cannot fit two values into one slot!")
+    if ((path1 >> 252) & 15) == ((path2 >> 252) & 15):
+        children = [zerohashes[depth+4]] * 16
+        children[(path1 >> 252) & 15] = make_double_key_hash(db, path1 << 4, path2 << 4, depth + 4, value1, value2)
+    else:
+        Lkey = ((path1 >> 252) & 15)
+        L = make_single_key_hash(path1 << 4, depth + 4, value1)
+        Rkey = ((path2 >> 252) & 15)
+        R = make_single_key_hash(path2 << 4, depth + 4, value2)
+        db.put(L, b'\x01' + path_to_key(path1 << 4) + value1)
+        db.put(R, b'\x01' + path_to_key(path2 << 4) + value2)
+        children = [zerohashes[depth+4]] * 16
+        children[Lkey] = L
+        children[Rkey] = R
+    h = hash_16_els(children)
+    db.put(h, b''.join(children))
+    return h
+            
+# Update a tree with a given key/value pair
+def update(db, root, key, value):
+    return _update(db, root, key_to_path(key), 0, value)
+
+def _update(db, root, path, depth, value):
+    if depth == 256:
+        return value
+    # Update an empty subtree: make a single-key subtree
+    if root == zerohashes[depth]:
+        k = make_single_key_hash(path, depth, value)
+        db.put(k, b'\x01' + path_to_key(path) + value)
+        return k
+    child = db.get(root)
+    # Update a single-key subtree: make a double-key subtree
+    if len(child) == 65:
+        origpath, origvalue = key_to_path(child[1:33]), child[33:]
+        return make_double_key_hash(db, path, origpath, depth, value, origvalue)
+    # Update a multi-key subtree: recurse down
+    else:
+        assert len(child) == 512
+        index = (path >> 252) & 15
+        new_value = _update(db, child[index*32: index*32+32], path << 4, depth + 4, value)
+        new_children = [new_value if i == index else child[32*i:32*i+32] for i in range(16)]
+        h = hash_16_els(new_children)
+        db.put(h, b''.join(new_children))
+        return h
+
+def multi_update(db, root, keys, values):
+    for k, v in zip(keys, values):
+        root = update(db, root, k, v)
+    return root
diff --git a/vitalik_merkle_optimizations/new_bintrie_optimized.py b/vitalik_merkle_optimizations/new_bintrie_optimized.py
new file mode 100644
index 0000000..9748b5c
--- /dev/null
+++ b/vitalik_merkle_optimizations/new_bintrie_optimized.py
@@ -0,0 +1,126 @@
+from ethereum.utils import sha3, encode_hex
+
+class EphemDB():
+    def __init__(self, kv=None):
+        self.reads = 0
+        self.writes = 0
+        self.kv = kv or {}
+
+    def get(self, k):
+        self.reads += 1
+        return self.kv.get(k, None)
+
+    def put(self, k, v):
+        self.writes += 1
+        self.kv[k] = v
+
+    def delete(self, k):
+        del self.kv[k]
+
+# Hashes of empty subtrees
+zerohashes = [b'\x00' * 32]
+for i in range(256):
+    zerohashes.insert(0, sha3(zerohashes[0] + zerohashes[0]))
+
+# Create a new empty tree
+def new_tree(db):
+    return zerohashes[0]
+
+# Convert a binary key into an integer path value
+def key_to_path(k):
+    return int.from_bytes(k, 'big')
+
+tt256m1 = 2**256 - 1
+
+# And convert back
+def path_to_key(k):
+    return (k & tt256m1).to_bytes(32, 'big')
+
+# Read a key from a given tree
+def get(db, root, key):
+    v = root
+    path = key_to_path(key)
+    for i in range(256):
+        if v == zerohashes[i]:
+            return b'\x00' * 32
+        child = db.get(v)
+        if len(child) == 65:
+            if (path % 2**256) == key_to_path(child[1:33]):
+                return child[33:]
+            else:
+                return b'\x00' * 32
+        else:
+            if (path >> 255) & 1:
+                v = child[32:]
+            else:
+                v = child[:32]
+        path <<= 1
+    return v
+
+# Make a root hash of a (sub)tree with a single key/value pair
+def make_single_key_hash(path, depth, value):
+    if depth == 256:
+        return value
+    elif (path >> 255) & 1:
+        return sha3(zerohashes[depth+1] + make_single_key_hash(path << 1, depth + 1, value))
+    else:
+        return sha3(make_single_key_hash(path << 1, depth + 1, value) + zerohashes[depth+1])
+
+# Make a root hash of a (sub)tree with two key/value pairs, and save intermediate nodes in the DB
+def make_double_key_hash(db, path1, path2, depth, value1, value2):
+    if depth == 256:
+        raise Exception("Cannot fit two values into one slot!")
+    if (path1 >> 255) & 1:
+        if (path2 >> 255) & 1:
+            child = zerohashes[depth+1] + make_double_key_hash(db, path1 << 1, path2 << 1, depth + 1, value1, value2)
+            db.put(sha3(child), child)
+            return sha3(child)
+        else:
+            L = make_single_key_hash(path2 << 1, depth + 1, value2)
+            R = make_single_key_hash(path1 << 1, depth + 1, value1)
+            db.put(L, b'\x01' + path_to_key(path2 << 1) + value2)
+            db.put(R, b'\x01' + path_to_key(path1 << 1) + value1)
+            child = L + R
+    else:
+        if (path2 >> 255) & 1:
+            L = make_single_key_hash(path1 << 1, depth + 1, value1)
+            R = make_single_key_hash(path2 << 1, depth + 1, value2)
+            db.put(L, b'\x01' + path_to_key(path1 << 1) + value1)
+            db.put(R, b'\x01' + path_to_key(path2 << 1) + value2)
+            child = L + R
+        else:
+            child = make_double_key_hash(db, path1 << 1, path2 << 1, depth + 1, value1, value2) + zerohashes[depth+1]
+    db.put(sha3(child), child)
+    return sha3(child)
+            
+# Update a tree with a given key/value pair
+def update(db, root, key, value):
+    return _update(db, root, key_to_path(key), 0, value)
+
+def _update(db, root, path, depth, value):
+    if depth == 256:
+        return value
+    # Update an empty subtree: make a single-key subtree
+    if root == zerohashes[depth]:
+        k = make_single_key_hash(path, depth, value)
+        db.put(k, b'\x01' + path_to_key(path) + value)
+        return k
+    child = db.get(root)
+    # Update a single-key subtree: make a double-key subtree
+    if len(child) == 65:
+        origpath, origvalue = key_to_path(child[1:33]), child[33:]
+        return make_double_key_hash(db, path, origpath, depth, value, origvalue)
+    # Update a multi-key subtree: recurse down
+    elif (path >> 255) & 1:
+        new_child = child[:32] + _update(db, child[32:], path << 1, depth + 1, value)
+        db.put(sha3(new_child), new_child)
+        return sha3(new_child)
+    else:
+        new_child = _update(db, child[:32], path << 1, depth + 1, value) + child[32:]
+        db.put(sha3(new_child), new_child)
+        return sha3(new_child)
+
+def multi_update(db, root, keys, values):
+    for k, v in zip(keys, values):
+        root = update(db, root, k, v)
+    return root
diff --git a/vitalik_merkle_optimizations/new_bintrie_test.py b/vitalik_merkle_optimizations/new_bintrie_test.py
new file mode 100644
index 0000000..4e0553d
--- /dev/null
+++ b/vitalik_merkle_optimizations/new_bintrie_test.py
@@ -0,0 +1,27 @@
+from new_bintrie import EphemDB, new_tree, get, update, make_merkle_proof, verify_proof, compress_proof, decompress_proof
+import random
+from ethereum.utils import sha3
+
+KEYS = 500
+
+db = EphemDB()
+t = new_tree(db)
+for i in range(KEYS):
+    t = update(db, t, sha3(str(i)), sha3(str(i**3)))
+print('%d elements added' % KEYS)
+for i in range(KEYS):
+    assert get(db, t, sha3(str(i))) == sha3(str(i**3))
+print('Get requests for present elements successful')
+for i in range(KEYS + 1, KEYS * 2):
+    assert get(db, t, sha3(str(i))) == b'\x00' * 32
+print('Get requests for absent elements successful')
+
+TL = 0
+for i in range(KEYS * 2):
+    key = sha3(str(i))
+    value = sha3(str(i ** 3)) if i < KEYS else b'\x00' * 32
+    proof = make_merkle_proof(db, t, key)
+    assert verify_proof(proof, t, key, value)
+    assert decompress_proof(compress_proof(proof)) == proof
+    TL += len(compress_proof(proof))
+print('Average total length at %d keys: %d, %d including key' % (KEYS, TL // KEYS // 2, TL // KEYS // 2 + 32))