def traverse(self, s):
"""Returns the auth nodes for leaf s + 1."""
for h in range(H):
if not ((s >> h) & 1):
tau = h
break
if tau > 0:
tempkeep = self.keep[(tau - 1) >> 1] # prevent overwriting
if not ((s >> (tau+1)) & 1) and tau < H - 1:
self.keep[tau >> 1] = self.auth[tau]
if tau == 0:
self.auth[0] = Node(h=0, v=leafcalc(s))
else:
self.auth[tau] = Node(h=0, v=g(self.auth[tau - 1].v + tempkeep.v))
for h in range(tau):
if h < H - K:
self.auth[h] = self.treehash[h].node
else:
offset = (1 << (H - 1 - h)) + h - H
rowidx = ((s >> h) - 1) >> 1
self.auth[h] = self.retain[offset + rowidx]
for h in range(tau if (tau < H - K) else H - K):
startidx = s + 1 + 3 * (1 << h)
if startidx < 1 << H:
self.treehash[h].restart(startidx)
return self.auth
def traverse(self, s):
"""Returns the auth nodes for leaf s + 1."""
for h in range(H):
if not ((s >> h) & 1):
tau = h
break
if tau > 0:
tempkeep = self.keep[(tau - 1) >> 1] # prevent overwriting
if not ((s >> (tau + 1)) & 1) and tau < H - 1:
self.keep[tau >> 1] = self.auth[tau]
if tau == 0:
self.auth[0] = Node(h=0, v=leafcalc(s))
else:
self.auth[tau] = Node(h=0, v=g(self.auth[tau - 1].v + tempkeep.v))
for h in range(tau):
if h < H - K:
self.auth[h] = self.treehash[h].node
else:
offset = (1 << (H - 1 - h)) + h - H
rowidx = ((s >> h) - 1) >> 1
self.auth[h] = self.retain[offset + rowidx]
for h in range(tau if (tau < H - K) else H - K):
startidx = s + 1 + 3 * (1 << h)
if startidx < 1 << H:
self.treehash[h].restart(startidx)
return self.auth
def update(self):
"""Performs one unit of computation on the stack. This can imply either
the introduction a new leaf node or the computation of a parent node"""
if self.completed:
return
if len(self.stack) >= 2 and self.stack[-1].h == self.stack[-2].h:
node_r = self.stack.pop()
node_l = self.stack.pop()
self.stack.append(Node(h=node_l.h + 1, v=g(node_l.v + node_r.v)))
else:
self.stack.append(Node(h=0, v=leafcalc(self.next_idx)))
self.next_idx += 1
if self.stack[-1].h == self.h:
self.completed = True
return
def update(self):
"""Performs one unit of computation on the stack. This can imply either
the introduction a new leaf node or the computation of a parent node"""
if self.completed:
return
if len(self.stack) >= 2 and self.stack[-1].h == self.stack[-2].h:
node_r = self.stack.pop()
node_l = self.stack.pop()
self.stack.append(Node(h=node_l.h + 1, v=g(node_l.v + node_r.v)))
else:
self.stack.append(Node(h=0, v=leafcalc(self.next_idx)))
self.next_idx += 1
if self.stack[-1].h == self.h:
self.completed = True
return
def update(self):
"""Performs one iteration of Treehash, i.e. adds one leaf node.
Note that this is different from Treehash.update() in the classic
traversal algorithm, where only one computational unit is performed."""
node1 = Node(h=0, v=leafcalc(self.next_idx))
while self.stackusage > 0 and STACK[-1].h == node1.h:
node2 = STACK.pop()
self.stackusage -= 1
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
STACK.append(node1)
self.stackusage += 1
self.next_idx += 1
if self.stackusage == 1 and STACK[-1].h == self.h:
self.completed = True
self.node = STACK.pop()
self.stackusage -= 1
def update(self):
"""Performs one iteration of Treehash, i.e. adds one leaf node.
Note that this is different from Treehash.update() in the classic
traversal algorithm, where only one computational unit is performed."""
node1 = Node(h=0, v=leafcalc(self.next_idx))
while self.stackusage > 0 and self.stack[-1].h == node1.h:
node2 = self.stack.pop()
self.stackusage -= 1
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
self.stack.append(node1)
self.stackusage += 1
self.next_idx += 1
if self.stackusage == 1 and self.stack[-1].h == self.h:
self.completed = True
self.node = self.stack.pop()
self.stackusage -= 1
def traverse(s):
"""Returns the auth nodes for leaf s + 1."""
for h in range(H):
if not ((s >> h) & 1):
tau = h
break
if tau > 0:
tempKEEP = KEEP[(tau - 1) >> 1] # prevent overwriting too soon
if not ((s >> (tau + 1)) & 1) and tau < H - 1:
KEEP[tau >> 1] = AUTH[tau]
if tau == 0:
AUTH[0] = Node(h=0, v=leafcalc(s))
else:
AUTH[tau] = Node(h=0, v=g(AUTH[tau - 1].v + tempKEEP.v))
for h in range(tau):
if h < H - K:
AUTH[h] = TREEHASH[h].node
else:
offset = (1 << (H - 1 - h)) + h - H
rowidx = ((s >> h) - 1) >> 1
AUTH[h] = RETAIN[offset + rowidx]
for h in range(tau if (tau < H - K) else H - K):
startidx = s + 1 + 3 * (1 << h)
if startidx < 1 << H:
TREEHASH[h].__init__(h, startidx)
for _ in range((H - K) >> 1):
l_min = H
h = H - K
for j in range(H - K):
if TREEHASH[j].completed:
low = H
elif TREEHASH[j].stackusage == 0:
low = j
else:
low = TREEHASH[j].height()
if low < l_min:
h = j
l_min = low
if h != H - K:
TREEHASH[h].update()
return AUTH
def stack_update(self, idx):
node1 = Node(h=0, v=leafcalc(idx))
if node1.h < H - K and idx == 3:
self.treehash[0].node = node1
while self.stack and self.stack[-1].h == node1.h:
if idx >> node1.h == 1:
self.auth[node1.h] = node1
else: # node1 is a right-node with row-index 2idx + 3
if node1.h < H - K and idx >> node1.h == 3:
self.treehash[node1.h].node = node1
elif node1.h >= H - K:
offset = (1 << (H - 1 - node1.h)) + node1.h - H
rowidx = ((idx >> node1.h) - 3) >> 1
self.retain[offset + rowidx] = node1
node2 = self.stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
self.stack.append(node1)
def stack_update(self, idx):
node1 = Node(h=0, v=leafcalc(idx))
if node1.h < H - K and idx == 3:
self.treehash[0].node = node1
while self.stack and self.stack[-1].h == node1.h:
if idx >> node1.h == 1:
self.auth[node1.h] = node1
else: # node1 is a right-node with row-index 2idx + 3
if node1.h < H - K and idx >> node1.h == 3:
self.treehash[node1.h].node = node1
elif node1.h >= H - K:
offset = (1 << (H - 1 - node1.h)) + node1.h - H
rowidx = ((idx >> node1.h) - 3) >> 1
self.retain[offset + rowidx] = node1
node2 = self.stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
self.stack.append(node1)
def keygen_and_setup():
"""Sets up TREEHASH and AUTH for the start of classic Merkle traversal."""
for h in range(H):
TREEHASH[h] = Treehash(h, completed=True)
stack = []
for j in range(2 ** H):
node1 = Node(h=0, v=leafcalc(j))
if j == 0:
TREEHASH[0].stack = [node1]
while stack and stack[-1].h == node1.h:
if not AUTH[node1.h]:
AUTH[node1.h] = node1
node2 = stack.pop()
node1 = Node(h=node1.h+1, v=g(node2.v + node1.v))
if node1.h < H and not TREEHASH[node1.h].stack:
TREEHASH[node1.h].stack.append(node1)
stack.append(node1)
return stack.pop()
def keygen_and_setup():
"""Sets up TREEHASH and AUTH for the start of classic Merkle traversal."""
for h in range(H):
TREEHASH[h] = Treehash(h, completed=True)
stack = []
for j in range(2**H):
node1 = Node(h=0, v=leafcalc(j))
if j == 0:
TREEHASH[0].stack = [node1]
while stack and stack[-1].h == node1.h:
if not AUTH[node1.h]:
AUTH[node1.h] = node1
node2 = stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
if node1.h < H and not TREEHASH[node1.h].stack:
TREEHASH[node1.h].stack.append(node1)
stack.append(node1)
return stack.pop()
def traverse(s):
"""Returns the auth nodes for leaf s + 1."""
tau = next(h for h in range(H) if not (s >> h) & 1)
if not (s >> (tau + 1)) & 1 and tau < H - 1:
KEEP[tau] = AUTH[tau]
if tau == 0:
AUTH[0] = Node(h=0, v=leafcalc(s))
else:
AUTH[tau] = Node(h=tau, v=g(AUTH[tau - 1].v + KEEP[tau - 1].v))
KEEP[tau - 1] = None
for h in range(tau):
if h < H - K:
AUTH[h] = TREEHASH[h].node
TREEHASH[h].node = None
else:
AUTH[h] = RETAIN[h].pop()
for h in range(min(tau, H - K)):
startidx = s + 1 + 3 * 2**h
if startidx < 2**H:
TREEHASH[h].__init__(h, startidx)
for _ in range((H - K) // 2):
l_min = float('inf')
h = None
for j in range(H - K):
if TREEHASH[j].completed:
low = float('inf')
elif TREEHASH[j].stackusage == 0:
low = j
else:
low = TREEHASH[j].height()
if low < l_min:
h = j
l_min = low
if h is not None:
TREEHASH[h].update()
return AUTH
def traverse(s):
"""Returns the auth nodes for leaf s + 1."""
tau = next(h for h in range(H) if not (s >> h) & 1)
if not (s >> (tau+1)) & 1 and tau < H - 1:
KEEP[tau] = AUTH[tau]
if tau == 0:
AUTH[0] = Node(h=0, v=leafcalc(s))
else:
AUTH[tau] = Node(h=tau, v=g(AUTH[tau - 1].v + KEEP[tau - 1].v))
KEEP[tau - 1] = None
for h in range(tau):
if h < H - K:
AUTH[h] = TREEHASH[h].node
TREEHASH[h].node = None
else:
AUTH[h] = RETAIN[h].pop()
for h in range(min(tau, H - K)):
startidx = s + 1 + 3 * 2**h
if startidx < 2 ** H:
TREEHASH[h].__init__(h, startidx)
for _ in range((H - K) // 2):
l_min = float('inf')
h = None
for j in range(H - K):
if TREEHASH[j].completed:
low = float('inf')
elif TREEHASH[j].stackusage == 0:
low = j
else:
low = TREEHASH[j].height()
if low < l_min:
h = j
l_min = low
if h is not None:
TREEHASH[h].update()
return AUTH
def keygen_and_setup():
"""Sets up TREEHASH, RETAIN and AUTH for the start of BDS traversal."""
for h in range(H - K):
TREEHASH[h] = Treehash(h, completed=True)
stack = []
for j in range(2**H):
node1 = Node(h=0, v=leafcalc(j))
if node1.h < H - K and j == 3:
TREEHASH[0].node = node1
while stack and stack[-1].h == node1.h:
if not AUTH[node1.h]:
AUTH[node1.h] = node1
else: # in this case node1 is a right-node with row-index 2j + 3
if node1.h < H - K and TREEHASH[node1.h].node is None:
TREEHASH[node1.h].node = node1
elif node1.h >= H - K:
RETAIN[node1.h].appendleft(node1)
node2 = stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
stack.append(node1)
return stack.pop()
def keygen_and_setup():
"""Sets up TREEHASH, RETAIN and AUTH for the start of BDS traversal."""
for h in range(H - K):
TREEHASH[h] = Treehash(h, completed=True)
stack = []
for j in range(2 ** H):
node1 = Node(h=0, v=leafcalc(j))
if node1.h < H - K and j == 3:
TREEHASH[0].node = node1
while stack and stack[-1].h == node1.h:
if not AUTH[node1.h]:
AUTH[node1.h] = node1
else: # in this case node1 is a right-node with row-index 2j + 3
if node1.h < H - K and TREEHASH[node1.h].node is None:
TREEHASH[node1.h].node = node1
elif node1.h >= H - K:
RETAIN[node1.h].appendleft(node1)
node2 = stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
stack.append(node1)
return stack.pop()
def keygen_and_setup():
"""Sets up TREEHASH, RETAIN and AUTH for the start of BDS traversal."""
for h in range(H - K):
TREEHASH[h] = Treehash(h, completed=True)
stack = []
for j in range(1 << H):
node1 = Node(h=0, v=leafcalc(j))
if node1.h < H - K and j == 3:
TREEHASH[0].node = node1
while stack and stack[-1].h == node1.h:
if j >> node1.h == 1:
AUTH[node1.h] = node1
else: # in this case node1 is a right-node with row-index 2j + 3
if node1.h < H - K and j >> node1.h == 3:
TREEHASH[node1.h].node = node1
elif node1.h >= H - K:
offset = (1 << (H - 1 - node1.h)) + node1.h - H
rowidx = ((j >> node1.h) - 3) >> 1
RETAIN[offset + rowidx] = node1
node2 = stack.pop()
node1 = Node(h=node1.h + 1, v=g(node2.v + node1.v))
stack.append(node1)
return stack.pop()
