wip: 区块链基础
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- 专业课程
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- 专业课程
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---
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# 区块链基础
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## 2024-2025学年下学期
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!!! warning "施工中"
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### 叫啥来着
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本目录包含区块链基础课程的相关资料。
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#### 教学资料
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- [南京大学慕课](https://drive.vanillaaaa.org/SharedCourses/软件工程学院/区块链基础/2024-2025学年下学期/课件/南京大学慕课)
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- [蚂蚁区块链](https://drive.vanillaaaa.org/SharedCourses/软件工程学院/区块链基础/2024-2025学年下学期/课件/蚂蚁区块链)
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- [作业](https://drive.vanillaaaa.org/SharedCourses/软件工程学院/区块链基础/2024-2025学年下学期/作业)
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def calculate_total_bitcoin():
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initial_reward = 50.0
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halving_interval = 210000
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total_btc = 0.0
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current_reward = initial_reward
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halving_count = 0
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while current_reward >= 1e-8:
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period_coins = halving_interval * current_reward
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total_btc += period_coins
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halving_count += 1
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current_reward /= 2
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print(f"\n最终减半次数: {halving_count}次")
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print(f"总发行量: {total_btc:,.8f} BTC ≈ {round(total_btc)} BTC")
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def estimate_mining_end_year():
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start_year = 2009
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blocks_per_halving = 210000
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block_time_minutes = 10
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minutes_per_year = 365 * 24 * 60
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blocks_per_year = minutes_per_year / block_time_minutes
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years_per_halving = blocks_per_halving / blocks_per_year
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halving_count = 0
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initial_reward = 50.0
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while initial_reward / (2 ** halving_count) >= 1e-8:
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halving_count += 1
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end_year = start_year + years_per_halving * halving_count
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print(f"\n预计全部挖完年份: {end_year:.0f}年")
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calculate_total_bitcoin()
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estimate_mining_end_year()
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\@writefile{toc}{\contentsline {section}{\numberline {1}比特币的总量上限计算}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {2}比特币的终止时间计算}{1}{}\protected@file@percent }
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\documentclass{article}
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\title{区块链基础第一次作业}
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\author{10225101408 朱炎}
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\date{2025.3.18}
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\begin{document}
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\maketitle
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比特币总量上限为2100万个且预计在2140年基本挖完的核心机制源于其区块奖励减半规则。
|
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\section{比特币的总量上限计算}
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||||||
比特币的初始奖励为50个比特币，每210000个区块奖励减半一次，第一个周期内产生$50 \times 210000 = 10500000$个比特币。
|
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||||||
则我们可以通过以下等比数列求和公式计算比特币总量上限：
|
|
||||||
\begin{equation}
|
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||||||
10500000 \times \sum_{n=0}^{\infty} (\frac{1}{2})^n = 10500000 \times \frac{1}{1 - \frac{1}{2}} = 21000000 \text{BTC}
|
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||||||
\end{equation}
|
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||||||
即2100万个比特币。
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\section{比特币的终止时间计算}
|
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||||||
比特币每210000个区块奖励减半一次，每个区块的产生时间约为10分钟，故210000个区块的生成耗时约为210000*10分钟 = 35000小时 = 1458天 = 4年。
|
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||||||
|
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||||||
比特币于2009年1月3日开始发行，到2140年约为131年，即32个周期。32个周期后，比特币的奖励为：
|
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||||||
\begin{equation}
|
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||||||
50 \times 2^{-32} \approx 1.16 \times 10^{-8} \text{BTC}
|
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||||||
\end{equation}
|
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||||||
而比特币的最小单位1聪（Satoshi）为$10^{-8}$比特币，故比特币的奖励将约等于0，挖矿终止。
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class Blockchain:
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def __init__(self, genesis_recipient=None, genesis_amount=0):
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||||||
self.utxo = {} # 格式: {tx_id: (receiver, amount)}
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# 生成创世交易（仅第一次初始化时调用）
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self.add_genesis(genesis_recipient, genesis_amount)
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def add_genesis(self, receiver, amount):
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# 添加创世区块
|
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genesis_tx_id = "genesis_tx_0x1"
|
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self.utxo[genesis_tx_id] = (receiver, amount)
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def validate_transaction(self, tx):
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# 验签
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|
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return False
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# 验证发送方余额
|
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sender_balance = sum(amt for (addr, amt) in self.utxo.values() if addr == tx.sender)
|
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|
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def add_transaction(self, tx):
|
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||||||
if self.validate_transaction(tx):
|
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||||||
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|
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||||||
self.utxo[tx_id] = (tx.receiver, tx.amount)
|
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||||||
return True
|
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||||||
return False
|
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|
||||||
from py_ecc.bls12_381 import G1, G2, add, multiply, is_inf, pairing, curve_order, field_modulus
|
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||||||
from py_ecc.fields import bls12_381_FQ as FQ
|
|
||||||
from functools import reduce
|
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||||||
import hashlib
|
|
||||||
|
|
||||||
def hash_to_g1(message: bytes):
|
|
||||||
G1_cofactor = 0x396c8c005555e1568c00aaab0000aaab
|
|
||||||
|
|
||||||
hashed = int.from_bytes(hashlib.sha256(message).digest(), 'big')
|
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||||||
x_val = hashed % field_modulus
|
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||||||
|
|
||||||
while True:
|
|
||||||
y_squared = (pow(x_val, 3, field_modulus) + 4) % field_modulus
|
|
||||||
y_val = pow(y_squared, (field_modulus + 1) // 4, field_modulus)
|
|
||||||
if pow(y_val, 2, field_modulus) == y_squared:
|
|
||||||
x = FQ(x_val)
|
|
||||||
y = FQ(y_val)
|
|
||||||
point = (x, y)
|
|
||||||
point = multiply(point, G1_cofactor)
|
|
||||||
if not is_inf(point):
|
|
||||||
return point
|
|
||||||
x_val = (x_val + 1) % field_modulus
|
|
||||||
|
|
||||||
import random
|
|
||||||
|
|
||||||
def generate_private_key():
|
|
||||||
return random.randint(1, curve_order - 1)
|
|
||||||
|
|
||||||
def generate_public_key(sk):
|
|
||||||
return multiply(G2, sk)
|
|
||||||
|
|
||||||
def sign(sk, message: bytes):
|
|
||||||
H_m = hash_to_g1(message)
|
|
||||||
return multiply(H_m, sk)
|
|
||||||
|
|
||||||
def verify(pk, message: bytes, signature) -> bool:
|
|
||||||
H_m = hash_to_g1(message)
|
|
||||||
left = pairing(G2, signature)
|
|
||||||
right = pairing(pk, H_m)
|
|
||||||
return left == right
|
|
||||||
|
|
||||||
def aggregate_signatures(signatures: list) -> tuple:
|
|
||||||
return reduce(add, signatures)
|
|
||||||
|
|
||||||
def aggregate_verify(pubkeys: list, messages: list, aggregate_sig: tuple) -> bool:
|
|
||||||
if len(pubkeys) != len(messages):
|
|
||||||
return False
|
|
||||||
product = 1
|
|
||||||
for pk, msg in zip(pubkeys, messages):
|
|
||||||
H_m = hash_to_g1(msg)
|
|
||||||
product *= pairing(pk, H_m)
|
|
||||||
left = pairing(G2, aggregate_sig)
|
|
||||||
return left == product
|
|
||||||
|
|
||||||
if __name__ == "__main__":
|
|
||||||
# 单个签名的情况
|
|
||||||
sk = generate_private_key()
|
|
||||||
pk = generate_public_key(sk)
|
|
||||||
message = b"Hello, BLS!"
|
|
||||||
signature = sign(sk, message)
|
|
||||||
print("验证结果:", verify(pk, message, signature))
|
|
||||||
print("错误消息验证:", verify(pk, b"Wrong message", signature))
|
|
||||||
|
|
||||||
# 多个签名的情况
|
|
||||||
num_signers = 3
|
|
||||||
sks = [generate_private_key() for _ in range(num_signers)]
|
|
||||||
pks = [generate_public_key(sk) for sk in sks]
|
|
||||||
messages = [f"Message {i}".encode() for i in range(num_signers)]
|
|
||||||
signatures = [sign(sk, msg) for sk, msg in zip(sks, messages)]
|
|
||||||
agg_sig = aggregate_signatures(signatures)
|
|
||||||
valid = aggregate_verify(pks, messages, agg_sig)
|
|
||||||
print("聚合验证结果:", valid)
|
|
||||||
corrupted_messages = [msg + b"no" for msg in messages]
|
|
||||||
invalid = aggregate_verify(pks, corrupted_messages, agg_sig)
|
|
||||||
print("篡改消息后的验证结果:", invalid)
|
|
||||||
|
|
@ -1,39 +0,0 @@
|
||||||
from wallet import Wallet
|
|
||||||
from transaction import Transaction
|
|
||||||
from blockchain import Blockchain
|
|
||||||
from bls import aggregate_signatures, aggregate_verify
|
|
||||||
|
|
||||||
alice = Wallet()
|
|
||||||
bob = Wallet()
|
|
||||||
blockchain = Blockchain( # 给Alice初始10个代币
|
|
||||||
genesis_recipient=alice.get_address(),
|
|
||||||
genesis_amount=10
|
|
||||||
)
|
|
||||||
|
|
||||||
alice_balance = sum(
|
|
||||||
amt for (addr, amt) in blockchain.utxo.values()
|
|
||||||
if addr == alice.get_address()
|
|
||||||
)
|
|
||||||
print("Alice 的初始余额:", alice_balance)
|
|
||||||
|
|
||||||
tx1 = Transaction(alice.get_address(), bob.get_address(), 10)
|
|
||||||
tx1.sign(alice)
|
|
||||||
print("交易1验证结果:", tx1.is_valid())
|
|
||||||
|
|
||||||
if blockchain.add_transaction(tx1):
|
|
||||||
print("交易1成功上链")
|
|
||||||
|
|
||||||
# Bob向Alice转账15个代币（失败，余额不足）
|
|
||||||
tx2 = Transaction(bob.get_address(), alice.get_address(), 15)
|
|
||||||
tx2.sign(bob)
|
|
||||||
print("交易2验证结果:", tx2.is_valid()) # True，但余额不足
|
|
||||||
print("交易2上链结果:", blockchain.add_transaction(tx2)) # False
|
|
||||||
|
|
||||||
# 聚合签名
|
|
||||||
carol = Wallet()
|
|
||||||
tx3_data = b"Multisig_Transaction"
|
|
||||||
signature_alice = alice.sign_transaction(tx3_data)
|
|
||||||
signature_carol = carol.sign_transaction(tx3_data)
|
|
||||||
agg_sig = aggregate_signatures([signature_alice, signature_carol])
|
|
||||||
valid = aggregate_verify([alice.pk, carol.pk], [tx3_data, tx3_data], agg_sig)
|
|
||||||
print("聚合签名验证结果:", valid) # True
|
|
||||||
|
|
@ -1,17 +0,0 @@
|
||||||
class Transaction:
|
|
||||||
def __init__(self, sender, receiver, amount, signature=None):
|
|
||||||
self.sender = sender # 公钥
|
|
||||||
self.receiver = receiver # 地址
|
|
||||||
self.amount = amount # 金额
|
|
||||||
self.signature = signature
|
|
||||||
|
|
||||||
def serialize(self) -> bytes:
|
|
||||||
# 序列化交易数据用于签名
|
|
||||||
return f"{self.sender}{self.receiver}{self.amount}".encode()
|
|
||||||
|
|
||||||
def sign(self, wallet):
|
|
||||||
self.signature = wallet.sign_transaction(self.serialize())
|
|
||||||
|
|
||||||
def is_valid(self) -> bool:
|
|
||||||
from bls import verify
|
|
||||||
return verify(self.sender, self.serialize(), self.signature)
|
|
||||||
|
|
@ -1,13 +0,0 @@
|
||||||
from bls import generate_private_key, generate_public_key
|
|
||||||
|
|
||||||
class Wallet:
|
|
||||||
def __init__(self):
|
|
||||||
self.sk = generate_private_key()
|
|
||||||
self.pk = generate_public_key(self.sk)
|
|
||||||
|
|
||||||
def get_address(self):
|
|
||||||
return self.pk # 公钥作为地址
|
|
||||||
|
|
||||||
def sign_transaction(self, tx_data: bytes):
|
|
||||||
from bls import sign
|
|
||||||
return sign(self.sk, tx_data)
|
|
||||||
Loading…
Reference in New Issue