[Python知识库]python中实现ECDSA

纯 python ECDSA签名/验证和 ECDH 密钥协议

import six
import timeit#查找任何特定代码执行的确切时间
from ecdsa.curves import curves

#定义do函数，计算时间
def do(setup_statements, statement):
    # extracted from timeit.py
    t = timeit.Timer(stmt=statement, setup="\n".join(setup_statements))
    # determine number so that 0.2 <= total time < 2.0
    for i in range(1, 10):
        number = 10 ** i #**为次方
        x = t.timeit(number)
        if x >= 0.2:
            break
    return x / number

NIST为数字测试套件关于NIST详解
GF§ (素数域)曲线，密钥长度为192、224、256、384和521bit
OpenSSL工具（openssl ecparam -list_curves）所知道的这些曲线的 "简称 "是：prime192v1、secp224r1、prime256v1、secp384r1和secp521r1。它包括比特币使用的256位曲线secp256k1。它还支持160到512位的Brainpool曲线的常规（非扭曲）变体。这些曲线的 "简称 "是：BrainpoolP160r1, brainpoolP192r1, brainpoolP224r1, brainpoolP256r1, brainpoolP320r1, brainpoolP384r1, brainpoolP512r1。少数来自SEC标准的小曲线也包括在内（主要是为了加快库的测试），它们是：secp112r1, secp112r2, secp128r1, 和secp160r1。没有包括其他的曲线，但要增加对更多素数域的曲线的支持并不难。

#不是很懂 sep=":",unit="s",form=".5f",form_inv=".2f",
prnt_form = (
    "{name:>16}{sep:1} {siglen:>6} {keygen:>9{form}}{unit:1} "
    "{keygen_inv:>9{form_inv}} {sign:>9{form}}{unit:1} "
    "{sign_inv:>9{form_inv}} {verify:>9{form}}{unit:1} "
    "{verify_inv:>9{form_inv}} {verify_single:>13{form}}{unit:1} "
    "{verify_single_inv:>14{form_inv}}"
)
print(
    prnt_form.format(
        siglen="siglen",
        keygen="keygen",
        keygen_inv="keygen/s",
        sign="sign",
        sign_inv="sign/s",
        verify="verify",
        verify_inv="verify/s",
        verify_single="no PC verify",
        verify_single_inv="no PC verify/s",
        name="",
        sep="",
        unit="",
        form="",
        form_inv="",
    )
)
for curve in [i.name for i in curves]:
    S1 = "import six; from ecdsa import SigningKey, %s" % curve
    S2 = "sk = SigningKey.generate(%s)" % curve #产生私钥
    S3 = "msg = six.b('msg')" #消息
    S4 = "sig = sk.sign(msg)" #签名
    S5 = "vk = sk.get_verifying_key()"#公钥由私钥得出  get_verifying_key()函数
    S6 = "vk.precompute()"#不懂
    S7 = "vk.verify(sig, msg)"#用公钥验证签名
    # 我们碰巧知道.generate()也在计算验证密钥，这是最耗时的部分。如果将代码改为懒惰地计算vk，我们就需要将这个基准改为在S5上循环，而不是在S2上。
    keygen = do([S1], S2)
    sign = do([S1, S2, S3], S4)
    verf = do([S1, S2, S3, S4, S5, S6], S7)
    verf_single = do([S1, S2, S3, S4, S5], S7)

    import ecdsa

    c = getattr(ecdsa, curve)#从名字上看获取属性值
    sig = ecdsa.SigningKey.generate(c).sign(six.b("msg"))
    #密钥对（keygen）、签署数据（sign）、验证这些签名（verify）、共享秘密（ecdh）以及在没有特定密钥预计算的情况下验证签名（no PC verify）、原始签名的大小（通常是签名可以被编码的最小方式）也在siglen栏中提供
    print(
        prnt_form.format(
            name=curve,#所有的曲线
            sep=":",
            siglen=len(sig),
            unit="s",
            keygen=keygen,
            keygen_inv=1.0 / keygen,
            sign=sign,
            sign_inv=1.0 / sign,
            verify=verf,
            verify_inv=1.0 / verf,
            verify_single=verf_single,
            verify_single_inv=1.0 / verf_single,
            form=".5f",#小数点后面为5位
            form_inv=".2f",#小数点后面为2位
        )
    )

print("")

ED25519和Cureve5519

ecdh_form = "{name:>16}{sep:1} {ecdh:>9{form}}{unit:1} {ecdh_inv:>9{form_inv}}"

print(
    ecdh_form.format(
        ecdh="ecdh",
        ecdh_inv="ecdh/s",
        name="",
        sep="",
        unit="",
        form="",
        form_inv="",
    )
)

for curve in [i.name for i in curves]:
    if curve == "Ed25519" or curve == "Ed448":
        continue
    S1 = "from ecdsa import SigningKey, ECDH, {0}".format(curve)
    S2 = "our = SigningKey.generate({0})".format(curve)#私钥
    S3 = "remote = SigningKey.generate({0}).verifying_key".format(curve)#公钥
    S4 = "ecdh = ECDH(private_key=our, public_key=remote)"
    S5 = "ecdh.generate_sharedsecret_bytes()"#产生共享密钥
    ecdh = do([S1, S2, S3, S4], S5)
    print(
        ecdh_form.format(
            name=curve,
            sep=":",
            unit="s",
            form=".5f",
            form_inv=".2f",
            ecdh=ecdh,
            ecdh_inv=1.0 / ecdh,
        )
    )

from ecdsa import SigningKey
sk = SigningKey.generate() # uses NIST192p生成私钥
vk = sk.verifying_key#在私钥的基础上生成公钥
signature = sk.sign(b"message")#用私钥对消息进行签名
assert vk.verify(signature, b"message")#用公钥去验证。assert为一断言函数：不满足条件直接触发异常忙不执行接下来的代码，括号中为condition

from ecdsa import SigningKey, NIST384p#384位NIST素域椭圆曲线，其中私钥/公钥都与特定的曲线相关联，更长的曲线更安全，但时间长，密钥和签名也长
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
signature = sk.sign(b"message")
assert vk.verify(signature, b"message")

#将签名密钥（私钥）序列化成不同的格式。
from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
sk_string = sk.to_string()#最短的调用，然后再重新创建私钥。to_string()：将括号内的数字转化为字符串，实际返回的类型bytes
sk2 = SigningKey.from_string(sk_string, curve=NIST384p)#重新创建私钥，第一个参数是我们要处理的字符，如果点编码无效或不在指定曲线上，from_string（）将引发MalformedPointError
print(sk_string.hex())
print(sk2.to_string().hex())

from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
sk_pem = sk.to_pem()#sk.to_pem()和sk.to_der()将把签名密钥序列化为OpenSSL使用的相同格式
sk2 = SigningKey.from_pem(sk_pem)#SigningKey.from_pem()/.from_der()将撤销这种序列化。这些格式包括了曲线名称，所以你不需要向反序列化器传递曲线标识符。如果文件是畸形的，from_der()和from_pem()将引发UnexpectedDER或MalformedPointError。
# sk and sk2 are the same key

from ecdsa import SigningKey, VerifyingKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk_string = vk.to_string()#公钥可以用同样的方式进行序列化
vk2 = VerifyingKey.from_string(vk_string, curve=NIST384p)
# vk and vk2 are the same key

from ecdsa import SigningKey, VerifyingKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk_pem = vk.to_pem()
vk2 = VerifyingKey.from_pem(vk_pem)
# vk and vk2 are the same key

import os
from ecdsa import NIST384p, SigningKey
from ecdsa.util import randrange_from_seed__trytryagain#产生随机数

def make_key(seed):
  secexp = randrange_from_seed__trytryagain(seed, NIST384p.order)
  return SigningKey.from_secret_exponent(secexp, curve=NIST384p)

seed = os.urandom(NIST384p.baselen) # or other starting point，返回一个适合加密的比特串
sk1a = make_key(seed)
sk1b = make_key(seed)
# note: sk1a and sk1b are the same key
assert sk1a.to_string() == sk1b.to_string()
sk2 = make_key(b"2-"+seed)  # different key  b为比特
assert sk1a.to_string() != sk2.to_string()

from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk.precompute()
signature = sk.sign(b"message")
assert vk.verify(signature, b"message")

# openssl ecparam -name prime256v1 -genkey -out sk.pem
# openssl ec -in sk.pem -pubout -out vk.pem
# echo "data for signing" > data
# openssl dgst -sha256 -sign sk.pem -out data.sig data
# openssl dgst -sha256 -verify vk.pem -signature data.sig data
# openssl dgst -sha256 -prverify sk.pem -signature data.sig data

#OpenSSL 使用 PEM 文件格式存储证书和密钥。PEM 实质上是 Base64 编码的二进制内容
import hashlib#
from ecdsa import SigningKey, VerifyingKey
from ecdsa.util import sigencode_der, sigdecode_der#从ecdsa.util写入和读取签名

with open("vk.pem") as f:#公钥文件
   vk = VerifyingKey.from_pem(f.read())

with open("data", "rb") as f:#open()为读取模式，with语句直接调用close方法，r为读模式，w/wb为写模式，rb模式打开二进制文件，消息data
   data = f.read()

with open("data.sig", "rb") as f:#消息签名可读模式
   signature = f.read()

assert vk.verify(signature, data, hashlib.sha256, sigdecode=sigdecode_der)#公钥验证签名，

with open("sk.pem") as f:#私钥文件
   sk = SigningKey.from_pem(f.read(), hashlib.sha256)

new_signature = sk.sign_deterministic(data, sigencode=sigencode_der)#用私钥签名生成一个新的签名

with open("data.sig2", "wb") as f:#写模式
   f.write(new_signature)

# openssl dgst -sha256 -verify vk.pem -signature data.sig2 data
#如果需要与OpenSSL 1.0.0或更早的版本兼容，可以使用ecdsa.util中的sigencode_string和sigdecode_string来分别写入和读取签名。
from ecdsa import SigningKey, VerifyingKey

with open("sk.pem") as f:
    sk = SigningKey.from_pem(f.read())
with open("sk.pem", "wb") as f:
    f.write(sk.to_pem())

with open("vk.pem") as f:
    vk = VerifyingKey.from_pem(f.read())
with open("vk.pem", "wb") as f:
    f.write(vk.to_pem())

#ecdsa.util.PRNG 工具在这里很方便：它需要一个种子并从中产生一个强的伪随机流。
#os.urandom的函数作为entropy=参数来做不同的事情
#ECDSA的签名生成也需要一个随机数，而且每个签名都必须使用不同的随机数（两次使用相同的数字会立即暴露出私人签名密钥）。
# sk.sign()方法需要一个entropy=参数，其行为与SigningKey.generate(entropy=)相同。
from ecdsa.util import PRNG
from ecdsa import SigningKey
rng1 = PRNG(b"seed")
sk1 = SigningKey.generate(entropy=rng1)
rng2 = PRNG(b"seed")
sk2 = SigningKey.generate(entropy=rng2)
# sk1 and sk2 are the same key

#如果你调用SigningKey.sign_deterministic(data)而不是.sign(data)，代码将生成一个确定性的签名，而不是随机的。
# 这使用RFC6979中的算法来安全地生成一个唯一的K值，该值来自于私钥和被签名的信息。每次你用相同的密钥签署相同的信息时，你将得到相同的签名（使用相同的k）。



#创建一个NIST521p密钥对
from ecdsa import SigningKey, NIST521p
sk = SigningKey.generate(curve=NIST521p)
vk = sk.verifying_key

#从一个主种子创建三个独立的签名密钥
from ecdsa import NIST192p, SigningKey
from ecdsa.util import randrange_from_seed__trytryagain

def make_key_from_seed(seed, curve=NIST192p):
    secexp = randrange_from_seed__trytryagain(seed, curve.order)
    return SigningKey.from_secret_exponent(secexp, curve)

sk1 = make_key_from_seed("1:%s" % seed)
sk2 = make_key_from_seed("2:%s" % seed)
sk3 = make_key_from_seed("3:%s" % seed)


#从磁盘上加载一个验证密钥，并使用十六进制编码以未压缩和压缩的格式打印出来（在X9.62和SEC1标准中定义）。
from ecdsa import VerifyingKey

with open("public.pem") as f:#加载验证密钥
    vk = VerifyingKey.from_pem(f.read())

print("uncompressed: {0}".format(vk.to_string("uncompressed").hex()))
print("compressed: {0}".format(vk.to_string("compressed").hex()))


#从压缩格式的十六进制字符串中加载验证密钥，以未压缩的格式输出。
from ecdsa import VerifyingKey, NIST256p

comp_str = '022799c0d0ee09772fdd337d4f28dc155581951d07082fb19a38aa396b67e77759'
vk = VerifyingKey.from_string(bytearray.fromhex(comp_str), curve=NIST256p)
print(vk.to_string("uncompressed").hex())


#与远程方进行ECDH密钥交换。
from ecdsa import ECDH, NIST256p

ecdh = ECDH(curve=NIST256p)
ecdh.generate_private_key()
local_public_key = ecdh.get_public_key()
#send `local_public_key` to remote party and receive `remote_public_key` from remote party
with open("remote_public_key.pem") as e:
    remote_public_key = e.read()
ecdh.load_received_public_key_pem(remote_public_key)
secret = ecdh.generate_sharedsecret_bytes()