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pre.py
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import binascii
import hashlib
from math import ceil
from typing import List
import ecdsa
from ecdsa import ellipticcurve, numbertheory
from ecdsa.util import bit_length
from crypto import signer
baseN = ecdsa.SECP256k1.order
encKeyLength = 16
class KFrag:
def __init__(self, random, value, precurpub):
self.random = random
self.value = value
self.precurpub = precurpub
class ReKeyFrag:
def __init__(self, reKeyR, reKeyU, random, precurpub):
self.reKeyR = reKeyR
self.reKeyU = reKeyU
self.random = random
self.precurpub = precurpub
class EccPoint():
def __init__(self, point:ellipticcurve.Point=None):
self.point = point
def setEccPoint(self, pub: str):
pubByte = bytes.fromhex(pub)
point = ecdsa.VerifyingKey.from_string(pubByte, ecdsa.SECP256k1, hashlib.sha256).pubkey.point
self.point = point
def __add__(self, other):
if other.point == None:
return EccPoint(self.point)
return EccPoint(self.point + other.point)
def __mul__(self, other:int):
return EccPoint(self.point * other)
def kdf(z, klen): # z为16进制表示的比特串（str），klen为密钥长度（单位byte）
klen = int(klen)
ct = 0x00000001
rcnt = ceil(klen/32)
zin = [i for i in bytes.fromhex(z)]
ha = b""
for i in range(rcnt):
msg = zin + [i for i in binascii.a2b_hex(('%08x' % ct).encode('utf8'))]
ha = ha + hashlib.sha256(bytes(msg)).digest()
ct += 1
return ha[0: klen]
def generateEncryptKey(pubOwner):
pubOwnerKey = ecdsa.VerifyingKey.from_string(bytes.fromhex(pubOwner), ecdsa.SECP256k1, hashlib.sha256)
priv_r = ecdsa.SigningKey.from_secret_exponent(int(signer.generatePrivateKey(), 16), ecdsa.SECP256k1, hashlib.sha256)
priv_u = ecdsa.SigningKey.from_secret_exponent(int(signer.generatePrivateKey(), 16), ecdsa.SECP256k1, hashlib.sha256)
sum = (priv_r.privkey.secret_multiplier + priv_u.privkey.secret_multiplier) % baseN
result = pubOwnerKey.pubkey.point * sum
encKey = ecdsa.VerifyingKey.from_public_point(result, ecdsa.SECP256k1, hashlib.sha256).to_string(encoding="compressed")
return kdf(encKey.hex(), encKeyLength), priv_r.get_verifying_key().to_string(encoding="compressed").hex(), priv_u.get_verifying_key().to_string(encoding="compressed").hex()
def hashToModInt(digest):
orderBits = bit_length(baseN)
orderBytes = int((orderBits + 7) / 8)
if len(digest) > orderBytes:
digest = digest[:orderBytes]
ret = int(digest.hex(), 16)
excess = len(digest) * 8 - orderBits
if excess > 0:
return ret >> excess
return ret
# def hashToModInt(digest):
# sum = int(digest, 16)
# order_minus_1 = baseN - 1
#
# return (sum % order_minus_1) + 1
def makeShamirPolyCoeff(threshold)->List[int]:
coeffs = list()
for _ in range(threshold-1):
key = int(signer.generatePrivateKey(), 16)
coeffs.append(key)
return coeffs
def hornerPolyEval(coeff: List[int], x: int) -> int:
result = coeff[0]
for i in range(1, len(coeff)):
result = (result * x) + coeff[i]
return result % baseN
def calcPart(a:int, b:int)->int:
p = (a - b) % baseN
res = (a * numbertheory.inverse_mod(p, baseN)) % baseN
return res
def calcLambdaCoeff(id_i: int, selected_ids: List[int]) -> int:
ids = [x for x in selected_ids if x != id_i]
if not ids:
return 1
result = calcPart(ids[0], id_i)
for id_j in ids[1:]:
result = (result * calcPart(id_j, id_i)) % baseN
return result
def generateKeyFragment(privOwner, pubRecipient, numSplit, threshold)->List[KFrag]:
precursorKey = int(signer.generatePrivateKey(), 16)
precursor = ecdsa.SigningKey.from_secret_exponent(precursorKey, ecdsa.SECP256k1, hashlib.sha256)
privInt = int(privOwner, 16)
pubRecipientKey = ecdsa.VerifyingKey.from_string(bytes.fromhex(pubRecipient), ecdsa.SECP256k1, hashlib.sha256)
dh_alice_point = signer.ecdh_point(pubRecipientKey.pubkey.point, precursorKey)
aAliceHash = hashlib.sha256()
aAliceHash.update(precursor.get_verifying_key().pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
aAliceHash.update(pubRecipientKey.pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
aAliceHash.update(dh_alice_point)
dAlice = aAliceHash.digest()
dAliceBN = hashToModInt(dAlice)
f0 = (privInt * numbertheory.inverse_mod(dAliceBN, baseN)) % baseN
precursorPub = precursor.get_verifying_key().to_string(encoding="compressed").hex()
kfrags = list()
if numSplit == 1 :
id = ecdsa.util.randrange(ecdsa.SECP256k1.order)
kfrag = KFrag(str(id), str(f0), precursorPub)
kfrags.append(kfrag)
else:
coeffs = makeShamirPolyCoeff(threshold)
coeffs.append(f0)
for _ in range(numSplit):
id = ecdsa.util.randrange(baseN)
dShareHash = hashlib.sha256()
dShareHash.update(precursor.get_verifying_key().pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
dShareHash.update(pubRecipientKey.pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
dShareHash.update(dh_alice_point)
dShareHash.update(id.to_bytes(32, byteorder='big', signed=False))
share = hashToModInt(dShareHash.digest())
rk = hornerPolyEval(coeffs, share)
kfrag = KFrag(str(id), str(rk), precursorPub)
kfrags.append(kfrag)
return kfrags
def assembleReencryptFragment(privRecipient:str, reKeyFrags:List[ReKeyFrag])->bytes:
privRecipientInt = int(privRecipient, 16)
privRecipientKey = ecdsa.SigningKey.from_secret_exponent(privRecipientInt, ecdsa.SECP256k1, hashlib.sha256)
precursor = bytes.fromhex(reKeyFrags[0].precurpub)
precursorPub = ecdsa.VerifyingKey.from_string(precursor, curve=ecdsa.SECP256k1)
dh_Bob_poit = signer.ecdh_point(precursorPub.pubkey.point, privRecipientInt)
dBobHash = hashlib.sha256()
dBobHash.update(precursorPub.pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
dBobHash.update(privRecipientKey.get_verifying_key().pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
dBobHash.update(dh_Bob_poit)
dBob = dBobHash.digest()
dBobBN = hashToModInt(dBob)
if len(reKeyFrags) == 1:
rPoint = EccPoint()
rPoint.setEccPoint(reKeyFrags[0].reKeyR)
uPoint = EccPoint()
uPoint.setEccPoint(reKeyFrags[0].reKeyU)
share_key = (rPoint + uPoint) * dBobBN
else:
eFinal = EccPoint()
vFinal = EccPoint()
ids = list()
for i in range(len(reKeyFrags)):
xs = hashlib.sha256()
xs.update(precursorPub.pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
xs.update(privRecipientKey.get_verifying_key().pubkey.point.x().to_bytes(32, byteorder='big', signed=False))
xs.update(dh_Bob_poit)
xs.update(int(reKeyFrags[i].random).to_bytes(32, byteorder='big', signed=False))
share = hashToModInt(xs.digest())
ids.append(share)
for i in range(len(ids)):
coeff = calcLambdaCoeff(ids[i], ids)
rPoint = EccPoint()
rPoint.setEccPoint(reKeyFrags[i].reKeyR)
uPoint = EccPoint()
uPoint.setEccPoint(reKeyFrags[i].reKeyU)
e = rPoint * coeff
v = uPoint * coeff
eFinal = e + eFinal
vFinal = v + vFinal
share_key = (eFinal + vFinal) * dBobBN
eckey = ecdsa.VerifyingKey.from_public_point(share_key.point, ecdsa.SECP256k1, hashlib.sha256).\
to_string(encoding="compressed")
return kdf(eckey.hex(), encKeyLength)