First test
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ZKP.md
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ZKP.md
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<img src='./PDPS.png' height=75% width=75% >
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```python
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from nacl.public import Box, PrivateKey, PublicKey
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from nacl.signing import SigningKey, SignedMessage
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from nacl.encoding import HexEncoder
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from ecdsa import ellipticcurve, curves, util, numbertheory
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import ecdsa as pyecdsa
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import hashlib
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import binascii
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from binascii import unhexlify
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import ecdsa as pyecdsa
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from ecdsa.ellipticcurve import INFINITY
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#SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10))
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SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10))
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```
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```python
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class Point(ellipticcurve.Point):
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def __init__(self, *args, **kwargs):
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kwargs.setdefault('order', SECP256k1.order)
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super(Point, self).__init__(SECP256k1.curve, *args, **kwargs)
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def __neg__(self):
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return Point( self.x(), -self.y())
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def __sub__(self, Q):
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a=self + -Q
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return Point(a.x(),a.y())
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```
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```python
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priv_key= PrivateKey.generate()
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signing_key=pyecdsa.SigningKey.generate( curve=SECP256k1)
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```
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```python
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#range for statistical zero-knowledge property.
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R=2**256 * 2**256 * 2**80
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B=16# 2**256
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K =16# 2**256
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```
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```python
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def long_to_bytes (val, endianness='big'):
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# one (1) hex digit per four (4) bits
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width = val.bit_length()
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# unhexlify wants an even multiple of eight (8) bits, but we don't
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# want more digits than we need (hence the ternary-ish 'or')
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width += 8 - ((width % 8) or 8)
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# format width specifier: four (4) bits per hex digit
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fmt = '%%0%dx' % (width // 4)
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# prepend zero (0) to the width, to zero-pad the output
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s = unhexlify(fmt % val)
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if endianness == 'little':
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# see http://stackoverflow.com/a/931095/309233
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s = s[::-1]
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return s
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```
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```python
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class Client(object):
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def __init__(O,key=None):
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if not key:
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O.k = signing_key=pyecdsa.SigningKey.generate( curve=SECP256k1)
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else :
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O.k = key
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def file_process(O,path="./slice.1_8.fec"):
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f="A"*32#open(path).read()
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D=util.string_to_number(f)
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b=util.string_to_number(O.k.to_string())
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s=D%b
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n=D//b
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D_1=(n * b) + s
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r = long_to_bytes(rr)
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print hashlib.sha1(f).hexdigest()
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print hashlib.sha1(r).hexdigest()
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b_id = SECP256k1.generator * n
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ro1= SECP256k1.generator * n
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ro2 = SECP256k1.generator * s
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#private, public
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return ((n,b,s), (b_id, ro1,ro2))
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def generate_challenge1(O):
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return util.randrange(R)
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```
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```python
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class server(object):
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def __init__(O, b_id, ro1,ro2):
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O.ro1=ro1
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O.ro2=ro1
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O.file_pub=b_id
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def commitment(O, challenge):
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f="A"*32#open("./slice.1_8.fec").read()
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a=util.string_to_number(f)
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O.b=challenge
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O.z=a%b
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O.m=a//b
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O.r = util.randrange(B**2)
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O.t = util.randrange(B**2)
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O.x1 = SECP256k1.generator * r
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O.x2 = SECP256k1.generator * t
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return ((O.x1,O.x2),(O.m,O.z,O.r,O.t))
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```
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```python
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c=Client()
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#s=server()
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#priv_c,pub_c=c.file_process()
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```
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```python
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def preprocessing():
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f=open("./slice.1_8.fec").read()
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D=util.string_to_number(f)
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b=util.string_to_number(signing_key.to_string())
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s=D%b
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n=D//b
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D_1=(n * b) + s
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#r = long_to_bytes(rr)
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print hashlib.sha1(f).hexdigest()
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#print hashlib.sha1(r).hexdigest()
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b_id = SECP256k1.generator * n
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ro1= SECP256k1.generator * n
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ro2 = SECP256k1.generator * s
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return ((n,b,s), (b_id, ro1,ro2))
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def generate_challenge(n,b,s):
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b_id = SECP256k1.generator * n
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ro1= SECP256k1.generator * n
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ro2 = SECP256k1.generator * s
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return (b_id, ro1,ro2)
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client_secret_priv, public_element = preprocessing()
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```
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73ea3b5e061b6cabed623d1f0f8ba0e2dd7a8ef4
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<img src='./algo_keys.png' height=25% width=50%>
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```python
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import ecdsa as pyecdsa
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SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10))
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SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10))
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def generate_priv_challenge():
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f=open("./slice.1_8.fec").read()
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blockid= hashlib.sha256(signing_key.sign(f)).hexdigest()
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a=util.string_to_number(f)
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b=util.string_to_number(signing_key.to_string())#encode())
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s=a%b
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n=a//b
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ro1= SECP256k1.generator * n
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ro2 = SECP256k1.generator * s
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return (blockid, ro1,ro2,n,s)
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```
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```python
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block_id,ro1,ro2,n,s = generate_priv_challenge()
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```
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<img src='./challenge.png' heigth=75% width=75%>
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```python
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def remote_commitment(chall):
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f=open("./slice.1_8.fec").read()
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a=util.string_to_number(f)
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b=chall
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z=a%b
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m=a//b
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print z
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r = util.randrange(B*B)
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t = util.randrange(B*B)
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#w= r^z
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#print w
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x1 = r * SECP256k1.generator
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x2 = t * SECP256k1.generator
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return ((x1,x2),(m,z,r,t))
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```
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```python
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chall = util.randrange(R)
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(commit,ch_resp)=commitment(chall)
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```
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```python
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chall2 = util.randrange(K)
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```
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```python
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def remote_resp(c, resp):
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m=resp[0]
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z=resp[1]
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r=resp[2]
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t=resp[3]
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y1= r+(c*z)
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y2= t+(c*m)
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return y1,y2
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```
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```python
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y1,y2 = host_resp(chall2, ch_resp)
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```
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```python
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chall = util.randrange(R)
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chall2 = util.randrange(K)
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P = SECP256k1.generator
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(commit,ch_resp)=remote_commitment(chall)
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y1,y2 = remote_resp(chall2, ch_resp)
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x1=commit[0]
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x2=commit[1]
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b_ = chall
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c = chall2
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z = ch_resp[1]
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m = ch_resp[0]
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```
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383769705759922238814820635125091393536751781330499963960027267106043604344928356482304970868177244815080981113707959740583852333897030317262689421782904643950974779849213407220
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<img src='./proof1.png'>
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```python
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as1_1= ( y1 * P ) + (-Point(x1.x(),x1.y()))#y1.P-x1
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as1_2= ( c * z ) * P #cz.P
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print "assert I", as1_1==as1_2
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print as1_1.x()
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print as1_2.x()
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as2_1=( y2 * P ) + ( -Point(x2.x(),x2.y()) )
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as2_2= (b_* m ) * P
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print "assert II", as2_1==as2_2
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print as2_1.x()
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print as2_2.x()
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```
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assert I True
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5876730895232555975670752555686052848272136747449052900777052125475456965293
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5876730895232555975670752555686052848272136747449052900777052125475456965293
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assert II False
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95958819438731652205001323648120835610712117261911186719618043262918945418931
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55940851260522358385586042305550878175039129341223631825528624425777497241555
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```python
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as2_1=(y2 * P) + (-Point(x2.x(),x2.y()))
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as2_2= (b_*m) * P
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print as2_1.x()
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print as2_2.x()
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```
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91728786092928355630891141238137171644308836139219436085412195700189316134122
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107279711877694500410709767952754959809170673439664368886384200698769658470714
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<img src='./equality.png'>
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```python
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SK=b=util.string_to_number(signing_key.to_string())
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chall*SK * ro1 - chall2 * (y2 * SECP256k1.generator + - Point(commit[0].x(),commit[0].y())
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```
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<ecdsa.ellipticcurve.Point at 0x106e16f50>
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```python
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%qtconsole
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```
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```python
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x1=commit[0]
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Y1=y1*SECP256k1.generator
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Y1=Point(Y1.x(),Y1.y())
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RO1=chall2*Point(ro1.x(),ro1.y())
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X1=Point(x1.x(),x1.y())
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RO1=Point(RO1.x(),RO1.y())
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assertion1 = Y1-X1-RO1
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```
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```python
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ro1.y()
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```
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```python
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sk=util.string_to_number(signing_key.to_string())
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curv=SECP256k1.curve
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#chall2*sk*ro2 - b*(y2.Gen-x2)
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tb1=chall2*sk*ro2
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x2=commit[1]
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#x2=Point(x2.x(),x2.y())
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Y2=SECP256k1.generator * y2
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Y2=Point(Y2.x(),Y2.y())
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X2=Point(x2.x(),x2.y())
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XY2=Y2-X2
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XY2 = - chall * XY2
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assertion2 = tb1 + XY2
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#Y3=Point(Y2.x(),Y2.y())
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#chall*(Y2-x2)
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#tb2 = chall*((SECP256k1.generator * y2) + invx2)
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#Z2=Point(tb2.x(),-tb2.y())
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#assertion2=tb1+Z2
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#chall
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```
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```python
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print assertion1==assertion2
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print assertion1.x()
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print assertion2.x()
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#Point(t1.x(),- t1.y())-Point(t1.x(),t1.y())
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```
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False
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7736584874372799755670583036719701680498164259870020736174578513076009517175
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26299729680235291815366724209282966839464132792531995892755583725140232542577
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