From 38d416b88e4830b9bb39e807bcdaa29ad0341bc0 Mon Sep 17 00:00:00 2001 From: pg Date: Thu, 1 Oct 2015 06:27:54 +0200 Subject: [PATCH] added more png --- PDPS.png | Bin 0 -> 85309 bytes ZKP.md | 416 ++++++++++++++++++++++++++++++++++++++++++++++++++ algo_keys.png | Bin 0 -> 176400 bytes challenge.png | Bin 0 -> 99858 bytes equality.png | Bin 0 -> 23570 bytes proof1.png | Bin 0 -> 25722 bytes 6 files changed, 416 insertions(+) create mode 100644 PDPS.png create mode 100644 ZKP.md create mode 100644 algo_keys.png create mode 100644 challenge.png create mode 100644 equality.png create mode 100644 proof1.png diff --git a/PDPS.png b/PDPS.png new file mode 100644 index 0000000000000000000000000000000000000000..1e595bfbbee49d326993075ccd256fddac406063 GIT binary patch literal 85309 zcmeGDRa9NgwuTD>0fGm2mq2hQcoN(pxVulB;O^URDel0UrSZ0s>h=T=+8t1PpKqWeo=f{G+%2 z9vT7yNyuDCNM1rnh*aL*#>5--c!L*2(sOa@-gcqpjTq5EPql`e`^(HeZ!_@__~K+Qb_zeQ(LDD 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0000000..3c54ba6 --- /dev/null +++ b/ZKP.md @@ -0,0 +1,416 @@ + + + + + + +```python +from nacl.public import Box, PrivateKey, PublicKey +from nacl.signing import SigningKey, SignedMessage + +from nacl.encoding import HexEncoder +from ecdsa import ellipticcurve, curves, util, numbertheory +import ecdsa as pyecdsa +import hashlib +import binascii +from binascii import unhexlify +import ecdsa as pyecdsa +from ecdsa.ellipticcurve import INFINITY + +#SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10)) +SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10)) +``` + + +```python + + +class Point(ellipticcurve.Point): + def __init__(self, *args, **kwargs): + kwargs.setdefault('order', SECP256k1.order) + super(Point, self).__init__(SECP256k1.curve, *args, **kwargs) + + def __neg__(self): + return Point( self.x(), -self.y()) + + def __sub__(self, Q): + a=self + -Q + return Point(a.x(),a.y()) + + +``` + + +```python +priv_key= PrivateKey.generate() +signing_key=pyecdsa.SigningKey.generate( curve=SECP256k1) + +``` + + +```python +#range for statistical zero-knowledge property. +R=2**256 * 2**256 * 2**80 +B=16# 2**256 +K =16# 2**256 +``` + + +```python +def long_to_bytes (val, endianness='big'): + + # one (1) hex digit per four (4) bits + width = val.bit_length() + + # unhexlify wants an even multiple of eight (8) bits, but we don't + # want more digits than we need (hence the ternary-ish 'or') + width += 8 - ((width % 8) or 8) + + # format width specifier: four (4) bits per hex digit + fmt = '%%0%dx' % (width // 4) + + # prepend zero (0) to the width, to zero-pad the output + s = unhexlify(fmt % val) + + if endianness == 'little': + # see http://stackoverflow.com/a/931095/309233 + s = s[::-1] + + return s + +``` + + +```python +class Client(object): + def __init__(O,key=None): + if not key: + O.k = signing_key=pyecdsa.SigningKey.generate( curve=SECP256k1) + else : + O.k = key + def file_process(O,path="./slice.1_8.fec"): + f="A"*32#open(path).read() + D=util.string_to_number(f) + b=util.string_to_number(O.k.to_string()) + + s=D%b + n=D//b + + D_1=(n * b) + s + r = long_to_bytes(rr) + + print hashlib.sha1(f).hexdigest() + print hashlib.sha1(r).hexdigest() + + + b_id = SECP256k1.generator * n + ro1= SECP256k1.generator * n + ro2 = SECP256k1.generator * s + #private, public + return ((n,b,s), (b_id, ro1,ro2)) + + def generate_challenge1(O): + return util.randrange(R) + + + +``` + + +```python +class server(object): + def __init__(O, b_id, ro1,ro2): + O.ro1=ro1 + O.ro2=ro1 + O.file_pub=b_id + + def commitment(O, challenge): + f="A"*32#open("./slice.1_8.fec").read() + a=util.string_to_number(f) + + O.b=challenge + O.z=a%b + O.m=a//b + O.r = util.randrange(B**2) + O.t = util.randrange(B**2) + O.x1 = SECP256k1.generator * r + O.x2 = SECP256k1.generator * t + + return ((O.x1,O.x2),(O.m,O.z,O.r,O.t)) + +``` + + +```python +c=Client() +#s=server() +#priv_c,pub_c=c.file_process() + +``` + + +```python +def preprocessing(): + f=open("./slice.1_8.fec").read() + D=util.string_to_number(f) + b=util.string_to_number(signing_key.to_string()) + + s=D%b + n=D//b + + D_1=(n * b) + s + #r = long_to_bytes(rr) + + print hashlib.sha1(f).hexdigest() + #print hashlib.sha1(r).hexdigest() + + + b_id = SECP256k1.generator * n + ro1= SECP256k1.generator * n + ro2 = SECP256k1.generator * s + + return ((n,b,s), (b_id, ro1,ro2)) + + +def generate_challenge(n,b,s): + + b_id = SECP256k1.generator * n + ro1= SECP256k1.generator * n + ro2 = SECP256k1.generator * s + + return (b_id, ro1,ro2) + + +client_secret_priv, public_element = preprocessing() + + + + +``` + + 73ea3b5e061b6cabed623d1f0f8ba0e2dd7a8ef4 + + + + + +```python +import ecdsa as pyecdsa + +SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10)) +SECP256k1 = pyecdsa.curves.find_curve((1, 3, 132, 0, 10)) + +def generate_priv_challenge(): + f=open("./slice.1_8.fec").read() + blockid= hashlib.sha256(signing_key.sign(f)).hexdigest() + a=util.string_to_number(f) + b=util.string_to_number(signing_key.to_string())#encode()) + s=a%b + n=a//b + ro1= SECP256k1.generator * n + ro2 = SECP256k1.generator * s + + return (blockid, ro1,ro2,n,s) + +``` + + +```python +block_id,ro1,ro2,n,s = generate_priv_challenge() +``` + + + + +```python +def remote_commitment(chall): + f=open("./slice.1_8.fec").read() + a=util.string_to_number(f) + b=chall + z=a%b + m=a//b + print z + r = util.randrange(B*B) + t = util.randrange(B*B) + #w= r^z + #print w + x1 = r * SECP256k1.generator + x2 = t * SECP256k1.generator + + return ((x1,x2),(m,z,r,t)) + + +``` + + +```python +chall = util.randrange(R) + +(commit,ch_resp)=commitment(chall) + +``` + + +```python +chall2 = util.randrange(K) +``` + + +```python +def remote_resp(c, resp): + m=resp[0] + z=resp[1] + r=resp[2] + t=resp[3] + + y1= r+(c*z) + y2= t+(c*m) + + return y1,y2 +``` + + +```python +y1,y2 = host_resp(chall2, ch_resp) +``` + + +```python +chall = util.randrange(R) +chall2 = util.randrange(K) + +P = SECP256k1.generator + + +(commit,ch_resp)=remote_commitment(chall) +y1,y2 = remote_resp(chall2, ch_resp) +x1=commit[0] +x2=commit[1] + +b_ = chall +c = chall2 + +z = ch_resp[1] +m = ch_resp[0] +``` + + 383769705759922238814820635125091393536751781330499963960027267106043604344928356482304970868177244815080981113707959740583852333897030317262689421782904643950974779849213407220 + + + + + +```python +as1_1= ( y1 * P ) + (-Point(x1.x(),x1.y()))#y1.P-x1 +as1_2= ( c * z ) * P #cz.P +print "assert I", as1_1==as1_2 +print as1_1.x() +print as1_2.x() +as2_1=( y2 * P ) + ( -Point(x2.x(),x2.y()) ) +as2_2= (b_* m ) * P +print "assert II", as2_1==as2_2 +print as2_1.x() +print as2_2.x() +``` + + assert I True + 5876730895232555975670752555686052848272136747449052900777052125475456965293 + 5876730895232555975670752555686052848272136747449052900777052125475456965293 + assert II False + 95958819438731652205001323648120835610712117261911186719618043262918945418931 + 55940851260522358385586042305550878175039129341223631825528624425777497241555 + + + +```python +as2_1=(y2 * P) + (-Point(x2.x(),x2.y())) +as2_2= (b_*m) * P +print as2_1.x() +print as2_2.x() + +``` + + 91728786092928355630891141238137171644308836139219436085412195700189316134122 + 107279711877694500410709767952754959809170673439664368886384200698769658470714 + + + + + + +```python +SK=b=util.string_to_number(signing_key.to_string()) +chall*SK * ro1 - chall2 * (y2 * SECP256k1.generator + - Point(commit[0].x(),commit[0].y()) +``` + + + + + + + + + +```python +%qtconsole +``` + + +```python +x1=commit[0] +Y1=y1*SECP256k1.generator +Y1=Point(Y1.x(),Y1.y()) +RO1=chall2*Point(ro1.x(),ro1.y()) +X1=Point(x1.x(),x1.y()) +RO1=Point(RO1.x(),RO1.y()) + +assertion1 = Y1-X1-RO1 +``` + + +```python +ro1.y() +``` + + +```python +sk=util.string_to_number(signing_key.to_string()) + +curv=SECP256k1.curve + +#chall2*sk*ro2 - b*(y2.Gen-x2) +tb1=chall2*sk*ro2 + +x2=commit[1] +#x2=Point(x2.x(),x2.y()) +Y2=SECP256k1.generator * y2 +Y2=Point(Y2.x(),Y2.y()) +X2=Point(x2.x(),x2.y()) +XY2=Y2-X2 +XY2 = - chall * XY2 + +assertion2 = tb1 + XY2 +#Y3=Point(Y2.x(),Y2.y()) + +#chall*(Y2-x2) +#tb2 = chall*((SECP256k1.generator * y2) + invx2) +#Z2=Point(tb2.x(),-tb2.y()) + +#assertion2=tb1+Z2 + + +#chall +``` + + +```python +print assertion1==assertion2 +print assertion1.x() +print assertion2.x() +#Point(t1.x(),- t1.y())-Point(t1.x(),t1.y()) +``` + + False + 7736584874372799755670583036719701680498164259870020736174578513076009517175 + 26299729680235291815366724209282966839464132792531995892755583725140232542577 + diff --git a/algo_keys.png b/algo_keys.png new file mode 100644 index 0000000000000000000000000000000000000000..d9bb2ae42a877bbb1bf1b13fb57a6137513cedd5 GIT binary patch literal 176400 zcmeFXV~}P+wk}-mvTfV8ZQHhO+qTUvb=kIU+tp>6U;{0xb@|6}$bK$Q$M@$p2h)w$PM6b;+f5dm85sY9Dt_9@ zz9xW2gP@4FFuk9kC1&0o7rj4#jQkIHaHvB82M31Ryp@eCe}!SISmo+(=XbZDU*g*M 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