Zhong - Helios Anonymity 2017.sagews

"""    This SageMath worksheet contains code for the 
        Equality of Discrete Logarithms Zero-Knowledge
        Proof System. The parameters p,q,g1 and hash 
        function should be used for the Assignment """

import hashlib

p = 19557005198709002903944860293031210393112763219086296641657077101075696217230957575932867920574816565856404011416908876733063974554042055901449481509845537165833627083609136426386625960849573203936690977282752217830467255076903813033768202255463477317279507253420233052258146393806024179130344501759742626253484354878829682461413002143954786668386100202257237258007726886368228024987052808444032800050116408995869561195208576647050961019393809940446490709061546503439488751331252440431940049716566765873615456614911458658341732120931319694200689362617296630728389003180670326151653001322354906363854478585334821235883

q = Integer((p-1)/2)


#m=1;
# g=2;
# m=0;
# x=ZZ.random_element(q);
# PK=power_mod(g,x,p);
# r=ZZ.random_element(q);
# R=power_mod(g,r,p);
# S=Integer(mod(power_mod(PK,r,p)*g**(m),p),p);
#g1 = 4; g2 = 3;
#x = ZZ.random_element(q);
# y1 = power_mod(g1,x,p);
# y2 = power_mod(g2,x,p);

def eqdlprove(p,q,g1,g2,y1,y2,x):
  r = ZZ.random_element(q);
  com1 = power_mod(g1,r,p);
  com2 = power_mod(g2,r,p);
  hash_value = hashlib.sha256(str(y1) + str(y2) + str(com1) + str(com2)).hexdigest();
  ch = Integer(int(hash_value,16),q);
  s = Integer(Mod(r + x * ch,q));
  return [ch,s,hash_value]

def myeqdlprove(g,c1,h,c2,x):
  g1=g;
  g2=h;
  r = ZZ.random_element(q);
  com1 = power_mod(g1,r,p);
  com2 = power_mod(g2,r,p);
  hash_value = hashlib.sha256(str(c1) + str(c2) + str(com1) + str(com2)).hexdigest();
  ch = Integer(int(hash_value,16),q);
  s = Integer(Mod(r + x * ch,q));
  return [ch,s]

def disjprove(p,q,S,PK,g,R,r):
  #r=ZZ.random_element(q);
  #PK=power_mod(g,x,p);
  #R=power_mod(g,r,p);
  #S=Integer(mod(power_mod(PK,r,p)*g**(m),p),p);
  #S=Integer(mod(power_mod(PK,r,p)*g**(m),p));
  #S=Integer(mod(power_mod(PK,r,p)*power_mod(g,m,p),p));
  ch0 = ZZ.random_element(q);
  rep0=ZZ.random_element(q);
  U0=mod(power_mod(g,rep0,p)/power_mod(R,ch0,p),p);
  V0=mod(power_mod(PK,rep0,p)/power_mod(S,ch0,p),p);
  u1=ZZ.random_element(q);
  U1=power_mod(g,u1,p);
  V1=power_mod(PK,u1,p);
  hash_value = hashlib.sha256(str(R) + str(S) + str(U0) + str(V0)+str(U1)+str(V1)).hexdigest();
  ch = Integer(int(hash_value,16),q);
  ch1=Integer(Mod((ch-ch0),q));
  rep1=Integer(Mod(u1+ch1*r,q));

  return [ch0,ch1,rep0,rep1]

def disjprove2(p,q,S,PK,g,R,r):
  #r=ZZ.random_element(q);
  #PK=power_mod(g,x,p);
  #R=power_mod(g,r,p);
  #S=Integer(mod(power_mod(PK,r,p)*g**(m),p),p);
  #S=Integer(mod(power_mod(PK,r,p)*g**(m),p));
  #S=Integer(mod(power_mod(PK,r,p)*power_mod(g,m,p),p));
  ch1 = ZZ.random_element(q);
  rep1=ZZ.random_element(q);
  U1=mod(power_mod(g,rep1,p)/power_mod(R,ch1,p),p);
  V1=mod(power_mod(PK,rep1,p)/power_mod(Integer(S*inverse_mod(g,p)),ch1,p),p);
  u0=ZZ.random_element(q);
  U0=power_mod(g,u0,p);
  V0=power_mod(PK,u0,p);
  hash_value = hashlib.sha256(str(R) + str(S) + str(U0) + str(V0)+str(U1)+str(V1)).hexdigest();
  ch = Integer(int(hash_value,16),q);
  ch0=Integer(Mod((ch-ch1),q));
  rep0=Integer(Mod(u0+ch0*r,q));

  return [ch0,ch1,rep0,rep1]

2046

[ch0,ch1,rep0,rep1]=disjprove2(p,q,S,PK,g,R,r)

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> NameError: name 'S' is not defined

471777347440367626918212757109010736981968888843601640976481725797355712944716646751332705419472153716560114622030660913358270423626682693405517995843828173577023353153090736852134794554442052363913373322025696200895393408913502915169992289177960579971337149457081988333689989766164257787288182173190925951772680319490407914023299815872180404209168873789699440709239900003811395375387631307708242872052425743192998393950906694411435123423414484523046812561634542036937539670416119870947657600348200679182706799584841683361353888707573193203405079459120989409464646428032591616175871690634566661815135457651033623657
              17333048191029285402656599149750941933567927997187611870139847625029826454555738839558396807532916927518988847759387330802584937018925689524146297088750054201161086390827911044019140074087516900493279893510552138594768435862916249986068757909765715691150545937089124440010653831932711108053017173622664836017817983855768560715169628853764713430291498898152726204281359304608823994043001349519258356133670075974717992000192282612691180140654682679866229519705611954462762220973353430156474960821565482452367993225920841591743203737053399667954463926297776377760833440012903343232328841851897710685575742181299749556001
              12599553145256429926520271162743653005564246354704734031159918290965218671553249727597951517206318753994276435815250895643234974375394519350697360112628788060297172521207352949866327315582151122029766118278437788597037985511115310708601736874564062131998445482913168626236389644382229978364165640524146318890166903013743217332577558006560566615043325023878139582313114378332273538417700437616728792487042302805478894632543568250737724809644648037741702496827141685184274726087152463278364653571504398375947509118077301360761198537632278233057366999981102772297225538461050302451712554133322997620116693204612210294996

def disjverify(g,PK,R,S,ch0,ch1,rep0,rep1):
    u0=mod(power_mod(g,rep0,p)/power_mod(R,ch0,p),p);
    v0=mod(power_mod(PK,rep0,p)/power_mod(S,ch0,p),p);
    u1=mod(power_mod(g,rep1,p)/power_mod(R,ch1,p),p);
    v1=mod(power_mod(PK,rep1,p)/power_mod(Integer(S*inverse_mod(g,p)),ch1,p),p);
    hash_value2 = hashlib.sha256(str(R) + str(S) + str(u0) + str(v0)+str(u1)+str(v1)).hexdigest();
    ch2 = Integer(int(hash_value2,16),q);
    ch=mod(ch0+ch1,q);
    return ch==ch2

disjverify(g,PK,R,S,ch0,ch1,rep0,rep1)

True

clear

<function clear at 0x7fd5203a75f0>

[ch,s,hash_value] = eqdlprove(p,q,g1,g2,y1,y2,x);
print("challenge = " + str(ch) + "\n")
print("solution = " + str(s)+ "\n")
print("hash_value" + str(hash_value))

challenge = 83155204311621940942984014210400273456747855202255373325138368703134416484655 solution = 3698248624868163379947345302858925915624106351186017645684648561651578630261522680981743122247020496664305166473612776983855464463579372685077221832041458310232632285251887866461887718032115411981831168131983095402897000297455431084965792003138761001958412974009297604156353911325468058532448438760935898988421818611199650604925086193748930096640023804983864823202283746461603762580964842672824581358963875525685604745209299920526100336290367640411262653994986280219928256914950768327633074738109361379006307552502029498754114097084532574841167506007431906574142991262823987762894968308178227661867078302199036034580 hash_valueb7d82d80f180e22c6d2638116371b455bd2af71ef13df2a327f8766b247fb92f

def eqdlverify(p,q,g1,g2,y1,y2,ch,s):
    com1 = Mod(power_mod(g1,s,p) * inverse_mod(power_mod(y1,ch,p),p),p);
    com2 = Mod(power_mod(g2,s,p) * inverse_mod(power_mod(y2,ch,p),p),p);
    hash_value = hashlib.sha256(str(y1) + str(y2) + str(com1) + str(com2)).hexdigest();
    return ch == Integer(int(hash_value,16),q)

eqdlverify(p,q,g1,g2,y1,y2,ch,s)

False

def setup(g):
   x=ZZ.random_element(q);
   PK=power_mod(g,x,p);
   key=[x,PK,g]
   return key

key=setup(3)
key

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "", line 2, in setup NameError: global name 'q' is not defined

def vote(v):
    g=key[2];
    PK=key[1];
    r=ZZ.random_element(q);
    R=power_mod(g,r,p);
    S=Integer(mod(power_mod(PK,r,p)*g**(v),p));
    C=[R,S]
    if v==1:
       [ch0,ch1,rep0,rep1]=disjprove(p,q,S,PK,g,R,r);
    else:
       [ch0,ch1,rep0,rep1]=disjprove2(p,q,S,PK,g,R,r);
    N=[ch0,ch1,rep0,rep1];
    b=[C,N]
    return b
    
    
    
    
    
               
           

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> IndexError: list index out of range

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> IndexError: list index out of range

# def vote(v,g,x,PK):
#     r=ZZ.random_element(q);
#     R=power_mod(g,r,p);
#     S=Integer(mod(power_mod(PK,r,p)*g**(v),p));
#     C=[R,S]
#     if v==1:
#        [ch0,ch1,rep0,rep1]=disjprove(p,q,S,PK,g,R,r);
#     else:
#        [ch0,ch1,rep0,rep1]=disjprove2(p,q,S,PK,g,R,r);
#     N=[ch0,ch1,rep0,rep1];          
#     return [R,S,N,x,g,PK]

def validate(b):
    g=key[2];
    PK=key[1];
    C=b[0];
    N=b[1];
    R=C[0];
    S=C[1];
    ch0=N[0];
    ch1=N[1];
    rep0=N[2];
    rep1=N[3];
    u0=mod(power_mod(g,rep0,p)/power_mod(R,ch0,p),p);
    v0=mod(power_mod(PK,rep0,p)/power_mod(S,ch0,p),p);
    u1=mod(power_mod(g,rep1,p)/power_mod(R,ch1,p),p);
    v1=mod(power_mod(PK,rep1,p)/power_mod(Integer(S*inverse_mod(g,p)),ch1,p),p);
    hash_value2 = hashlib.sha256(str(R) + str(S) + str(u0) + str(v0)+str(u1)+str(v1)).hexdigest();
    ch2 = Integer(int(hash_value2,16),q);
    ch=mod(ch0+ch1,q);    
    if ch == ch2:
         return "accept"
    else:
         return "reject"

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> NameError: name 'b' is not defined

def tally(Bb,sk):
     R_r=1;
     S_r=1;
     for b in Bb:
         if validate(b) == 'reject':
          result="invalid";
          pi_e="null" 
          break;    
         else:
          result="accept" 
          R_r=Integer(mod(b[0][0]*R_r,p));
          S_r=Integer(mod(b[0][1]*S_r,p));
     if result != "invalid":
        g_r=Integer(mod(S_r*inverse_mod(power_mod(R_r,sk,p),p),p));
        c1=R_r;
        c2=Integer(mod(S_r*Integer(inverse_mod(g_r,p)),p));
        [ch,s]=myeqdlprove(g,c1,h,c2,sk)
        pi_e=[ch,s]
        for i in range(100):
            if power_mod(g,i,p) == g_r:
               result=i;
     return [result,pi_e]         
              
        

myhas=hashlib.sha256('Anonymity_Privacy_and_Cybercrime_Zhong_').hexdigest(); 
myhas

'20351442a61b827a45107600114f448b40e55c1f185d5ad20cadbfa613f84065'

def myvote():
    Bb=[0]*15;          
    for i in range(15):
     if i < 5:
      Bb[i]=vote(1);
     else:
      Bb[i]=vote(0);
    return Bb          
              

Bb=myvote();
h=key[1];
g=key[2];
sk=key[0];              
[result,pi_e]  =tally(Bb,sk)
result

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "", line 5, in myvote File "", line 2, in vote NameError: global name 'key' is not defined