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fullyHomo.py
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fullyHomo.py
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import random
import math
import bigfloat
import ast
from circuit import *
from common import *
debug=False
# Parameters
"""
Lambda #security parameter
w size of the plain text integer
"""
Lambda = 4 #security parameter
w=1 #size of the plain text integer here it is zero or 1 so only 1 bit
def D(gamma,rho,p):
#q=random.randrange(1,int(2**gamma/p-1))
q=random.randrange(int(2*gamma),int(2**gamma/p-1)) #Avoiding smaller values
#q=random.randrange(1,int(2*gamma)) #Control over length of public keys
r=random.randrange(-2**rho,2**rho)
#r=1
x=p*q+r
return x
def D1(gamma,rho,p,i):
q=random.randrange(int(2**(gamma+i-1)/p),int(2**(gamma+i)/p-1))
#q=random.randrange(int(4*(gamma+i-1)/p),int(16*(gamma+i)+1)) #Control over length of public keys
r=random.randrange(-2**rho,2**rho)
#r=0
x=2*(p*q+r)
return x
def Initialize(Lambda):
if Params.theta==0:
Params.rho=int(w*log2(Lambda)) # size of noise
Params.rho1=int(w*log2(Lambda)+1) # size of secondary noise
Params.eta=int(Params.rho*Lambda*log2(Lambda)**2) #size of private key
Params.gamma=int(w*(Params.eta**2)*log2(Lambda)) #Bit length of integers in public key
Params.tho=int(Params.gamma+w*log2(Lambda))# number of integers in the public key
Params.kappa = Params.gamma + 2
Params.theta = Lambda
Params.bigo = int(w * Params.kappa * log2(Lambda)/32)
Params.prec = int(log2(Params.theta)+3.5)
Params.n = Params.prec+1
Params.logtheta = int(log2(Params.theta))+1
def SomeWhatKeyGen(Lambda):
Initialize(Lambda)
largestKey=8**(Params.eta*(2**Params.rho1))-1
smallestKet=8**(Params.eta*(2**Params.rho1)-1)+1
p = random.randrange(smallestKet,largestKey,2)
sk = p
x0=1
while mods(x0,p)%2 != 0:
pk0=[]
for i in range(0,Params.tho/32+1):
t=D(Params.gamma,Params.rho,p)
while t in pk0:
t=D(Params.gamma,Params.rho,p)
pk0.append(t)
x0=max(pk0)
pk0.remove(x0)
if x0%2==0:
x0=x0+1
m = x0/p
if m%2==0:
m+=1
else:
m+=2
x0=m*p
pk0=[x0]+pk0
x=[]
for i in range (1,Params.gamma+1):
x.append(D1(Params.gamma,Params.rho,p,i))
pk=(pk0,x)
return (sk,pk)
def SomeWhatEncrypt(pk,m,p=1):
#use p for debugging purpose
(pk0,x)=pk
t=Params.tho/32
l=random.randrange(2,int(Params.tho/128))
s=0
pk2=pk0[:]
for i in range(0,l):
k=pk2[random.randrange(1,t)]
#pk2.remove(k)
#t-=1
s+=k
#print m,mods((m+2*s)%pk[0],p)%2
r = random.randrange(-2**Params.rho1,2**Params.rho1)
#r = 0
return (m+2*r+2*s)%pk0[0]
def SomeWhatEvaluate(pk,cl,ck):
(pk0,x0)=pk
k=ck(cl)
x=x0[:]
while x:
k=k%x[-1]
del x[-1]
return k
def SomeWhatDecrypt(sk,c):
t = sk/2
if debug:
x = int(bigfloat.div(c,sk,bigfloat.precision(1000)))
y = c/sk
print "SomeWhatDecrypt:x:",x
print "SomeWhatDecrypt:y:",y
print "SomeWhatDecrypt:c%sk:",c%sk
print "SomeWhatDecrypt:c-x*sk:",c-x*sk
return (c-(c+t)/sk)%2
def KeyGen(Lambda):
global globsk #For debugginh
(sk0,pk0)=SomeWhatKeyGen(Lambda)
globsk = sk0 #For debugging
#Params.kappa = int(Params.gamma * Params.eta / Params.rho1)
'''Tweak to approximate to nearest integer'''
t=sk0/2+1
xp=int((2**Params.kappa+t)/sk0) # Approximating to nearest integer
S = []
lenS=0
while lenS!=Params.theta:
i=random.randrange(1,Params.bigo)
if i not in S:
S.append(i)
lenS+=1
s={}
for i in range(1,Params.bigo+1):
if i in S:
s[i]=1
else:
s[i]=0
n = 2**(Params.kappa)
m = 2**(Params.kappa+1)
u = {}
approx = xp/Params.theta
var = approx/Params.theta
for i in range(1,Params.bigo+1):
u[i]=random.randrange(0,m)
su=0
for i in S[:-1]:
x =random.randrange(approx-var,approx+var)
u[i]=x
su+=u[i]
i=S[-1]
u[i]=xp-su
y={}
for i in range(1,Params.bigo+1):
y[i]=bigfloat.div(u[i],n,bigfloat.precision((Params.kappa+Params.gamma)))
#DEBUG
if debug:
su = 0
su2=0
for i in S:
su2+=u[i]
su=bigfloat.add(su,y[i],bigfloat.precision(Params.kappa+Params.gamma))
inv = bigfloat.mul(n,y[i],bigfloat.precision(Params.kappa+Params.gamma))
print u[i]
print inv
print "sumxp=",su2
print "sumf=",su
print "xp=", xp
print "xp/n=", bigfloat.div(xp,n,bigfloat.precision(Params.kappa+Params.gamma))
print "m=",m
print Params.theta
print Params.bigo
print S
print s
#END DEBUG
(pk1,x)=pk0
pk = (pk1,x,y)
return (s,pk)
def Encrypt(pk,m,calcZ=True,s=None):
#s is the secret key to be used for debugging purposes
(pk0,x,y)=pk
c0 = SomeWhatEncrypt((pk0,x), m)
if calcZ:
z=[None]*(Params.bigo+1)
for i in range(1,Params.bigo+1):
k=bigfloat.mul(c0,y[i],bigfloat.precision((Params.kappa+Params.gamma)))
z[i]=float(bigfloat.mod(k,2.0,bigfloat.precision(Params.prec)))
if z[i]>=2.0:
z[i]=0
c = (c0,z)
else:
c = c0
if debug:
su=0
for i in range(1,Params.bigo+1):
if s and s[i]==1:
su=bigfloat.add(su,z[i],bigfloat.precision(Params.kappa+Params.gamma))
print "Enc_sum%2=",bigfloat.mod(su,8,bigfloat.precision((Params.prec+Params.gamma)))
q=bigfloat.div(c0,globsk,bigfloat.precision(Params.kappa+Params.gamma))
print "(Enc_c/sk)%2=",bigfloat.mod(q,8,bigfloat.precision((Params.prec+Params.gamma)))
print "c0=",c0
return c
def Evaluate(pk,cl,ck,s={}):
#S is for debugging
(pk0,x,y)=pk
cl0=[]
for (i,j) in cl:
cl0.append(i)
c0 = SomeWhatEvaluate((pk0,x), cl0, ck)
z=[None]*(Params.bigo+1)
for i in range(1,Params.bigo+1):
k=bigfloat.mul(c0,y[i],bigfloat.precision((Params.kappa+Params.gamma)))
z[i]=float(bigfloat.mod(k,2,bigfloat.precision((Params.prec))))
if debug:
su=0
yo=0
for i in range(1,Params.bigo+1):
if s[i]==1:
yo=bigfloat.add(yo,y[i],bigfloat.precision((Params.kappa+Params.gamma)))
su=bigfloat.add(su,z[i],bigfloat.precision(Params.kappa+Params.gamma))
print "Enc_sum%2=",bigfloat.mod(su,8,bigfloat.precision((Params.prec+Params.gamma)))
q=bigfloat.div(c0,globsk,bigfloat.precision(Params.kappa+Params.gamma))
print "(c0/sk)=",q
q=bigfloat.mul(c0,yo,bigfloat.precision((Params.kappa+Params.gamma)))
print "(c0*yo)=",q
q=bigfloat.div(1,globsk,bigfloat.precision(Params.kappa+Params.gamma))
print "(1/sk)=",q
print "(yo)=",yo
print "(c0*1/sk)=",bigfloat.mul(q,c0,bigfloat.precision((Params.prec+Params.gamma)))
q=bigfloat.div(c0,globsk,bigfloat.precision((Params.prec+Params.gamma)))
print "(c0/sk)=",q
c = (c0,z)
return c
def Decrypt(sk,c,calcZ=True,sk1=1):
#sk1 is for debugging purpose
su=0
if calcZ:
(c0,z) = c
for i in range(1,Params.bigo+1):
if sk[i]!=0:
su=bigfloat.add(su,z[i],bigfloat.precision(Params.prec))
else:
c0 = c
if Keys.PK==None:
print "Error: Z vector must be provided when public key not available"
exit()
y = Keys.PK[2]
for i in range(1,Params.bigo+1):
if sk[i]!=0:
z = bigfloat.mul(c0,y[i],bigfloat.precision(Params.kappa))
z = float(bigfloat.mod(z,2,bigfloat.precision(Params.prec)))
su=bigfloat.add(su,z,bigfloat.precision(Params.prec))
su=int(bigfloat.round(su))
m = (c0-su) % 2
return m
def EncryptVector(pk,v,calcZ=True):
l=v[:]
c=[]
while l:
m = l[0]
c0 = Encrypt(pk, m, calcZ=calcZ)
c.append(c0)
del l[0]
return c
def DecryptVector(sk,c, calcZ=True):
l=c[:]
v=[]
while l:
c0 = l[0]
v0 = Decrypt(sk, c0, calcZ)
v.append(v0)
del l[0]
return v
def EvaluateVector(pk,cl,ck,calcZ=True):
(pk0,x0,y)=pk
r=[]
if calcZ:
cl0=[]
for (i,j) in cl:
cl0.append(i)
else:
cl0=cl
ck.setReductionVector(x0) #This is added to Trees constructor
r0 = ck.eval(cl0)
if calcZ:
for c0 in r0:
z=[None]*(Params.bigo+1)
for i in range(1,Params.bigo+1):
k=bigfloat.mul(c0,y[i],bigfloat.precision(Params.kappa))
z[i]=float(bigfloat.mod(k,2,bigfloat.precision(Params.prec)))
c = (c0,z)
r.append(c)
else:
r=r0
return r
def EncryptKey(sk,pk):
v=[]
for i in range(1,Params.bigo+1):
m = sk[i]
c=Encrypt(pk, m, calcZ=False)
#c = sk[i]
v.append(c)
return v
def TestSomeWhatCrypt():
(sk,pk) = SomeWhatKeyGen(Lambda)
m1=1
m2=1
for i in range(0,1000):
c1=SomeWhatEncrypt(pk, m1)
c2=SomeWhatEncrypt(pk, m2)
c=SomeWhatEvaluate(pk,[c1,c2],mul)
print SomeWhatDecrypt(sk, c)
def Test():
m1=0
m2=0
m3=1
m4=1
(sk,pk)=KeyGen(Lambda)
c1=Encrypt(pk, m1)
for i in range(0,100):
c2=Encrypt(pk, m2)
cc1=Encrypt(pk, m3)
cc2=Encrypt(pk, m4)
#print c1
c3=Evaluate(pk,[cc1,cc2],mul,sk)
c4=Evaluate(pk,[c1,c2],mul,sk)
c5=Evaluate(pk,[c2,c3],mul,sk)
c6=Evaluate(pk,[c1,c3],mul,sk)
c7=Evaluate(pk,[c4,c5],add,sk)
c=Evaluate(pk,[c7,c6],add,sk)
#print c
print Decrypt(sk, c)
c1 = c
def TestVector():
# m1=[1,0,0,1,1,0,1,1]
# m2=[0,1,1,1,0,0,1,0]
m1=[1,0,0,1]
w1=[0,0,1,0]
m2=[0,1,1,1]
w2=[0,0,1,1]
(sk,pk)=KeyGen(Lambda)
for i in range(0,1):
c1=EncryptVector(pk, m1)
wc1=EncryptVector(pk, w1)
c2=EncryptVector(pk, m2)
wc2=EncryptVector(pk, w2)
#print c1
t=Tree(Circuits.WEIGHTED_SUM_4, pk)
c=EvaluateVector(pk,c1+wc1+c2+wc2,t)
print c
print DecryptVector(sk, c1)
print DecryptVector(sk, c2)
print DecryptVector(sk, c)
def TestHamming():
m1=[1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1]
(sk,pk)=KeyGen(Lambda)
c1=EncryptVector(pk, m1)
d = DecryptionCircuit()
w=d.hammingWeightCircuit(len(m1),3)
t=Tree(w)
c2=EvaluateVector(pk, c1, t)
print DecryptVector(sk, c2)
def TestDecryption():
m1 = 1
(sk,pk)=KeyGen(Lambda)
for i in range(0,100):
esk = EncryptKey(sk, pk)
c1=Encrypt(pk, m1, sk)
# sum = 0
# for i in range(1,Params.bigo+1):
# if sk[i]==1:
# print floatToBin([c1[1][i]],Params.n)
# sum+=c1[1][i]
# print sum
d = DecryptionCircuit(pk,esk)
d.setPrivateKey(sk)
# c2=d.partialRecrypt(c1[0])
# m2 = DecryptVector(sk, c2)
# l=len(m2)/2
# m3=m2[0:l]
# m4=m2[l:]
# print m3
# print m4
# print bin2float(m3, Params.n+1)
# print bin2float(m4, Params.n+1)
# d = DecryptionCircuit(pk,esk)
# c2=d.partialRecrypt(c1[0])
# m2 = DecryptVector(sk, c2)
# print c1[0]%2
# print bin2float(m2, Params.prec+3)
# m3 = Decrypt(sk, c1)
# print "D=",m3
c2=d.recryptWrapper(c1[0])
m2 = Decrypt(sk, c2)
print m2
#print bin2float(m2, 19)
def TestVectorWithBootStrap():
# m1=[1,0,0,1,0,1,1,0]
# m2=[0,0,1,1,0,1,0,1]
m1=[1,0,0,1]
w1=[0,0,1,1]
m2=[0,1,1,1]
w2=[0,0,1,1]
(sk,pk)=KeyGen(Lambda)
Keys.PK=pk
for i in range(0,1):
c1=EncryptVector(pk, m1, calcZ=False)
wc1=EncryptVector(pk, w1, calcZ=False)
c2=EncryptVector(pk, m2, calcZ=False)
wc2=EncryptVector(pk, w2, calcZ=False)
#print c1
esk=EncryptKey(sk, pk)
d=DecryptionCircuit(pk,esk)
t=Tree(Circuits.WEIGHTED_SUM_4,pk,d)
c=EvaluateVector(pk,c1+wc1+c2+wc2,t,calcZ=False)
print c
print DecryptVector(sk, c1, calcZ=False)
print DecryptVector(sk, c2, calcZ=False)
print DecryptVector(sk, c, calcZ=False)
if __name__=="__main__":
import profile
#profile.run('TestVector()')
TestVectorWithBootStrap()