def rsa(p,q,k):
t = time() # we start the clock here
rngs = deque() # store the rngs for testing
n = p*q
phi = (p-1) * (q-1)
e = (p-1) # this block of code choses e so that gcd(e,phi)=1
while ( gcd(e,phi) != 1):
e = randint(2, phi-1)
x_0 = (p-1) # this block of code choses x_0 so that gcd(x_0,phi)=1
while ( gcd(e,phi) != 1):
x_0 = randint(2, phi-1)
z=0
for a in range(k): # here we generate k values
x_0 = pow(x_0,e,n)
rngs.append(x_0%2)
t=time()-t
print('--------')
print('{0} bits generated with RSA'.format(k))
print('Generating time: {0}'.format(t))
sarray = stest(rngs)
sarray.insert(0,t)
return sarray
def bbs(p,q,k): #Blum Blum Shub Random Bit generator. Input two large primes 3mod4 and the number of bits in the output
t = time() # start the clock
rngs = deque() # store the rngs for testing
n = p*q
phi = (p-1) * (q-1) # phi is the number of elements in the multiplicative group of Z/nZ
x_0 = (p-1) # x_0 is the seed
while ( gcd(x_0,phi) != 1): #this block of code chooses x_0 so that gcd(x_0,phi)=1
x_0 = randint(2, phi-1)
z=0 # initialize z (the bit component)
for a in range(k): # generate sequence of k integers
x_0 = (x_0*x_0) % n
if (x_0 > n / 2):
x_0 = n - x_0
z = x_0 % 2
rngs.append(z)
t=time()-t
print('--------')
print('{0} bits generated with BBS'.format(k))
print('Generating time: {0}'.format(t))
sarray = stest(rngs)
sarray.insert(0,t)
return sarray
def bm(p,k):
t=time() #start the clock
rngs=deque()
#find primitive root mod p and set to g
phi=p-1
pf=pfac(phi) # pf is the array of prime factors of phi
works = 0 #find a primitive root modp
while works == 0:
works = 1
g=randint(2,p-2)
for j in pf:
if pow(g,int(phi/j),p)==1:
works=0
break
x_0 = randint(2,p-1) #x_0 is the seed
for a in range(k): #generate a sequence of k integers
x_0=pow(g,x_0,p)
if x_0 < float(p-1)/2:
z=1 #z is the actual bit
else:
z=0
rngs.append(z)
t=time()-t
print('--------')
print('{0} bits generated with BM'.format(k))
print('Generating time: {0}'.format(t))
sarray = stest(rngs)
sarray.insert(0,t)
return sarray
def dec(p,k): #Dual Elliptic Curve Deterministic Random Bit Generator with k bits generated by the curve y^2 = x^3 + ax + b over Z/pZ where p is a prime 3mod4
rngs = deque()
t = time() # start the clock
n = 2 # number seed is multiplied by at each step
a=0
b=0
while(4*pow(a,3)+27*pow(b,2)==0): #here we ensure the curve is nonsingular
a=randint(1,p-1)
b=randint(1,p-1)
c=0 # used to produce seed
while(c!=1): # (x,y) is the seed
x = randint(0,p-1)
c = pow(x^3 + a*x + b, int((p-1)/2), p)
y = pow(x^3 + a*x + b, int((p+1)/4), p)
z=0 # initialize z (the bit component)
for a in range(k): # generate sequence of k points
(x,y) = ecmult(x,y,n,a,b,p)
z = (x + y) % 2
rngs.append(z)
t=time()-t
print('--------')
print('{0} bits generated with Dual E. Curve'.format(k))
print('Generating time: {0}'.format(t))
sarray = stest(rngs)
sarray.insert(0,t)
return sarray
