def generateN():
'''
This function is used to generate two prime numbers p, q while guaranteeing:
1. p != q
2. p, q are coprime to e
3. 2 left most bits of p and q are set
ret: p, q, n
'''
generator = PrimeGenerator(bits=128)
p = -1
q = -1
while (True):
p = generator.findPrime()
q = generator.findPrime()
while (q == p):
q = generator.findPrime()
if gcd((p - 1), e) == 1 and gcd((q - 1), e) == 1:
break
with open("p.txt", "w") as fp:
print(p, end='', file=fp)
with open("q.txt", "w") as fp:
print(q, end='', file=fp)
print("p and q generated")
def create_keys():
#creates the keys
e = BitVector(intVal = 65537)
uno = BitVector(intVal = 1)
tres = BitVector(intVal = 3)#used for checking the last two bits
generator = PrimeGenerator( bits = 128, debug = 0 )
p = BitVector(intVal = generator.findPrime())
while (p[0:2] != tres and int (e.gcd(BitVector(intVal = int(p)-1))) != 1):
p = BitVector(intVal = generator.findPrime())
q = BitVector(intVal = generator.findPrime())
while (q[0:2] != tres and int (e.gcd(BitVector(intVal = int(q)-1))) != 1 and p != q):
q = BitVector(intVal = generator.findPrime())
n = int(p) *int( q)
n = BitVector(intVal = n)
to = BitVector(intVal =((int(p)-1)*(int(q)-1)))
d = e.multiplicative_inverse(to)
d = int(d)
e = int (e)
n = int (n)
p = int (p)
q = int (q)
with open('private_key.txt', 'w') as f :
f.write(str(d)+"\n")
f.write(str(n)+"\n")
f.write(str(p)+"\n")
f.write(str(q)+"\n")
with open('public_key.txt', 'w') as f:
f.write(str(e)+"\n")
f.write(str(n)+"\n")
def create_keys():
#creates the keys
e = BitVector(intVal=65537)
uno = BitVector(intVal=1)
tres = BitVector(intVal=3) #used for checking the last two bits
generator = PrimeGenerator(bits=128, debug=0)
p = BitVector(intVal=generator.findPrime())
while (p[0:2] != tres and int(e.gcd(BitVector(intVal=int(p) - 1))) != 1):
p = BitVector(intVal=generator.findPrime())
q = BitVector(intVal=generator.findPrime())
while (q[0:2] != tres and int(e.gcd(BitVector(intVal=int(q) - 1))) != 1
and p != q):
q = BitVector(intVal=generator.findPrime())
n = int(p) * int(q)
n = BitVector(intVal=n)
to = BitVector(intVal=((int(p) - 1) * (int(q) - 1)))
d = e.multiplicative_inverse(to)
d = int(d)
e = int(e)
n = int(n)
p = int(p)
q = int(q)
with open('private_key.txt', 'w') as f:
f.write(str(d) + "\n")
f.write(str(n) + "\n")
f.write(str(p) + "\n")
f.write(str(q) + "\n")
with open('public_key.txt', 'w') as f:
f.write(str(e) + "\n")
f.write(str(n) + "\n")
def key_gen():
# use e = 65537
e = 65537
# find values for p and q
prime_generator = PrimeGenerator(bits=128)
gcd_p = 0
gcd_q = 0
p = BitVector(size=0)
q = BitVector(size=0)
# while the generated primes don't meet the conditions, repeat the calculation
while gcd_p != 1 and gcd_q != 1 and p == q:
p = BitVector(intVal=prime_generator.findPrime())
q = BitVector(intVal=prime_generator.findPrime())
# set first two and last bit
p[0:2] = BitVector(bitstring='11')
p[127] = 1
q[0:2] = BitVector(bitstring='11')
q[127] = 1
# check if p-1 and q-1 are co-prime to e
gcd_p = gcd(p.int_val() - 1, e)
gcd_q = gcd(q.int_val() - 1, e)
return p.int_val(), q.int_val()
def prime_gen(
e): ## compute the p and q values. Test that those are valid values.
generator = PrimeGenerator(bits=32, debug=0)
p = generator.findPrime()
q = generator.findPrime()
if p == q: ##test 1
p, q = prime_gen(e)
return p, q
tempp = p
tempq = q
test1 = 0
test2 = 0
while (tempp > 0 & tempq > 0): ##test2
if tempp == 3:
test1 = 1
if tempq == 3:
test2 = 1
tempp = tempp >> 1
tempq = tempq >> 1
if test1 != 1 & test2 != 1:
p, q = prime_gen(e)
return p, q
if gcd((p - 1), e) != 1 & gcd((q - 1), e) != 1: ##test3
p, q = prime_gen(e)
return p, q
return p, q
def GenerateKeys(eVAL):
## Setup the prime generator
pg = PrimeGenerator(bits=128, debug=0)
while (True):
p = pg.findPrime()
q = pg.findPrime()
## Check p and q are different
if p == q: continue
## Check left two MSB's are 1 (bin command returns 0b appended at front)
if not (bin(p)[2] and bin(p)[3] and bin(q)[2] and bin(q)[3]): continue
## Check that the totients of p and q are co-prime to e
if (GCD(p - 1, eVAL) != 1) or (GCD(q - 1, eVAL) != 1): continue
break
## Calculate modulus
n = p * q
## Calculate totient of n
tn = (p - 1) * (q - 1)
modBV = BitVector(intVal=tn)
eBV = BitVector(intVal=eVAL)
## Calculate multiplicative inverse
d = eBV.multiplicative_inverse(modBV)
d = int(d)
## Create public and private sets
public, private = [eVAL, n], [d, n]
## Return items
return public, private, p, q, eVAL
def generate():
number = PrimeGenerator(bits = 128,debug = 0)
flag = False
while True:
l = BitVector(bitstring = '11')
p = number.findPrime()
q = number.findPrime()
p_bv = BitVector(intVal = p)
q_bv = BitVector(intVal = q)
#If the two left bits are set then keep it false otherwise make it true
if p_bv[0:2] == l and q_bv[0:2] == l:
flag = True
#if the two numbers are the same than break then set the flag to true
if p == q:
flag == False
else:
flag == True
#check for co prime
if coprime(p-1,e) == 1 and coprime(q-1,e) == 1:
flag = True
if flag == True:
break
else:
flag = False
return p,q
def createKeys(eVAL):
## Setup the prime generator
pg = PrimeGenerator(bits=128, debug=0)
while(True):
p = pg.findPrime()
q = pg.findPrime()
## Check p and q are different
if p == q: continue
## Check left two MSB's are 1 (bin command returns 0b appended at front)
if not (bin(p)[2] and bin(p)[3] and bin(q)[2] and bin(q)[3]): continue
## Check that the totients of p and q are co-prime to e
if (bgcd(p-1, eVAL) != 1) or (bgcd(q-1, eVAL) !=1): continue
break
## Calculate modulus
n = p * q
## Calculate totient of n
tn = (p - 1) * (q-1)
modBV = BitVector(intVal = tn)
eBV = BitVector(intVal = eVAL)
## Calculate multiplicative inverse
d = eBV.multiplicative_inverse(modBV)
d = int(d)
## Create public and private sets
public, private = [eVAL, n], [d, n]
## Return items
return public, private, p, q, eVAL
def generate_p_q(e, num_bits_desired): p = 0 q = 0 generator = PrimeGenerator(bits = num_bits_desired) while (p == q): p = generator.findPrime() q = generator.findPrime() while(gcd(p-1, e)!=1): p = generator.findPrime() while(gcd(q-1, e)!= 1): q = generator.findPrime() return p, q
def create_keys():
#creates the keys
e = BitVector(intVal = 3)
uno = BitVector(intVal = 1)
tres = BitVector(intVal = 3)#used for checking the last two bits
generator = PrimeGenerator( bits = 128, debug = 0 )
p = BitVector(intVal = generator.findPrime())
while (p[0:2] != tres and int (e.gcd(BitVector(intVal = int(p)-1))) != 1):
p = BitVector(intVal = generator.findPrime())
q = BitVector(intVal = generator.findPrime())
while (q[0:2] != tres and int (e.gcd(BitVector(intVal = int(q)-1))) != 1 and p != q):
q = BitVector(intVal = generator.findPrime())
n = int(p) *int( q)
n = BitVector(intVal = n)
to = BitVector(intVal =((int(p)-1)*(int(q)-1)))
d = e.multiplicative_inverse(to)
priv = (d, n, p, q)
pub = (e,n)
return (pub, priv)
def generateN():
'''
This function is used to generate two prime numbers p, q while guaranteeing:
1. p != q
2. p, q are coprime to e
3. 2 left most bits of p and q are set
ret: p, q, n
'''
generator = PrimeGenerator(bits=128)
p = -1
q = -1
while (True):
p = generator.findPrime()
q = generator.findPrime()
while (q == p):
q = generator.findPrime()
if gcd((p - 1), e) == 1 and gcd((q - 1), e) == 1:
break
return p, q, p * q
def genKey():
e = 3
finish = False
p = 0
q = 0
print ("###################")
while (finish == False):
somenum = PrimeGenerator(bits=128, debug=0)
p = somenum.findPrime()
q = somenum.findPrime()
# print (p),
#print (q)
finish = True
if (int(bin(p)[2]) * int(bin(p)[3]) * int(bin(q)[2]) * int(bin(q)[3]) == 0):
finish = False
if p == q:
finish = False
pb = bin(p)
qb = bin(q)
'''
print (pb[2])
print (qb[2])
print (pb[3])
print (qb[3])
'''
if (gcd(p - 1, e) != 1) or (gcd(q - 1, e) != 1):
finish = False
n = p * q
# print (n)
tn = (p - 1) * (q - 1)
print "tn"
print (tn)
tnbv = BitVector(intVal=tn)
ebv = BitVector(intVal=e)
print ("ebv")
print (ebv)
print ("tnbv")
print (tnbv)
dbv = ebv.multiplicative_inverse(tnbv)
d = dbv.int_val()
print ("dbv")
print (dbv)
#print (d)
puk = [e, n]
prk = [d, n]
return (puk, prk, p, q)
def keyGeneration():
# this function randomly generate p and q for encryption and decryption
myGenerator = PrimeGenerator(bits=int(blockSize / 2))
done = False
while not done:
pValue = myGenerator.findPrime()
qValue = myGenerator.findPrime()
co_prime = GCD(pValue - 1, eValue) and GCD(
qValue - 1,
eValue) # condition that p value and q value are co-prime to e
not_equal = pValue != qValue # condition that p and q are not equal
if co_prime and not_equal:
done = True
return pValue, qValue
def keyGeneration(pFileName, qFileName):
# this function randomly generate p and q for encryption and decryption
myGenerator = PrimeGenerator(bits=int(blockSize / 2))
done = False
while not done:
pValue = myGenerator.findPrime()
qValue = myGenerator.findPrime()
co_prime = GCD(pValue - 1, eValue) and GCD(
qValue - 1,
eValue) # condition that p value and q value are co-prime to e
not_equal = pValue != qValue # condition that p and q are not equal
if co_prime and not_equal:
done = True
with open(pFileName, 'w') as file:
file.write(str(pValue))
with open(qFileName, 'w') as file:
file.write(str(qValue))
def KeyGeneratorRSA():
e = 3
#Build PrimeGenerator with 128 bits
pp = PrimeGenerator(bits=128)
while True:
#Generate p,q and check them
p = BitVector(intVal=pp.findPrime())
q = BitVector(intVal=pp.findPrime())
if p != q and p[0] & p[1] & q[0] & q[1] and bgcd(
int(p) - 1, e) == 1 and bgcd(int(q) - 1, e) == 1:
break
#Get n
n = int(p) * int(q)
#public key
pubKey = [e, n]
return pubKey, n
def generation(p_file, q_file):
generator = PrimeGenerator(bits=128)
while True:
# Generate p and q using Provided Prime Generator and change to bitvector to test the first two bits
p = BitVector(intVal=generator.findPrime(), size=128)
q = BitVector(intVal=generator.findPrime(), size=128)
# p and q can not be equal
if p != q:
# First two bits of p and q have to be set
if q[0] and q[1] and p[1] and p[0]:
# p-1 and q-1 have be co-prime to e
if gcd((p.int_val() - 1), e) and gcd(q.int_val() - 1, e):
# All the constraints satisfied, write to the corresponding file
with open(p_file, "w") as fp:
fp.write(str(p.int_val()))
with open(q_file, "w") as fp:
fp.write(str(q.int_val()))
return
def generate_key_pair():
prime_gen = PrimeGenerator(bits=128, debug=0)
while True:
p = prime_gen.findPrime()
q = prime_gen.findPrime()
if p == q:
continue # ensure that the extremely unlikely case of p=q didn't occur
if not (bin(p)[2] and bin(p)[3] and bin(q)[2] and bin(q)[3]):
continue # ensure leading bits are 1
if (bgcd(p - 1, e) != 1) or (bgcd(q - 1, e) != 1):
continue # totients must be co-prime to e
break
mod_n = p * q # modulus is the product of the primes
tot_n = (p - 1) * (q - 1) # totient of n
mod_bv = BitVector(intVal=tot_n)
e_bv = BitVector(intVal=e)
d_loc = int(e_bv.multiplicative_inverse(mod_bv))
return (e, mod_n), (d_loc, mod_n), p, q
def KeyGeneratorRSA():
e=65537
pp=PrimeGenerator(bits =128)
while True:
p=BitVector(intVal=pp.findPrime())
q=BitVector(intVal=pp.findPrime())
if p != q and p[0]&p[1]&q[0]&q[1] and bgcd(int(p)- 1,e) ==1 and bgcd(int(q)-1,e)==1:
break
n=int(p)*int(q)
n_totient=(int(p)-1)*(int(q)-1)
totient_modulus = BitVector(intVal=n_totient)
e_bv = BitVector(intVal=e)
d = e_bv.multiplicative_inverse(totient_modulus)
pubKey = [e,n]
priKey = [int(d),n]
return pubKey,priKey,p,q
def gen_key(e):
while (True):
prime = PrimeGenerator(bits=128)
p = prime.findPrime()
q = prime.findPrime()
if p != q:
if (bin(p)[2] and bin(p)[3] and bin(q)[2] and bin(q)[3]):
#print(bin(p),bin(q))
if gcd((p - 1), e) == 1 and gcd((q - 1), e) == 1:
break
n = p * q
tn = (p - 1) * (q - 1)
e_bv = BitVector(intVal=e)
tn_bv = BitVector(intVal=tn)
d_bv = e_bv.multiplicative_inverse(tn_bv)
d = int(d_bv)
pub = [e, n]
prv = [d, n]
return (prv, pub, p, q)
def keygeneration():
e_val = 65537
e_bitvec = BitVector(intVal=e_val)
while True:
generator = PrimeGenerator(bits=128, debug=0)
p = generator.findPrime()
q = generator.findPrime()
p_bitvec = BitVector(intVal=p, size=128)
q_bitvec = BitVector(intVal=q, size=128)
##check if p and q satisfy three conditions, if not generate new p and q
if p_bitvec[0] & p_bitvec[1] & q_bitvec[0] & q_bitvec[1]:
if p != q:
if (int(BitVector(intVal=(p - 1)).gcd(e_bitvec)) == 1) & (int(
BitVector(intVal=(q - 1)).gcd(e_bitvec)) == 1):
break
##calculte totient_n and d
n = p * q
totient_n = (p - 1) * (q - 1)
tn_bitvec = BitVector(intVal=totient_n)
d_bitvec = e_bitvec.multiplicative_inverse(tn_bitvec)
key = [e_val, int(d_bitvec), n, p, q]
return key
def generate_values(num_bits_for_p_q, e, private_key_file, public_key_file):
# Prime number generator from given script
pg = PrimeGenerator(bits=num_bits_for_p_q, debug=0)
# Find a proper p value
while ( True ) :
p_candidate = pg.findPrime()
# if the first two bits are not set, find a new prime
if (p_candidate>>126) != 3 :
continue
# if the totient of p is not rel prime to e, find new prime
if gcd( p_candidate - 1 , e ) != 1 :
continue
# Otherwise the number is good
break
# Find a proper q value
while ( True ) :
q_candidate = pg.findPrime()
# if p and q are the same, find a new q
if( p_candidate is q_candidate ) :
continue
# if the first two bits are not set, find a new prime
if ( q_candidate>>126 ) != 3 :
continue
# if the totient of q is not rel prime to e, find new prime
if gcd( q_candidate - 1 , e ) != 1 :
continue
# otherwise number is good
break
# the modulus n
n = p_candidate * q_candidate
#The totient of n
tot_n = ( p_candidate - 1 ) * ( q_candidate - 1 )
# make e a BitVector for calculating the MI
tot_n_bv = BitVector( intVal=tot_n )
e_bv = BitVector( intVal=e )
d_bv = e_bv.multiplicative_inverse( tot_n_bv )
d = int( d_bv )
key_set = (e, d, n, p_candidate, q_candidate)
with open(private_key_file, 'w') as f :
f.write("d="+str(d)+"\n")
f.write("n="+str(n)+"\n")
f.write("p="+str(p_candidate)+"\n")
f.write("q="+str(q_candidate)+"\n")
with open(public_key_file, 'w') as f:
f.write("e="+str(e)+"\n")
f.write("n="+str(n)+"\n")
#print("pad count : "+str(pad))
int_pad = ord(pad)
#print("pad int : "+str(int_pad))
bin_pad = bin(int_pad)[2:].zfill(8)
#print("pad bin : "+str(bin_pad))
padding = padding + bin_pad
#print("pad size : "+str(padding))
pad_length = len(padding)
print("pad length : "+str(pad_length))
primeNumGenerate = PrimeGenerator ( bits = n_rsa // 2)
check = 0
while(check == 0):
p = primeNumGenerate.findPrime()
q = primeNumGenerate.findPrime()
while ( p == q ):
p = primeNumGenerate.findPrime()
q = primeNumGenerate.findPrime()
print("p : "+str(p))
print("q : "+str(q))
n = p*q
print("n : "+str(n))
totient = (p-1)*(q-1)
print("totient : "+str(totient))
class GenerateKeys():
def __init__(self, modSize):
self.e = 65537
self.d = None
self.p = None
self.q = None
self.n = None
self.e_bv = None
self.d_bv = None
self.p_bv = None
self.q_bv = None
self.n_bv = None
self.totient_n = None
self.public_key = None
self.private_key = None
#Code for the PrimeGenerator was written by Purdue Professor Dr. Avinash Kak
self.generator = PrimeGenerator(bits = (modSize/2), debug = 0)
#Function below generates primes numbers of a given size
def GenPrime(self):
return self.generator.findPrime()
#Binary implementation of Euclid's Algorithm
#Algorithm written in the "bgcd()" method below was written by Purdue Professor Dr. Avinash Kak
def bgcd(self, a, b):
if a == b: return a
if a == 0: return b
if b == 0: return a
if (~a & 1):
if (b &1):
return self.bgcd(a >> 1, b)
else:
return self.bgcd(a >> 1, b >> 1) << 1
if (~b & 1):
return self.bgcd(a, b >> 1)
if (a > b):
return self.bgcd( (a-b) >> 1, b)
return self.bgcd( (b-a) >> 1, a )
#Method below generates two prime numbers (p and q) such that they meet certain criteria to be
#used in a 256-bit implementation of the RSA Encryption Algorithm
def GenPQ(self):
while True:
#Generate Primes for P and Q
self.p_bv = BitVector(intVal = self.GenPrime(), size = 128)
while not (self.p_bv[0]&self.p_bv[1]):
self.p_bv = BitVector(intVal = self.GenPrime(), size = 128)
self.q_bv = BitVector(intVal = self.GenPrime(), size = 128)
while not (self.q_bv[0]&self.q_bv[1]):
self.q_bv = BitVector(intVal = self.GenPrime(), size = 128)
#Check if (p-1) and (q-1) are co-prime to e and if p != q
if self.p_bv != self.q_bv:
if (self.bgcd((int(self.p_bv)-1), self.e) == 1) and (self.bgcd((int(self.p_bv)-1), self.e) == 1):
break
self.p = int(self.p_bv)
self.q = int(self.q_bv)
#Method below generates the "d" value which is a component of the RSA encryption algorithm public key
def GenD(self):
totient_n_mod = BitVector(intVal = self.totient_n)
self.e_bv = BitVector(intVal = self.e)
self.d_bv = self.e_bv.multiplicative_inverse(totient_n_mod)
self.d = int(self.d_bv)
#Method below generates both public and private keys to be used by a 256-bit implementation
#of the RSA encryption algorithm
def GenKeys(self):
self.GenPQ() #Generate P and Q Values
self.n = self.p * self.q #Set n
self.n_bv = BitVector(intVal = self.n)
self.totient_n = (self.p - 1) * (self.q - 1) #Set totient of n
self.GenD() #Generate d value
self.public_key = [copy.deepcopy(self.e), copy.deepcopy(self.n)] #Set Public-Key
self.private_key = [copy.deepcopy(self.d), copy.deepcopy(self.n)] #Set Private-Key
#Method below prints generated key-values for RSA encryption algorithm to output file
def PrintKeys(self):
keyFile = open("keys.txt", "w")
keyFile.write("Public-Key: %s\n" % self.public_key)
keyFile.write("Private-Key: %s\n" % self.private_key)
keyFile.write("P-Value = %ld\n" % self.p)
keyFile.write("Q-Value = %ld\n" % self.q)
keyFile.close()
