In: Computer Science
If you have any doubts plz ask me in the comment box:
import math
print("RSA ENCRYPTOR/DECRYPTOR")
print("*****************************************************")
#Input Prime Numbers
print("PLEASE ENTER THE 'p' AND 'q' VALUES BELOW:")
p = int(input("Enter a prime number for p: "))
q = int(input("Enter a prime number for q: "))
print("*****************************************************")
#Check if Input's are Prime
'''THIS FUNCTION AND THE CODE IMMEDIATELY BELOW THE FUNCTION CHECKS
WHETHER THE INPUTS ARE PRIME OR NOT.'''
def prime_check(a):
if(a==2):
return True
elif((a<2) or ((a%2)==0)):
return False
elif(a>2):
for i in range(2,a):
if not(a%i):
return false
return True
check_p = prime_check(p)
check_q = prime_check(q)
while(((check_p==False)or(check_q==False))):
p = int(input("Enter a prime number for p: "))
q = int(input("Enter a prime number for q: "))
check_p = prime_check(p)
check_q = prime_check(q)
#RSA Modulus
'''CALCULATION OF RSA MODULUS 'n'.'''
n = p * q
print("RSA Modulus(n) is:",n)
#Eulers Toitent
'''CALCULATION OF EULERS TOITENT 'r'.'''
r= (p-1)*(q-1)
print("Eulers Toitent(r) is:",r)
print("*****************************************************")
#GCD
'''CALCULATION OF GCD FOR 'e' CALCULATION.'''
def egcd(e,r):
while(r!=0):
e,r=r,e%r
return e
#Euclid's Algorithm
def eugcd(e,r):
for i in range(1,r):
while(e!=0):
a,b=r//e,r%e
if(b!=0):
print("%d = %d*(%d) + %d"%(r,a,e,b))
r=e
e=b
#Extended Euclidean Algorithm
def eea(a,b):
if(a%b==0):
return(b,0,1)
else:
gcd,s,t = eea(b,a%b)
s = s-((a//b) * t)
print("%d = %d*(%d) + (%d)*(%d)"%(gcd,a,t,s,b))
return(gcd,t,s)
#Multiplicative Inverse
def mult_inv(e,r):
gcd,s,_=eea(e,r)
if(gcd!=1):
return None
else:
if(s<0):
print("s=%d. Since %d is less than 0, s = s(modr), i.e.,
s=%d."%(s,s,s%r))
elif(s>0):
print("s=%d."%(s))
return s%r
#e Value Calculation
'''FINDS THE HIGHEST POSSIBLE VALUE OF 'e' BETWEEN 1 and 1000 THAT
MAKES (e,r) COPRIME.'''
for i in range(1,1000):
if(egcd(i,r)==1):
e=i
print("The value of e is:",e)
print("*****************************************************")
#d, Private and Public Keys
'''CALCULATION OF 'd', PRIVATE KEY, AND PUBLIC KEY.'''
print("EUCLID'S ALGORITHM:")
eugcd(e,r)
print("END OF THE STEPS USED TO ACHIEVE EUCLID'S ALGORITHM.")
print("*****************************************************")
print("EUCLID'S EXTENDED ALGORITHM:")
d = mult_inv(e,r)
print("END OF THE STEPS USED TO ACHIEVE THE VALUE OF 'd'.")
print("The value of d is:",d)
print("*****************************************************")
public = (e,n)
private = (d,n)
print("Private Key is:",private)
print("Public Key is:",public)
print("*****************************************************")
#Encryption
'''ENCRYPTION ALGORITHM.'''
def encrypt(pub_key,n_text):
e,n=pub_key
x=[]
m=0
for i in n_text:
if(i.isupper()):
m = ord(i)-65
c=(m**e)%n
x.append(c)
elif(i.islower()):
m= ord(i)-97
c=(m**e)%n
x.append(c)
elif(i.isspace()):
spc=400
x.append(400)
return x
#Decryption
'''DECRYPTION ALGORITHM'''
def decrypt(priv_key,c_text):
d,n=priv_key
txt=c_text.split(',')
x=''
m=0
for i in txt:
if(i=='400'):
x+=' '
else:
m=(int(i)**d)%n
m+=65
c=chr(m)
x+=c
return x
#Message
message = input("What would you like encrypted or
decrypted?(Separate numbers with ',' for decryption):")
print("Your message is:",message)
#Choose Encrypt or Decrypt and Print
choose = input("Type '1' for encryption and '2' for
decrytion.")
if(choose=='1'):
enc_msg=encrypt(public,message)
print("Your encrypted message is:",enc_msg)
print("Thank you for using the RSA Encryptor. Goodbye!")
elif(choose=='2'):
print("Your decrypted message is:",decrypt(private,message))
print("Thank you for using the RSA Encryptor. Goodbye!")
else:
print("You entered the wrong option.")
print("Thank you for using the RSA Encryptor. Goodbye!")
RSA ENCRYPTOR/DECRYPTOR
*****************************************************
PLEASE ENTER THE 'p' AND 'q' VALUES BELOW:
Enter a prime number for p: 3
Enter a prime number for q: 5
*****************************************************
RSA Modulus(n) is: 15
Eulers Toitent(r) is: 8
*****************************************************
The value of e is: 999
*****************************************************
EUCLID'S ALGORITHM:
8 = 0*(999) + 8
999 = 124*(8) + 7
8 = 1*(7) + 1
END OF THE STEPS USED TO ACHIEVE EUCLID'S ALGORITHM.
*****************************************************
EUCLID'S EXTENDED ALGORITHM:
1 = 8*(1) + (-1)*(7)
1 = 999*(-1) + (125)*(8)
s=-1. Since -1 is less than 0, s = s(modr), i.e., s=7.
END OF THE STEPS USED TO ACHIEVE THE VALUE OF 'd'.
The value of d is: 7
*****************************************************
Private Key is: (7, 15)
Public Key is: (999, 15)
*****************************************************
What would you like encrypted or decrypted?(Separate numbers with
',' for decryption):HELLO
Your message is: HELLO
Type '1' for encryption and '2' for decrytion.1
Your encrypted message is: [13, 4, 11, 11, 14]
Thank you for using the RSA Encryptor. Goodbye!
PLEASE ENTER THE 'p' AND 'q' VALUES BELOW:
Enter a prime number for p: 3
Enter a prime number for q: 5
*****************************************************
RSA Modulus(n) is: 15
Eulers Toitent(r) is: 8
*****************************************************
The value of e is: 999
*****************************************************
EUCLID'S ALGORITHM:
8 = 0*(999) + 8
999 = 124*(8) + 7
8 = 1*(7) + 1
END OF THE STEPS USED TO ACHIEVE EUCLID'S ALGORITHM.
*****************************************************
EUCLID'S EXTENDED ALGORITHM:
1 = 8*(1) + (-1)*(7)
1 = 999*(-1) + (125)*(8)
s=-1. Since -1 is less than 0, s = s(modr), i.e., s=7.
END OF THE STEPS USED TO ACHIEVE THE VALUE OF 'd'.
The value of d is: 7
*****************************************************
Private Key is: (7, 15)
Public Key is: (999, 15)
*****************************************************
What would you like encrypted or decrypted?(Separate numbers with
',' for decryption):13,4,11,11,14
Your message is: 13,4,11,11,14
Type '1' for encryption and '2' for decrytion.2
Your decrypted message is: HELLO