Question

1. RSA: Public and Private Key Encryption
2. im doing this on an ubuntu virtual machine but unsure how to
   1. Create your public and private keys
   2. and create and encrypted message using python
   3. Then encrypt the message with your private key
   4. I need output of a
      1. Message you sent (in plain text and encrypted)
      2. Message you received (in plain text and encrypted)

Answer 1

answer: all of the above points in the given code.

feel free to ask any further queries.

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
Thank you for using the RSA Encryptor. Goodbye!