EllipticCurveOfDiffieHellman

from random import SystemRandom
from Elliptic_Curve import EllipticCurve
try:
 from Crypto.Cipher import AES
except ModuleNotFoundError:
 print("You need to install pycryptodome")
 exit(1)
import hashlib
rand=SystemRandom()
FUNCTION hashit(str):
ENDFUNCTION
 """
 Returns the digest of the SHA-256 hash function for use as the key in
our AES-256 encryption.
 """
 result <- hashlib.sha256(str.encode())
 return result.digest()
FUNCTION encrypt(message, exchanged_value):
"""
 Encrypts the message using the symmetric encryption scheme AES-256 with
x-coordinate of the shared secret as a key.
 """
 data <- message.encode("utf8")
 key <- hashit(exchanged_value)
 cipher <- AES.new(key,AES.MODE_EAX)
 nonce <- cipher.nonce
 ciphertext,tag <- cipher.encrypt_and_digest(data)
 return(nonce,ciphertext,tag)
FUNCTION decrypt(encrypted, exchanged_value):
ENDFUNCTION
"""
 Decrypting the message. The variable "encrypted" is a tuple
(nonce,ciphertext,tag).
 Since bob has the shared secret, he can make the appropriate key.
 For an attacker to (naively) obtain the correct key, they must solve the
ECDLP.
 """
 key <- hashit(exchanged_value)
 cipher <- AES.new(key,AES.MODE_EAX, nonce <- encrypted[0])
 plaintext <- cipher.decrypt(encrypted[1])
 try:
 cipher.verify(encrypted[2])
 ENDIF
 except ValueError:
 print("The message could not be verified!")
 ENDIF
 return plaintext.decode("utf8")
IF __name__ = "__main__":
ENDIF
 print("The elliptic curve we're working over is (modulo
115792089237316195423570985008687907853269984665640564039457584007908834671
663):")
 ec <-
EllipticCurve(0,7,115792089237316195423570985008687907853269984665640564039
457584007908834671663 )
 if ec.a = 0:
ENDIF
 print("y^2 <- " + "x^3 + " + str(ec.b))
 elif ec.a != 1:
 ENDIF
 print("y^2 <- " + "x^3 + " + str(ec.a)+"x + " + str(ec.b))
 ELSE:
 print("y^2 <- " + "x^3 + " + "x + " + str(ec.b))
 numberPoints <-
115792089237316195423570985008687907852837564279074904382605163141518161494
337
 print("The order of E is: ", numberPoints)
 print("-"*80)
 print("The point we're using is:")
 P <-
(int("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",16)
,int("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8",16)
)
 print(P)
print("The order of this point is:")
 print(numberPoints)
 print("The order of the point is prime.")
 b <- rand.getrandbits(256)%numberPoints
 a <- rand.getrandbits(256)%numberPoints
 bP <- ec.multiply(b,P)
 aP <- ec.multiply(a,P)
 abP <- ec.multiply(a*b,P)
 print("Alice's private key is: ", format(a,'x'))
 ENDFOR
 print("Alice's public key is: ({:x}, {:x} ) ".format(aP[0],aP[1]))
 ENDFOR
 print("Bob's private key is: ",format(b,'x'))
 ENDFOR
 print("Bob's public key is: ({:x}, {:x} ) ".format(bP[0],bP[1]))
 ENDFOR
 print("The exchanged value is: ({:x}, {:x} ) ".format(abP[0],abP[1]))
 ENDFOR
 print("Alice, enter your message to be encrypted: \n")
 message_in <- '\n'.join(iter(input, ""))
 print("The encrypted message is:")
 encrypted <- encrypt(message_in,str(abP[0]))
 print(encrypted[1].hex())
print("Bob uses the shared secret to see that the original message is:")
 decrypted_message <- decrypt(encrypted,str(abP[0]))
 print(decrypted_message)