import MLib

import Conics

#Conoic sections are affine groups under a geometric addition rule

#similar to Elliptic Curves, but with no need for a point at infinity.

#Pell Conics are the special conics of the form x^2-dy^2=4. Each

#conic is isomorphic to a Pell Conic of the same discriminant.

#For instance the curve xy=1, when taken mod N, corresponds to

#the multiplicative group mod N and is isomorphic to the Pell Conic

#x^2-y^2=4 where (x,y) on the Pell Conic corresponds to ((x-y)/2,(x+y)/2)

#when we mod by an odd N.

#We can then use the ideas of the typical RSA Encryption to encrypt

#a point on a Pell Conic and use knowledge of the conic and of the

#prime factorization of N=pq to find a private key quickly via the

#Chinese Remainder Theorem. This is what this program does

#Setup: Specify the discriminant of the Pell Conic. Specify N=pq,

#N is public and p,q are private. Choose a code ie an integer

#e to encode the points. Use the Chinese Remainder Theoerem to

#find the inverse k of e for this curve.

print('--Initialize the Curve--')

print('-The curve will be the Pell Conic x^2-dy^2=4 mod N=pq')

d = MLib.fund_disc(int(input('Input the Discriminant d:')))

p = int(input('Input the first prime factor of N: '))

while MLib.isprime(p)==0:

p = int(input('That was not prime, please input a prime: '))

q = int(input('Input the second prime factor of N: '))

while MLib.isprime(q)==0:

q = int(input('That was not prime, please input a prime: '))

while p==q:

q = int(input('That number will not work, try another: '))

N=p*q

C=[d,N]

A=[d,p]

B=[d,q]

r=Conics.conic_size(A) #Size of C mod p

s=Conics.conic_size(B) #Size of C mod q

M=r*s #Size of C mod N (due to CRT)

#Input key

e = int(input('Input the Public Key: '))

while MLib.gcd(e,M)!=1:

e = int(input('That key will not do, try another: '))

#Output reverse key

k = Conics.conic_inv(e,A,B)

print('')

print('--Public Information--')

print('The Conic: x^2 -', d,'y^2 = 4')

print('The Modular Number: ', N)

print('The Key: ', e)

print('')

print('--Private Information--')

print('The Factorization: ', N,'=', p,'*', q)

print('The Size of the Conic: ', M,'=', r,'*',s)

print('The Reverse Key: ', k)

print('')

choice=1

while choice==1:

#Point to encode

a = int(input('Type the x-value of the point to encode: '))

b = int(input('Type the y-value of the point to encode: '))

P=[a,b]

on=Conics.is_on(P,C)

while on == 0:

print('That point is not on the curve. Try again.')

a = int(input('Type the x-value of the point to encode: '))

b = int(input('Type the y-value of the point to encode: '))

P=[a,b]

on=Conics.is_on(P,C)

Q = Conics.mult_pt(P,C,e)

print('')

print('Encoded point: ', Q)

print('')

print("Decoding...")

print(Conics.mult_pt(Q,C,k))

print('')

choice = int(input('Encode another point? '))