def size_modp(self, p): #If we already know this size, return it from the saved list. if len(self.sizes)>0: for n in range(len(self.sizes)): if self.sizes[n][1]==p: return self.sizes[n][0] #Computes the size mod 2 N = 1 if p==2: for x in range(2): for y in range(2): if (y**2-((x**3) +self.coef[0]*x +self.coef[1]))%2 ==0: N=N+1 self.sizes.append([N,p]) return N #If we don't know the size of E mod p where p is odd, then we use Euler's Criterion to check #if x^3+ax+b is a square mod p or not. for x in range(p): X=(x**3) +self.coef[0]*x +self.coef[1] L=MLib.euler_crit(X,p) if L== 1 : N=N+2 if L==0: N=N+2 if N > p+3 +2*int(p**(0.5)): break self.sizes.append([N,p]) print(p,N," : ", N-(p+1), 2*(p**(0.5))) #For visual progress reports while running. return N
#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
