hey
i am trying to write a program to find x and y for equations of the form :
y^2 mod p = (x^3+ax+b)mod p
y--> unknown. range from 0 to p-1.
x-->unknown. range from 0 to p-1.
p--> a large prime number.
i am currently using plain brute force to solve this problem. that is, for every value of x, y is varied from 0 to p-1 till lhs equals rhs.
while this works fine for smaller numbers (uptil 5 digit primes), for larger primes the program takes too long (over 3 hours) to give me the answer. is there any other, faster way to solve the above equation?
p.s. i am using matlab.