Given an elliptic curve equation y2 = x3 + 25x + 17 (mod 29), answer the following questions.
 Given an elliptic curve equation y^{2} = x^{3} + 25x + 17 (mod 29), answer the following questions.

4 marks 

4 marks 

4 marks 
 An important usage of the elliptic curves is to factorize big integers. Comparing to the difference of squares method, the advantage of ECbased factorization is that it can be parallelized easily. This question asks you to practice integer factorization with ECbased method.
The smallest 3digit prime is p = 101. And you need to find another prime q as follows. Take the last three digits of your student ID, and then run the maple command “nextprime()” and set the result as q. For example, if my ID is “7654321”, then the last three digits are “321”, then q = nextprime(321)= 331. Now, set n = p*q (note that the value q must be derived from your own student ID but not copy this constant 331).
Set up two elliptic curves randomly (so they are up to your own choice) and factorize the number n=p*q you obtained above. Observe your maple result, which curve gives you the factors p, q faster?