1. Given an elliptic curve equation y² = x³ + 25x + 17 (mod 29), answer the following questions.

1. An important usage of the elliptic curves is to factorize big integers. Comparing to the difference of squares method, the advantage of EC-based factorization is that it can be parallelized easily. This question asks you to practice integer factorization with EC-based method.

The smallest 3-digit 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?