This question is based on this question, in which it is asked if there is a polynomial time algorithm which finds out if a given number is expressible as the sum of two squares. One of the answers pointed out that this problem is essentially as hard as Integer Factorization.

The wiki article on integer factorization says the following.

Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem, the RSA problem. An algorithm which efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure.

This prompted me to ask if there were any similar consequences if a polynomial time algorithm for finding out if a given number is expressible as the sum of two squares is discovered?

ADDENDUM: Note that I am interested only in whether the integer can be represented in such a way, not in how it is represented.