As far as I understand, this is not sufficient.
Some things that are needed in addition are (at least):
* constant time math operations (multiply, divide, exponentiation, etc.)
* no branching based on secrets (running the code results in no branch conditions based on secret data)
Here's an interesting article on implementing a form of Elliptic Curve Cryptography without even local timing attacks: http://blog.cr.yp.to/20140323-ecdsa.html