I have developed a web site during an internship, using a database with accounts. I used the crypt() method from PHP, with a secured algorithm plus salt (found on the web with a lot of feedback). Obviously, I'd like to talk about it in my report but, would it be a security issue since that report will be made public?

I think that it wouldn't matter because the method itself is pretty secure, but maybe, if the attacker knows about the algorithm, it would make it a little bit easier to brute force.

Should you make the algorithm public?
Trying to hide implementation details (such as which hashing algorithm you use) to preserve security is the very definition of security through obscurity. There is broad consensus that obscurity should not be your only line of defense.
If you need to keep your hash algorithm a secret, you are doing it wrong and need to pick a better hashing algorithm. When you use a good algorithm, there is no reason not to tell the world about it since they won't be able to crack your hashes anyway.
Also note that in your case the salt will give you away. If someone gets hold of your database, they will be able to read what algorithm was used from that. So obscurity does not make brute forcing harder here. Advertising a weak scheme, however, might encourage attackers. A strong one could have the opposite effect. The point Mike Goodwin makes in his answer should also be taken into account.
Is crypt() secure?
The relevant question to ask is therefore if crypt() is secure enough. Let's have a look at the PHP manual:

password_hash() uses a strong hash, generates a strong salt, and applies proper rounds automatically. password_hash() is a simple crypt() wrapper and compatible with existing password hashes. Use of password_hash() is encouraged.
Some operating systems support more than one type of hash. In fact, sometimes the standard DES-based algorithm is replaced by an MD5-based algorithm.



The standard DES-based crypt() returns the salt as the first two characters of the output. It also only uses the first eight characters of str, so longer strings that start with the same eight characters will generate the same result (when the same salt is used).

The function uses different algorithms depending on how you format the salt. Some of the algorithms are very weak, and the strong ones might not be available on all systems. So depending on the algorithm used, there are a number of problems here:

For some algorithms crypt() only applies one round of hashing. That is too fast, and will enable a brute force attack.
Under some circumstances crypt() will use MD5, which is known to be weak.
Only using the first eight characters completely nullifies the benefits of long passwords.

I therefore suggest that you  switch to password_hash(). It lets you use bcrypt - a tried and tested algorithm. Then you can proudly tell the world about your hashing scheme.
