If there is no specific mixing algorithm, it will not provide anonymity. For example, the MD5 encryption system performs a one-way hash. The hash value is not resolvable. But some sites compare with their database records. For example, the MD5 version of the term "bitcoin" is "cd5b1e4947e304476c788cd474fb579a". MD5 decrypter sites previously register the hash value of the "bitcoin" word into their system. Later, when the user searches for "cd5b1e4947e304476c788cd474fb579a" in the system, it finds the word "bitcoin".
First of all, MD5 is not an encryption algorithm or system, it is a hash algorithm. They are two very different things.
Secondly, there are no such Bitcoin objects that algorithms can perform on to do anything. That is simply not how Bitcoin works.
If there is no specific mixing algorithm in the mixer sites, it means that there is no anonymity. Because the whole address pool was created by the site in a normal way. The login address and the exit address are certain. The FBI can request and receive information about the address of the bitcoin on the site.
Yes, this is exactly what can happen, and exactly why you should only use mixers you trust. The mixer knows EXACTLY where the Bitcoin came from and EXACTLY where the Bitcoin is going to. They know everything, and if they are compromised, so is your anonymity. There is nothing that can be done to make a mixer that does not know the specifics of the mixing that they do. The point of the mixer is to prevent outside parties from knowing where your Bitcoin came from and is going, but the mixer will most certainly know those details.
