Is a password cyphered by itself as secure as hash? My Question(s)

I am wondering if I have a password (long enough) and I cypher it by itself (let's ignore the salt) in this way:

cy_hash(mypassword)=cypher(text=mypassword,key=mypassword)


Then, is cy_hash as secure as md5, sha1, sha512, etc?  

Also:


Is there any theoretical comparison between these methods?  
Has this method ever been used in practice? If not, why?  
Is there any research on this hash?


My research efforts

As for my research efforts, I have looked around and found the following Q&amp;As:


Is it safe to encrypt a string using same string as key?
 (at StackOverflow)
how much is secure to encrypt a password using itself (as encryption key) for storing it on a unsecure media? (at Crypto.StackExchange)


but those Q&amp;As do not answer my question. You can safely skip linking to them.
There is an important misconception on your part: in general cryptographic hashes such as MD5, SHA-1 or SHA-512 should not be used to directly hash a password. A password hash or PBKDF should be used. Examples are PBKDF2, bcrypt, scrypt and Argon2. These functions also take a salt and work factor to provide additional protection.

There are a few problems with your idea:


as noted in the comments, a cipher generally takes a key with one or more specific, pre-defined sizes;
a cipher would output a size as large or larger than the input which would leak the password size (and require VARBINARY in databases, larger buffer allocation etc.);
it is missing additional parameters such as a salt or iteration count to make it a password hash;
it would have almost the same performance as just hashing the password (it would offer no advantages, in other words).


No, there is likely little to no research as it would be dismissed out of hand. There was however a password hash competition quite recently where it could have been entered (and immediately dismissed).



Note that MD5 and SHA-1 have been broken and should generally not be used anymore.