First of all, the implementation of a hashing function could be faulty in terms of software engineering. That doesn't mean the implementation is insecure per se, but means that you are not returning the expected values according to the specifications.
N=10 test cases is a ridiculously ridiculous amount of testing to certify that a hashing function is ready for production. I am currently speaking about software engineering, not yet security
A concrete example
sha256("Hello Stack") equals 433247cccfd4105b7b60e810e372f3850ba4e518eb5fb0474e198228ddaabf65
Wherever in the world you are, that is the universal hash of that string. The security properties of sha256 are defined in the hash's specification.
If you have a faulty implementation, then it will have to return something necessarily different.
Now suppose for a second your sha256 does the following
yourSha256("Help Stack") equals 433247cccad4105b7b60e810e372f3850ba4e508eb5fb0474e198228ddaabf65
That's basically not sha256, because the correct value is
What I am saying is that in the world of hash functions, the properties of uniqueness and randomization have to be demonstrated at specification level, and they apply to the hash's specification. Any code that returns value other than the expected hash is not a correct implementation of the hash.
A bug comparing the hashes
So you have function
H(x) that is deemed secure. I won't discuss further. Then you have two implementations
org.acme.H (yours) and
com.initech.H (another vendor's).
You must integrate two systems so that they compute and exchange hashes.
H is secure by definition, but Acme is faulty. That means on the 11th test case it is returning results different than Initech. That will mean whatever interaction between the systems will be inconsistent and/or failing. e.g. the two system use such hash to checksum a file, but since they yield different values they consider the file out of date.
So far, that's not a mere security problem
Exploitable faulty implementation
If you rely on that hash heavily and use it for security purposes, and have no other implementation from any other vendor, you might have vulnerabilities.
E.g. if your faulty hash code starts to return predictable values, an attacker can discover (part of) the plaintext after a number of similar-text attacks.
That is not a problem with the hash definition, but it's the binary code not returning the correct value. Simply because you are not using secure H(x), you are using
trash(x) where trash is a brand new weak function.
Cryptographic functions are famous for timing attacks, where the amount of time to encrypt a block (emphasis mine) is variable and reveals info about the key. Hashing functions have the desirable property to take the same amount of time for blocks of equal length. It is worth to note that it is perfectly normal for a hash function to take increasingly time according to the payload size. Namely, the larger the file, the longer the time to hash it. Full stop!
Memory aging and leaked plaintext
I could imagine that a faulty implementation leaves traces of the original plaintext allocated in memory, without properly clearing these areas and returning them to the system. Combined with a buffer overflow attack, that could reveal pieces of plain text if not all.
But that is something unrelated to only 10 test cases. You won't find it with additional cases like
assertThat(acmeHash(x),is(equalTo(superTestedHash(x)))) which is a great way to test custom implementations
Consideration on timing attack
This is just a consideration. Suppose your correct-but-insecure-implementation of the hash yields a result so that the time it takes to yield it is related to the plaintext itself.
I quite don't see much security issue. Hash functions are public, so that you will run it on your machine. You have to know the plaintext before running it.
Compared to time attacks in crypto functions, the problem there is that you use the timing not to break the cyphertext or plaintext, but to break the key which is the other secret element. In hashing there is no key, so plaintext and hash digest are always known.