I am afraid the terminology you use is not canonical.
A hash (function) is any function that maps a big variable-length data structure to a smaller (fixed-length) data structure.
A checksum is a special hash (function) which has the purpose of detecting accidental errors during transmission or storage. (This makes them different from hash functions used for example in hash tables. For example relevant question: minimum how many badly transmitted bits are needed to break the error detection in the case of a specific checksum?)
A cryptographic hash function is another kind of special hash function which also has a very good definition on wikipedia.
(Basically these are the definitions on Wikipedia, and I think they are fine. If the terminology you use would be canonical we would use the name 'checksum table' instead of 'hash table', and it would be quite illogical also, because the term 'checksum' really includes purpose in its name 'checking something').
Won't that be fairly common? Java's hashCode and the .Net GetHashCode both return 4 byte ints and there are presumably a lot of HashMap and Dictionary objects out there using short strings as keys.
It's very common; the norm even. My point was that "A hash (function) is any function that maps a big variable-length data structure to a smaller (fixed-length) data structure." is incorrect; the source size isn't relevant.
The source size is extremely relevant, in the property that the function is able to work with variable sized input including large input. This definition has obviously embedded its purpose unto itself. The reason we have such cryptographically secure hash functions corresponds to the need to digest large data.
A hash (function) is any function that maps a big variable-length data structure to a smaller (fixed-length) data structure.
A checksum is a special hash (function) which has the purpose of detecting accidental errors during transmission or storage. (This makes them different from hash functions used for example in hash tables. For example relevant question: minimum how many badly transmitted bits are needed to break the error detection in the case of a specific checksum?)
A cryptographic hash function is another kind of special hash function which also has a very good definition on wikipedia.
(Basically these are the definitions on Wikipedia, and I think they are fine. If the terminology you use would be canonical we would use the name 'checksum table' instead of 'hash table', and it would be quite illogical also, because the term 'checksum' really includes purpose in its name 'checking something').