Is there a way of encryption that can take a string of any length and produce a sub-10-character hash? I want to produce reasonably unique ID's but based on message contents, rather than randomly.
I can live with constraining the messages to integer values, though, if arbitrary-length strings are impossible. However, the hash must not be similar for two consecutive integers, in that case.
You can use any commonly available hash algorithm (eg. SHA-1), which will give you a slightly longer result than what you need. Simply truncate the result to the desired length, which may be good enough.
For example, in Python:
>>> import hashlib
>>> hash = hashlib.sha1("my message".encode("UTF-8")).hexdigest()
>>> hash
'104ab42f1193c336aa2cf08a2c946d5c6fd0fcdb'
>>> hash[:10]
'104ab42f11'