I'm looking to encrypt some 64 bit integers, with a maximum cipher text size of 128bits. The encrypted numbers will be displayed in some public places, so shorter, "vanity" sizes is a primary design constraint.
It's not critical that these integers remain private for ever; ideally they would just be hard enough to decrypt that it would be cost ineffective to do so. My rough goal is that it should cost about $20 on commodity hardware to break.
Most modern ciphers produce cipher text that is frequently too large, and older ciphers are marked as insecure with no discussion of how insecure they are. I looked at Blowfish and 3DES, but both have large warnings on the Internet saying to use something more advanced.
A finally, stretch requirement would be to have some kind of authentication tag (e.g. an AEAD). It appears the popularity of authenticated encryption happened after block sizes had moved up to 128 bit.
My initial use case is for anti scraping (making it hard to guess IDs), where I had planned to rotate the encryption keys every couple of days.