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I have very short messages which I want to keep to 32-bits encrypted (ie one block). The keys can (and should) be as large as possible to maximize security.

However, I don't know many ciphers with 32-bit modes. Are there any that offer 90+ bit security? Which has the most cryptanalysis?

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If you care about security, and don't care much about performance, you might consider a Format Preserving Encryption mode such as FF1; this is a mode of operation that uses a 128-bit block cipher to form an arbitrary sized block cipher; this arbitrary size includes a size of 32 bits.

It is believed (I don't think we have a proof in hand) that, if instantiated with AES, it is as strong as AES (with the caveat inherent with having a block size of 32 bits); hence you have at least 128 bits of security.

Performance isn't great (performing an encryption or decryption of a single block involves 10 AES operations), however depending on what your use case is, it may be quite acceptable.

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You can easily encrypt a short message with any cipher. The only question is of course cipher text size. You can avoide storing a full block with the relevant modes of operation but you still want a IV/nonce. For instance AES CTR with a short none(according to ho many times you need to encrypt something with same key) could easily work.

We can take the above approach, increase key size and limit the number of times we send a message to the extreme and just use a one time pad. Agree in advance on enough keys to send the short message as many times you will need. This is information theoretically secure also for short messages.

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