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"The problem, when solved, will be simple."

Conway's Game of Life

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comment Encryption with data loss protection
Perhaps it's not what you need, but you may be interested in locality sensitive hashing -- it's what Google uses to identify identical web pages, even where there's slight difference in HTML content (different ads, etc.). It's been a while since I've looked at LSH, but I think it allows the recipient to calculate the distance of their copy of the book from the original book.
comment HMAC for short messages
Without answering your question too fully: HMACing a short message does not expose meaningfully more key information than HMACing a long message, since the first step in HMAC is to hash the message (appended to a transformation of the key). In HMAC (K,m) = H ((K ⊕ opad) || H ((K ⊕ ipad) || m)), the message m is nested inside of two hash functions.