Generating a pseudo-natural phrase from a big integer in a reversible way

Question

I have a large and "unique" integer (actually a SHA1 hash).

Note: While I'm talking here about SHA1 hashes, this is not a cryptography / security question! I'm not trying to break SHA1. Imagine a random 160-bit integer instead of SHA1 if that will help.

I want (for no other reason than to have fun) to find an algorithm to map that SHA1 hash to a computer-generated (pseudo-)English phrase. The mapping should be bidirectional (i.e., knowing the algorithm, one must be able to calculate the original SHA1 hash from that phrase.)

The phrase need not make sense. I would even settle for a whole paragraph of nonsense. (Though quality — englishness — of a paragraph should probably be better than for a mere phrase.)

A better algorithm would produce shorter, more natural-looking, more unique phrases.

A variation: it is OK if I will be able to work only with a part of hash. Say, first six hex digits is fine.

The possible usage of the generated phrase: the human readable version of Git commit ID, to use as a motto for a given program version, which is built from that commit. (As I said, this is "for fun". I don't claim that this is very practical — or be much more readable than the SHA1 itself.)

Possible approach: In the past I've attempted to build a probability table (of words), and generate phrases as Markov chains, seeding the generator (picking branches from probability tree), according to the bits I read from the SHA. This was not very successful, the resulting phrases were too long and ugly. I'm not sure if this was a bug, or the general flaw in the algorithm, since I had to abandon it early enough.

Now I'm thinking about attempting to solve the problem once again. Any advice on how to approach this? Do you think Markov chain approach can work here? Something else?

Answer 1

A very simple approach would be: Take list of say 1024 nouns, 1024 verbs and 1024 adjectives each. Your phrase could then be sentence of the form

noun[bits_01-10] verb[bits11-20] adjective[bits21-30] verb[bits31-40],
noun[bits_41-50] verb[bits51-60] adjective[bits61-70] verb[bits71-80],
noun[bits_81-90] verb[bits91-100] adjective[bits101-110] verb[bits111-120] and 
noun[bits_121-130] verb[bits131-140] adjective[bits141-150] verb[bits151-160].

With a bit more linguistic thought you can probably construct slightly more complicated ad thus not so repetitive looking sentences (say, a bit for singular / plural, a bit of two for different tenses,...). Longer word lists use up a few more bits but my guess is that you reach rather exotic words quite fast.

Answer 2

We'll, lets see... The english language has about 1,000,000 words. That's about 20 bits per word. SHA1 is 160 bits, so you'll need 8 words. Theoretically, All you'll have to do is to take the n'th word of the oxford english dictionary, where n is a group of 20 bits at a time.

Now, to make it more natural, you can try to add "in/at/on/and/the..." between words, according to their type (nouns,verbs...) using some simple algorithm. (You should remove all these words from your base dictionary, of course).

The algorithm is reversible: Just remove all the words you've added, and convert each word to it's 20-bit index.

Also, try google "insult generator". Some of those generators are pretty nice. I'm not sure about the number of combinations, though.

You can buy the Oxford English Dictionary on CD-ROM with more than 500,000 words (19-bit). I'm not sure if it would be easy to extract the words and their types, however. I'm not sure if it is legal, but I think you can't claim a patent on dictionary entries...