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I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
- Isaac Newton,
Brewster's Memoirs of Newton.
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On this page, I shall occasionally highlight some of the "other pebbles" besides those on the shores of high-energy physics that have caught my eye. I doubt I shall, as it were, "pick up" most of these other pebbles though should the opportunity arise, I would be remiss not to pocket one or two. Essentially what I am going to do here is summarily recount some of the thought-provoking discussions I have had with people who are working in the following interesting areas. My apologies for any misconceptions and omissions, intended or otherwise. I'll start off with zero-knowledge proofs.
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| Zero-Knowledge Proofs |
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Picture this setup. Pat is the person with the password and Vanna is the gatekeeper of sorts who allows people through. Would it be possible to set up a scheme whereby Vanna would correctly allow Pat through and exclude others, but still have no knowledge of Pat's password? Well, zero-knowledge proofs allows precisely that. I found this to be an intriguing idea when it was first explained to me.
Zero-knowledge proofs are interactive proofs that yield nothing beyond the validity of the assertion. A rough example might help here. Let us assume that the prover, Pat, can colour any planar map with only 3 colours and this is the assertion to be verified. Now, the verifier, Vanna, generates a map which Pat then colours. Verifying that Pat can indeed 3-colour that particular map, Vanna then generates a different map. The above process is repeated over and over again until Vanna establishes to sufficiently high probability that Pat indeed has the proof. However, the method by which Pat colours the map was never revealed to Vanna; hence, the phrase zero-knowledge. The original idea, which was proposed by Goldwasser, Micali and Rackoff, has been used by cryptographers to construct rather robust authentication systems.
There are obviously a lot of more technical subtleties involved which I shall not go into here and this topic is very much an area of active research. I guess the wikipedia is probably a good place to start learning more about the subject if one is interested.
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