Monty Cantsin writes: 01> It would be neat if you could quote people and prove that they signed 02> the particular paragraph quoted without supplying the entire text. Is 03> there a way to do this? (It seems impossible, but so does mental 04> poker.) 05> 06> A crude approach would be to sign every paragraph or line separately, 07> but that's obviously inelegant. 08> 09> Monty Cantsin 10> Editor in Chief 11> Smile Magazine 12> http://www.neoism.org/squares/smile_index.html 13> http://www.neoism.org/squares/cantsin_10.htm An easy way to do this works only if the quoted paragraph comes from the very end of the text. You can supply the cumulative hash of all the material before the quoted part, then the quotation itself, which goes all the way to the end of the document. From this the hash of the whole document can be calculated, and the signature checked. A more general approach calculates the document hash in a line oriented way. Normally we start at the top and work down through the document to get the hash, which is signed. Instead, we would calculate a hash for each line of the document separately, and then combine them using a tree. In the example above hashes would be calculated for lines 1-13. Call these H1A - H13A. Then second level hashes could be calculated by taking H1A through H13A in pairs: H1B = hash(H1A,H2A) H2B = hash(H3A,H4A) H3B = hash(H5A,H6A) ... H6B = hash(H11A,H12A) H7B = H13A We repeat this until we have one hash for the whole document: H1C = hash(H1B,H2B) H2C = hash(H3B,H4B) H3C = hash(H5B,H6B) H4C = H7B H1D = hash(H1C,H2C) H2D = hash(H3C,H4C) H1E = hash(H1D,H2D) We sign the final hash, H1E. Now you can extract a paragraph, say lines 6 and 7 above. The hashes H6A and H7A can be calculated from this. Supply the other hashes needed to calculate the final hash: H5A, H8A, H1C, H2D, will be enough. This will allow calculating H1E and the signature can be verified. The required number of hashes will generally be logarithmic in the size of the missing part of the document.