In some settings, documents being cryptographically processed are modifications of ones which have already been cryptogrpahically processed. For example, you may be sending out a signed form letter to many different recipients, and each letter differs only in the name of the addressee. The idea of incremental cryptography, as proposed by Bellare, Goldreich and Goldwasser, is to design schemes which take advantage of this to speed up the cryptographic processing. Thus, in the above example, rather than signing each letter from scratch, sign the first one, and then quickly update the signature as the letter is updated.
In our papers on incremental cryptography we provide schemes for incremental message authentication, signatures, hashing, and encryption. We consider various "update" operations of increasing complexity, including text replacement, text insert and delete, and finally general cut and paste. We note and address new security concerns that arise in this setting.
One of the applications of incremental cryptography is to virus protection via finger printing. Here the stored files are quite large, and it would be much quicker to update cryptograhic tags incrementally.