I'm planning on implementing the "cryptographic protection of databases" on page 61 of Schneier, to create a directory of a professional organization that would be useless to telemarketers. [hash last name to get DES key and location of encrypted data in list.] [ problems of brute-force and popular-last-names attacks ]

If you're only concerned about telemarketers, this amount of obscurity may be enough - anybody competent enough to hash a list of, say, 10000 last names x 1000 first names into your database is at least an *interesting* telemarketer :-) If you're concerned about telemarkers from the NSA/FBI/KGB, then the algorithm isn't enough anyway, because even if you make the search space large/slow enough to make it hard to list the whole list, it's still easy to look up "Goren" or "Stewart" or "McCarthy" to see if they're card-carrying members; it won't protect the usual suspects. An intermediate variant is to use a password as part of the hash; if everybody has their own password, the table size is N**2, or you can give everyone the same password without increasing the table size, and still be able to distribute the list on FTP. [This version is probably most useful for Secret Societies, where key distribution and privacy are taken seriously - the Masons could use a 33*N-entry hash table, and you *still* wouldn't be able to tell whether any members were the Illuminati! :-) ] By giving everyone different passwords and adding logN dummy records to the database, you could also tell whose copy was leaked (if only one copy leaks out; you obviously need more entries to detect multiple leaks.) On the question of whether there are functions I(m) = H(H(m)) for popular hashes, by definition there are, since H(H(m)) is one. For most of the cryptographically useful functions, though, there aren't any that are faster than running the hash function twice. Some exceptions are hashes like a**x mod p, x**a mod p, and obviously (a*x+c) mod p. But DES is known not to be a group, and MD5 is ugly enough it probably isn't group-like either. Bill