What I am trying to prevent is to have a collection of "important" numbers in plaintext on a laptop, which will be moving around geographically and susceptible to theft.

A salted hash is a good way to make sure that these numbers are not stored in plaintext - and it is easy. The issue is that I will eventually, in a secured location without network access, need to reverse this hash (hence a rainbow table).

The laptops are already using full-disk encryption, but this provides only a single layer of defense against exposure - I am thinking about how to add another layer without doubling the number of passphrases to remember (or forget).

What I am trying to prevent is to have a collection of "important" numbers in plaintext on a laptop

Noone suggested that. We said specifically said to put that information in the secret database, the one "that's under lock and key (of course)".

You're ok with haveing a secret table that maps public ids to real ids. You were thinking of implementing that table as a rainbow table. All we're suggesting is that you implement that table in a much more straightforward manner:

 work db             secret db
 (laptop)            (under lock and key)
+-----------+---     +-----------+---------+
| public id | ...    | public id | real id |
+-----------+---     +-----------+---------+
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The public id would simply be a unique random number. (Safer than a hash, and avoids the problem of collisions.)

Now, this assumes the database is created before being placed on the laptop, but that's consistent with everything you've told us so far. You can still use the above method if you collect the numbers in the field, but only if the field has access to the a remote service that provides the following function:

$public_id = get_new_public_for($real_id);
[download]

This is a good solution, save that I am not in constant contact with the people collecting the data, nor their laptops. So, to do this I would require some means of pre-arranging the relationship between "public" and "real" ids.

Do all the laptops have all the important numbers?

Or just each have one (or a few), and any reversal done (and the DB stored), in your secure location?

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In the absence of evidence, opinion is indistinguishable from prejudice.

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No, I will only be collecting a few hundred or thousand numbers, roughly split between two laptops. Reversal will be in a secure location.