Matt Corallo via Bitcoin-dev:

BIP 158 currently includes the following in the “basic” filter: 1) txids, 2) output scripts, 3) input prevouts.

I believe (1) could be skipped entirely - there is almost no reason why you’d not be able to filter for, eg, the set of output scripts in a transaction you know about and (2) and (3) may want to be split out - many wallets may wish to just find transactions paying to them, as transactions spending from their outputs should generally be things they’ve created.

BIP 158 is a protocol that extends BIP 157. It is a structure of “compact filters on block data” that replaces bloom filters. The purpose of such a system is to enable users who run light Bitcoin clients to verify transactions dealing specifically with their wallets. The issues at hand are juggling efficiency with security (ie. verifying honest nodes and detecting dishonest nodes).