In line with the research direction of achieving practical efficiency with respect to the cryptographic building blocks we use and require in our protocols, our recent research pre-print Efficient Aggregatable BLS Signatures with Chaum-Pedersen Proofs describes our efficiency improvements for verification of BLS signatures for both individual as well as aggregated signatures.
In more detail and more technical terms, in our new scheme individual signature verification requires no pairings and only operations in the first source group of the pairing and the aggregated signature verification requires only operations in the first source group besides two pairings. Both cases represent an improvement when compared to standard BLS verification for individual and aggregated signatures.
Such efficiency improvements will come in handy when implementing and integrating into Substrate our accountable light client system (described in this thread) that is the core building block for secure bridges between PoS blockchains with BLS signature support in general and for a Polkadot-Kusama bridge in particular. More concretely, our improvements would allow both a BLS signature aggregator (that needs to check the validity of the individual signatures he is aggregating) and a light client verifier to run more efficiently.