18 Exploring BLS multi-signatures
This chapter covers
- Aggregate signature of multiple users
- Subgroups using membership keys
- Pairing mathematics for verification
In this chapter, I’ll dive into an advanced signature system that takes advantage of elliptic curve pairings. The method is an extension of BLS signatures that use pairings to accomplish the same digital signature task described in chapter 5. The advantage of this method is the ability to combine multiple signatures into one verification step.
Chapters 18 and 19 include a lot of mathematical variables. To help keep track of them, you will find a list of all the variables used throughout the entire book in appendix C.
18.1 Introduction to multi-signatures
The initials BLS show up in two places within the pairing literature. In chapter 14, I mentioned BLS curves, associated with the authors Barreto, Lynn, and Scott. BLS signatures are associated with the authors Boneh, Lynn, and Shacham. Lynn is the same in both, but everyone else is different. The theory of digital signatures using pairings presented in this chapter follows the BLS signature scheme. It is an extension from BLS short signature to multiple signers.