Compact Multi-Signatures for Smaller Blockchains學習筆記

1. 引言

Boneh等人2018年論文《Compact Multi-Signatures for Smaller Blockchains》
在《Simple Schnorr Multi-Signatures with Applications to Bitcoin》論文的Musig方案的基礎上，做了改進。（參見博客 Simple Schnorr Multi-Signatures with Applications to Bitcoin 學習筆記）

本論文的設計目標是：
reduce the size of the Bitcoin blokchain。

• 支持signature compression。
• 支持public-key aggregation。
• multi-signature scheme：a number of parties signed a common message $m$。
• 基於Schnorr signatures和BLS signatures。
• 支持plain public key model，即：users do not need to prove knowledge or possession of their secret key。
• 構建了第一個short accountable-subgroup multi-signature (ASM) scheme。
• ASM的signature size 僅爲$\mathcal{O}(\mathcal{k})$ bits over the description of $S$，其中$\mathcal{k}$爲security parameter。
• aggregate public key 僅爲 $\mathcal{O}(\mathcal{k})$ bits，與$n$無關。

1.1 ASM定義

ASM (accountable-subgroup multi-signature)是指：
enables any subset $S$ of a set of $n$ parties to sign a message $m$ so that a valid signature discloses which subset generated the signature (hence the subset $S$ is accountable for signing $m$)。

代碼實現:
https://github.com/lovesh/signature-schemes
https://github.com/KZen-networks/multi-party-schnorr