# Efficient Aggregate Signatures With Same Key

Suppose Alice has a set of messages $$\mathcal M$$ and generates signature pairs for each message $$(m_1,s_1)$$, $$(m_2,s_2)$$, ... $$(m_n,s_n)$$ using the same key. She then transfers these signature pairs to Bob, who knows Alice's public key.

Can Bob, without interacting with Alice, generate a new aggregate signature for the entire message set, i.e. ($$\mathcal M, s')$$, that validates with Alice's public key?

If I understand it correctly, this is achievable using BLS signatures, but I was wondering if there is a simpler and more efficient method available if there is only one signer. I am mainly concerned with validation speed.

• corrected typos and verifiable. check please. – kelalaka Jan 14 at 13:09