Join Log in
Score:0
Arian B avatar Crypto

Is BLS multi-signature aggregation separable?

in flag
Arian B

In BLS multi-signature aggregation scheme we can combine different signatures of different peers into one single signature, and then we can verify whether the aggregated signature is truly signed by the claimed peers.

My questions is, having an aggregated signature, is it possible to separate the signatures and achieve the individual signatures of the peers? For example, having an aggregated signatures of A, B, and C, is it possible to separate it and get the original signature of A?

I would appreciate any resource.

34
0 + 0
Score:2
poncho avatar Crypto
my flag
poncho

For example, having an aggregated signatures of A, B, and C, is it possible to separate it and get the original signature of A?

Well, in BLS, an aggregated signature just the sum of the original sigantures; $\text{sign}(A,B,C) = \text{sign}(A) + \text{sign}(B) + \text{sign}(C)$ (where $\text{sign}(A,B,C)$ stands for the aggregate signature of $A, B, C$, and the addition is done on the pairing-friendly elliptic curve)

Hence, if you're just given the aggregated signature $\text{sign}(A,B,C)$, there isn't enough information to recover one of the original signatures.

However, if you do have the signatures of $B$ and $C$, you can subtract them out to reconstruct the original signature of $A$; $\text{sign}(A) = \text{sign}(A,B,C) - \text{sign}(B) - \text{sign}(C)$

0 + 0
Arian B avatar
in flag
Arian B
Thank you for your answer, that makes sense. You without having others signatures, it's impossible to compute individual signature.
0
Reply
Arian B avatar
in flag
Arian B
another question, if we have a signature in BLS, sign(A), and we have a big prime number, P, can we derive sign(A) having sign(A) ^ P?
0
Reply
poncho avatar
my flag
poncho
@ArianB: yes, we can compute $P^{-1} \bmod q$ (where $q$ is the group order), and so $\text{sign}(A) = (\text{sign}(A)^P)^{P^{-1}}$
0
Reply
ธงชาติไทย
Elon Musk
I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.