CISA Research

Cross-Input Signature Aggregation for Bitcoin

Welcome CISA friends!

This website aims to reflect the current state of research into applying cross-input signature aggregation to Bitcoin and related protocols. It also maintains a list of open tasks that contributors interested in the topic can apply themselves to.


This page gives a very high-level overview of CISA before diving deeper into the different topics in the rest of the pages on this website.

Schnorr signature linearity property

Schnorr signatures have a linearity property that allows for simpler aggregation of such signatures when compared to their ECDSA counterparts. Since the Taproot softfork activation in 2021, Schnorr signatures can be used in Bitcoin which opens the door to proposals that could allow usage of aggregate signatures in the Bitcoin protocol in the future.


The base for CISA was layed in BIP 340 (Schnorr signatures) and the activation of the Taproot softfork in 2021. Originally, CISA was considered to be part of the Taproot proposal but this idea was abandoned in order to keep the complexity of the proposal manageable.

Signature Aggregation != Key Aggregation (e.g. MuSig, FROST)

A common source of confusion among bitcoiners new to this topic is how CISA relates to another topic that has been under static development throughout the past years: Multisignature with Key Aggregation via protocols like MuSig or FROST.

With a protocol like MuSig the involved keys are aggregated to a single key and this single key signs a single message. Given (n public keys, 1 message), n parties identified by n separate public keys create a single signature to sign the same message. The public keys pk_1, …, pk_n can aggregated into a single public key agg_pk via an algorithm KeyAgg, and agg_pk is all the verifier needs. The verification API is like this: bool VerifyMultisig(msg, agg_pk). In other words, the the verifier does not need to know who’s behind agg_pk.

In a CISA context, there are different keys that sign a different message, a different input in the transactions, but their signatures are still aggregated. Given (n pairs (public key, message): n parties identified by n separate public keys, each having also have a separate message to sign, create a single signature. Now look at the verification API: bool VerifySigagg((pk_1, msg_1), ..., (pk_n, msg_n)). Here, the verifier really needs to know all the public keys plus the one-to-one association with messages.

Aside from a different aggregation result and the correspondingly different API for verification, process-wise the primary difference is that MuSig must be performed already during address creation while CISA can be done at signing time or even later depending on which flavor is used. These differences in the protocols also lead to different security guarantees for each approach.

Still, what’s true is that in practice the algorithms may look similar and in an upcoming (full) aggregation protocol, signing could look a lot like the signing protocol in MuSig2. But we should really treat signature aggregation and multisigs as separate concepts that provide different functionalities and have different interfaces.

Half-Agg vs. Full-Agg

There are two flavors of CISA whose trade-offs need to be evaluated and contrasted to come to the best possible application for each of them. On a very high level their key differences are 1. Space savings: half-agg saves up to almost half the space of the aggregated signatures while the result of full-agg is the same size as one single signature. 2. Interactivity: full-agg requires interaction between the signers at signing time while half-agg does not.

Additionally, it should be noted that both techniques can be combined, meaning the result signature of full-agg can be further aggregated with other signatures using half-agg post-signing time if when interactivity is prohibited.


As part of the Bitcoin protocol CISA can be both used to aggregate signatures of a single transaction, a set of transactions as well as even a whole block. Furthermore, CISA can also be used to aggregate signatures used in off-chain/layer-2 protocols that rely on signatures, for example the gossip layer of the Lightning Network.