Bitcoin Magazine
Not ECDSA. Not Schnorr. Meet DahLIAS.
Combination signatures aren’t new. They’ve been round for the reason that early 2000s. However constructing one that truly works in Bitcoin’s safety mannequin, with Bitcoin’s elliptic curve, has by no means been confirmed. Builders speculated it is perhaps attainable. They shared hand-wavy sketches and stated, “maybe it’d work like MuSig2, but across transaction inputs.” The concept lingered for years as developer folklore, shut, by no means provably confirmed.
That modified just lately, when Jonas Nick and Tim Ruffing of Blockstream Analysis, along with Yannick Seurin of Ledger, printed a paper that turned this cryptographic ghost story right into a concrete, provable outcome. DahLIAS is the primary formal, safe building of a full constant-size combination signature (CISA) scheme that works on Bitcoin’s native curve!
However that’s lots of phrases, so let’s break that down:
- Full aggregation: A number of signatures throughout totally different inputs are mixed into one — and the result’s a 64 byte signature whose measurement stays fixed, irrespective of what number of signers or inputs.
- Cross-input: Every signer can authorize totally different inputs, and all mix into one signature.
It provides no important new assumptions past these already relied on by Bitcoin. DahLIAS builds a brand new cryptographic primitive utilizing the identical math Bitcoin already depends on, unlocking a completely new form of signature.
Let’s Discuss About Curves and Signatures
Digital signatures are how Bitcoin proves {that a} person has licensed a transaction. If you go to spend bitcoin, your pockets makes use of a non-public key to signal a message, and the community verifies that signature utilizing the matching public key.
Bitcoin makes use of the secp256k1 curve. It’s quick, environment friendly, and has been battle-tested over time. It helps signature schemes like ECDSA (Bitcoin’s authentic signature algorithm) and Schnorr (added via Taproot in 2021), that are presently the one signature schemes permitted by Bitcoin consensus.
Historically, full signature aggregation relied on mathematical operations not supported by Bitcoin’s curve, secp256k1, which made it appear out of attain. These options have sometimes relied on different sorts of elliptic curves. For instance, BLS (Boneh–Lynn–Shacham) signatures use a particular form of curve referred to as a pairing-friendly curve, which allows superior operations like combining many signatures, even on totally different messages, into one.
The issue is that BLS signatures don’t work on secp256k1. Whereas Schnorr was a pure improve from ECDSA, since each depend on the identical form of elliptic curve, including BLS could be a a lot larger leap and a departure from Bitcoin’s present safety mannequin. Although technically attainable, it might introduce new cryptographic assumptions and add important complexity to the protocol. Supporting a curve that’s pairing-friendly, like BLS12-381, could be a significant change for Bitcoin.
That is a part of why full signature aggregation has by no means been executed on secp256k1.
Till now.
What Combination Signatures Truly Do
Most Bitcoin customers are conversant in multisignatures. In a multisig pockets, a number of individuals collectively authorize the spending of a single UTXO or some particular “coin”. Everybody indicators the identical enter knowledge. This setup is helpful for issues like shared custody wallets.
Combination signatures work in a different way. As a substitute of a number of individuals signing the identical enter or coin, every signer authorizes a distinct UTXO in a transaction. These separate signatures are then compressed into one compact proof. With DahLIAS, which means a single 64-byte signature on Bitcoin’s secp256k1 curve that verifies all inputs without delay.
Which means if in case you have 5 inputs from 5 totally different individuals, the transaction wants 5 totally different signatures. With an combination signature, all of these could be bundled into one. Even when every signer is spending a distinct enter and signing a distinct a part of the transaction, the result’s one signature that proves all the transaction was correctly licensed.
It’s like zipping a complete listing of approvals into one file. The signature is compact, however nonetheless verifiably proves that every signer licensed their particular UTXO.
As a substitute of verifying 10 separate signatures, you confirm one.
This helps realign incentives for privateness. By decreasing the signature overhead to a single 64-byte proof, DahLIAS lowers the price of combining inputs in CoinJoins, making it financially smarter to decide on privateness than to go with out it.
Why Half-Aggregation Bought Shut
Shortly after Schnorr signatures have been launched on Bitcoin, builders explored half-aggregation, as a technique to compress a number of signatures however they weren’t mounted measurement. Every enter contributes to the scale of the signature, so the transaction nonetheless grows with each participant. DahLIAS fixes this by enabling full-aggregation throughout inputs and signers. Irrespective of how many individuals are concerned or what they’re signing, all their signatures compress into one constant-size, 64-byte proof.
What DahLIAS Truly Unlocks
The primary profit right here is that DahLIAS are decreasing the scale of advanced transactions.
DahLIAS makes use of a two-round interactive signing course of. It’s just like MuSig2 in that regard, but it surely isn’t a multisignature protocol as a result of it doesn’t require all contributors to co-sign the identical message. As a substitute, it aggregates totally different signatures on totally different messages throughout the transaction.
DahLIAS can also be sooner to confirm than checking every signature individually, as much as twice as quick in some circumstances. Decrease verification prices make it simpler for extra individuals to run full nodes, which helps protect Bitcoin’s decentralization over time.
Importantly, DahLIAS comes with robust cryptographic ensures. The scheme contains formal safety proofs. Earlier ‘folklore’ approaches to full signature aggregation lacked this, and a few have been even later proven to be insecure. Luckily they weren’t adopted prematurely.
It’s value repeating: DahLIAS just isn’t a multisig protocol. It isn’t akin to MuSig2 or FROST from a purposeful standpoint, even when it shares related cryptographic constructing blocks. It serves a distinct objective. It provides a brand new technique to encode many unbiased approvals into one clear, verifiable bundle.
Future Instructions
You would possibly assume: if DahLIAS is so highly effective, why isn’t it a BIP? Why not suggest it for Bitcoin consensus?
DahLIAS signatures don’t appear to be Schnorr or ECDSA signatures. The verification algorithm is totally different. As a substitute of taking a single public key, message, and signature, a DahLIAS verifier takes lists of public keys and messages, and a single 64-byte proof.
This makes DahLIAS incompatible with Bitcoin’s present consensus guidelines. Supporting it on the base layer would require a consensus change. This paper doesn’t suggest that change, but it surely does one thing equally vital.
This paper exhibits {that a} full signature aggregation scheme for Bitcoin’s native curve is feasible.
That alone is a significant step ahead.
To make DahLIAS a part of Bitcoin, somebody would want to write down a Bitcoin Enchancment Proposal (BIP), perhaps even utilizing secp256k1lab. Which means specifying the scheme intimately, contemplating its implications for consensus and implementation, and constructing group assist. This paper lays the cryptographic basis for that dialog.
The actual worth of the DahLIAS paper is what it proves. Full signature aggregation on secp256k1 isn’t just a thought experiment. It’s concrete. It’s environment friendly. It’s safe. For years, the thought lived in developer folklore. Now, it’s written down, analyzed, and confirmed. All that’s left is to carry it to Bitcoin—if we wish it.
This can be a visitor put up by Kiara Bickers. Opinions expressed are solely their very own and don’t essentially mirror these of BTC Inc or Bitcoin Journal.
This put up Not ECDSA. Not Schnorr. Meet DahLIAS. first appeared on Bitcoin Magazine and is written by Kiara Bickers.
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