Schnorr vs ECDSA: What's the Difference? A Bitcoin Signature Example

Crypto Basics

24 October 2026

The most practical difference is not about "which is more secure" — both rely on the same elliptic curve cryptography assumptions and offer comparable security. The real difference lies in the mathematical structure: Schnorr signatures are "linear," while ECDSA is not. This linear property allows Schnorr to do something ECDSA cannot: combine multiple public keys and multiple signatures into a single public key and a single signature, making them look exactly like a standard single-signature transaction on-chain. This is the core reason Bitcoin introduced Schnorr through the Taproot upgrade in 2021.

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Linear vs Non-linear: One Word Defines the Watershed

In ECDSA's signature verification equation, public keys and signatures do not have a simple additive relationship, so you cannot "add" two signatures together to get a valid aggregated signature. Schnorr's equation is s = r + c·x (r is a random nonce, c is the challenge hash, x is the private key), creating a linear relationship between the signature and the private key. This means partial signatures from multiple parties can be directly added together.

The consequences of this mathematical difference are very concrete: With ECDSA, a 2-of-2 multisig requires 2 public keys and 2 signatures on-chain, and verifiers must check each one. With Schnorr, 2 parties can use the MuSig protocol to combine their public keys into one and their signatures into one, so only a single public key and a single signature appear on-chain. A 50-of-50 multisig transaction would be roughly the same size as a single-signature transaction.

What This Means for Ordinary Bitcoin Users

Lower fees, and multisig no longer "exposes its identity." ECDSA multisig transactions are noticeably larger than single-signature transactions on the blockchain, resulting in higher miner fees, and on-chain analysts can easily see that "this is a multisig wallet." With Schnorr aggregation, multisig transactions are indistinguishable from ordinary transfers on-chain. This improves privacy while also bringing fees down to near single-signature levels. If you use a Taproot-enabled wallet for multisig, these cost savings are very real.

But the size difference for a single signature is very small. Some sources mention that a serialized Schnorr signature is about 8 bytes smaller. For the most common single-signature transfers, the fee difference is negligible. Schnorr's advantages mainly appear in multisig and complex script scenarios, not in making "every transaction much cheaper."

A Point That Is Easy to Misunderstand: ECDSA's "Malleability" Issue

ECDSA signatures have malleability: for a valid signature (r, s), (r, n-s) is also valid. This means a third party can modify the signature data without changing the transaction's validity, thereby changing the transaction ID. This caused problems in Bitcoin's early days and was one of the things SegWit was designed to address. Schnorr signatures are designed to avoid this problem—the signature is uniquely determined. But this does not mean Schnorr makes Bitcoin "more secure"—ECDSA's malleability has already been handled at the existing protocol layer through other means. Schnorr just makes things cleaner.

Do You Need to Care About This Right Now?

If you are just making ordinary transfers, whether you use an ECDSA address (starting with 1, 3, or bc1q) or a Taproot address (starting with bc1p), the actual experience difference is minimal. The small fee difference depends on current on-chain congestion and transaction structure, and should not be your primary reason for choosing an address type.

If you use a multisig wallet (for example, to co-manage funds with a partner, or to set up a 2-of-3 backup with hardware wallets), the fee and privacy advantages brought by Schnorr and MuSig2 are worth considering. But this assumes your wallet software already supports Taproot and MuSig2, and that all participants are willing to upgrade. Currently, mainstream wallets have fairly widespread support for Taproot, while the rollout of MuSig2 multisig depends on the specific wallet product.

If you are running a Lightning Network node, Schnorr enables PTLCs (Point Time Locked Contracts) to replace HTLCs, improving routing privacy and efficiency. However, this is a change at the node operation level that ordinary users will not directly perceive.

Key Differences at a Glance

Dimension	ECDSA	Schnorr
Security assumption	Elliptic curve discrete logarithm	Same
Single signature size	Slightly larger	Slightly smaller (about 8 bytes less)
Multisig aggregation	No native aggregation, recorded individually on-chain	Supports MuSig aggregation into a single signature
Multisig privacy	Identifiable as multisig on-chain	Indistinguishable from single-signature
Malleability	Exists (`(r,s)` and `(r,n-s)` are both valid)	None
Bitcoin activation time	2009 (original scheme)	November 2021 (Taproot)