Bitcoin needs to overcome its scalability problem to accommodate mainstream adoption. While the Bitcoin base layer remains relatively unchanged, scaling solutions like Schnorr signatures can improve the scalability and privacy of the network. 

In this guide, we delve into Schnorr signatures, how they work, their role in the Bitcoin network, and how they differ from ECDSA.

What Are Schnorr Signatures?

Schnorr signatures are a digital signature scheme that combines multiple signatures into one valid signature when verifying and authorizing transactions. 

That reduces the requirements for processing Bitcoin multi-signature transactions and improves privacy by making all transactions look like single-signature transactions. 

The digital signature is produced by the Schnorr signature algorithm created by cryptographer Claus P. Schnorr. The Schnorr algorithm was patented until 2008, which expired months before Satoshi Nakamoto released the Bitcoin whitepaper. It may not have been used for Bitcoin at the time because it lacked the testing and popularity required to secure such a critical network. 

How Do Schnorr Signatures Work?

A transaction can’t be completed in the Bitcoin network without a digital signature. Digital signatures are mathematical codes used to prove the authenticity and validity of transactions in the network. 

Schnorr signatures were introduced in Bitcoin’s Taproot upgrade to improve the network’s privacy, efficiency, and security. 

The signature uses elliptic curve cryptography (ECC) and is known for its simplicity in streamlining the process of signing transactions. ECC provides a secure and efficient way to perform mathematical operations.

The main benefit of Bitcoin Schnorr signatures is key and signature aggregation. The digital signature allows the aggregation of multiple signatures, combining them into one valid signature for all public keys. 

For instance, Alice, Bob, and Charlie have a multi-signature wallet. To perform a Bitcoin transaction, they must all include their signatures. Verifying all three public keys and signatures requires three times the computation and takes up more block space than single-signature transactions, which increases fees. 

Schnorr signatures solve this problem by combining the three public keys into one valid key and combining their three signatures to form a single signature through aggregation. A validator will only have to verify one public key and one signature, which reduces the transaction size and frees up block space. The transaction fees will also be lower.

Schnorr signature aggregation makes multi-signature transactions indistinguishable from standard transactions and prevents observers from knowing which users have signed a transaction, enforcing confidentiality. Additionally, they have non-malleability properties that make them resistant to tampering and modification.

Role of Schnorr Signatures in Bitcoin

Schnorr signatures were implemented in Bitcoin in November 2021 within the Taproot upgrade as an alternative to the Elliptic Curve Digital Signature Algorithm (ECDSA). They are backward compatible with older versions of the Bitcoin network software, allowing them to be introduced through a soft fork upgrade. 

Schnorr signatures play a significant role in enhancing Bitcoin’s security, privacy, and efficiency. They are a first-layer scaling solution that reduces the data load within a block by creating a more compact representation of multi-signature transactions. 

The signature algorithm improves the network’s security through added protection against signature modification and spam attacks. Additionally, Bitcoin multi-signature transactions under the Schnorr signature algorithm are indistinguishable from standard single-signature transactions, which preserves user confidentiality. 

Signature aggregation on the Bitcoin network saves space and computation resources during transaction verification, increasing scalability. 

Schnorr Signatures Vs ECDSA: What’s the Difference?

Since the Taproot upgrade that introduced Bitcoin Schnorr Signatures is a soft fork, users continue to use the preceding mechanism, the Elliptic Curve Digital Signature Algorithm (ECDSA), for signature generation.

Let’s look at how Schnorr Signatures differ from ECDSA:

  • Schnorr signature aggregation eliminates the need for multiple signatures and keys to authorize transactions and has smaller signature sizes than the bulky transaction sizes in ECDSA. 
  • The Schnorr signature algorithm introduces improved resistance to spam attacks and protection against signature tampering, while ECDSA has limited privacy features.
  • Schnorr signatures support batch verification, which gives the scheme a faster verification time and is less resource-intensive than ECDSA.
  • Schnorr signatures make multi-signature transactions indistinguishable from standard single-signature transactions, which improves user privacy.
  • Schnorr signatures have provable security and linearity and are non-malleable, while ECDSA is inherently malleable. 

While the Taproot upgrade has already activated Schnorr signatures, ECDSA is widely considered a secure signature scheme. Therefore, blocks will continue to have both Schnorr and ECDSA schemes, and the choice between them will depend on use cases and security requirements. 

Conclusion

While trusted by many, Bitcoin’s original verification process, ECDSA, can be resource-intensive, leading to higher fees and slower transaction times. Schnorr signatures are an innovative way to solve the challenges of ECDSA and improve Bitcoin scalability and privacy. 

The Taproot upgrade allows the aggregation of multiple signatures into one valid signature, frees up block space, and requires fewer computational resources and fees. The new signature scheme is a step toward increased mainstream adoption of Bitcoin.