What do Schnorr Signatures Mean for Bitcoin?

Introduction

Bitcoin widely employs the Elliptic Curve Digital Signature Algorithm (ECDSA) to verify ownership. Through this algorithm, users can derive a public key from a private key. Remarkably, while the public key can be easily obtained from the private key, the reverse operation is infeasible. The private key serves as a passport into the Bitcoin network, allowing users to generate addresses for receiving tokens and enabling them to spend those tokens later.

In this article, we will explore an alternative to ECDSA—the Schnorr signature algorithm—and the exciting changes it is set to bring to Bitcoin.

A Brief Overview of Digital Signatures

The principle of digital signatures is similar to that of traditional handwritten signatures, but with much higher security. While anyone can invest time and effort in forging a handwritten signature, a robust digital signature is nearly impossible to break. Digital signatures have numerous applications, one of the most common being the communication of specific information to the public.

Using a private key (a string of numbers that must be kept secret), a user can create a public key, relying on the complex mathematical operations of the secp256k1 curve. Subsequently, the public key can be used to generate a public address.

It is important to note that sharing the public key is entirely secure. It can be publicly posted on personal websites or social media, allowing others to verify the identity of the publisher through the public key. Similarly, a public address can be shared safely to receive cryptocurrency from others.

Users can generate their personal digital signatures using their private keys. After composing a message and signing it with the private key, a signature is created. Anyone can compare this signature with the public key to verify its authenticity.

What does this have to do with Bitcoin? In fact, all Bitcoin transactions include digital signature information, indicating, "I am sending the tokens I received earlier." When information is sent to other nodes in the network, they verify whether the ECDSA signature matches. If it does not match, the nodes will reject the information.

What Is Schnorr Signature?

Schnorr signatures represent a fundamentally different mechanism. Although its operation is similar to that of the currently used ECDSA, its advantages are more pronounced. In fact, Schnorr signatures predate ECDSA, leading many to wonder why this mechanism was not initially adopted in Bitcoin.

A plausible explanation is that the inventor of the mechanism, Claus P. Schnorr, had patented it. Although the patent expired in early 2008, prior to the release of the Bitcoin white paper, the mechanism had not yet been fully standardized at that time. As a result, Satoshi Nakamoto opted for the more widely accepted open-source ECDSA.

Why Schnorr Signatures Have Advantages

Compared to other mechanisms, Schnorr signatures are significantly simpler, which enhances their security. While Schnorr signatures may not seem particularly meaningful at first glance, they possess a powerful characteristic: linearity. Simply put, this feature makes Schnorr signatures especially suitable for certain operations, particularly in multi-signature transactions.

Although Bitcoin supports multi-signatures, the results are often less than satisfactory. When creating a multi-signature address, the sender of the funds does not need to understand the spending conditions set by the users and may not even know they are sending funds to a multi-signature address; the only distinguishing factor is that the address starts with a "3."

However, the limitations of this model become apparent when transferring funds. Suppose there are three individuals—Alice, Bob, and another person—using the same setup. If one person needs to spend 5 bitcoins, all three must provide their public keys and valid signatures. The entire network becomes aware of this situation by observing the blockchain, which is not ideal for privacy. Moreover, if a more complex multi-signature setup is used (for example, requiring 8 out of 10 participants to sign), it occupies more block space, resulting in longer transaction times and higher fees. The more bytes in a transaction, the higher the fees paid.

Schnorr signatures are seen as a solution for privacy and scalability. As we have observed, Schnorr signatures support signature aggregation, meaning that the signatures of multiple signers can be combined into a single signature. Consequently, the length of the "master signature" is the same as that of a conventional single-user signature, significantly saving space. Additionally, it becomes difficult for outsiders to discern which participants signed the transaction from the mixed signatures. This means that in an m-of-n mechanism, funds can only be accessed once all participants have signed, making it impossible for external observers to determine whether it is a single-party transaction or a multi-signature transaction.

Crucially, Schnorr signatures will serve as a cornerstone for further developments in blockchain technology. Once implemented, they will help improve related technologies in cryptocurrencies, such as atomic swaps and the Lightning Network.

When Will Schnorr Signatures Be Implemented in Bitcoin?

The specific timeline for implementation is yet to be determined. Like most upgrades to the Bitcoin protocol, Schnorr signatures need to gain broader acceptance among Bitcoin users before implementation, a process that may take some time. Major contributors to Bitcoin, including Pieter Wuille, Jonas Nick, and Tim Ruffing, have submitted a Bitcoin Improvement Proposal (BIP), but further refinements are still needed.

Blockstream has introduced the MuSig signature scheme, which allows for the aggregation of signatures and keys and may serve as a foundation for Bitcoin's own Schnorr signature mechanism. Schnorr signatures can be integrated into the code as a soft fork, meaning that this change will not split the network but will require users to "opt in." Despite this, there is optimism that the integration of Schnorr signatures is on the horizon, though achieving consensus is not something that happens overnight.

Conclusion

Schnorr signatures are one of the most anticipated milestones in Bitcoin's current roadmap. Through a single upgrade, privacy and scalability will significantly improve. Additionally, Schnorr signatures will pave the way for the further development of advanced structures such as Bitcoin smart contracts and Taproot.

Risk Warning

While the cryptocurrency market offers significant growth potential and innovation opportunities, it also carries a high level of market risk and price volatility. The value of crypto assets can fluctuate dramatically in a short period, potentially leading to substantial financial losses for investors. Additionally, the cryptocurrency market faces multiple risk factors, including technical risks, legal and regulatory uncertainties, cybersecurity threats, and market manipulation. We strongly advise users to conduct thorough research and due diligence before making any investment decisions and to consult professional financial advisors. All investment decisions are made at the user’s own risk. Thank you for your trust and support of Venkate!

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