Schnorr Signature

Publication Date :

29 Jan, 2025

Blog Author :

Edited by :

Reviewed by :

Table Of Contents

What Is Schnorr Signature?

Schnorr signature is a simple and efficient scheme for short digital signatures. It is a public cryptographic algorithm used for verifying and generating digital signatures. The scheme combines a number of keys into one complex transaction to generate a single key.

You are free to use this image on your website, templates, etc.. Please provide us with an attribution link.

The single key generated is unique and uses a private key to sign messages and another public key to verify signatures. The scheme reduces data load by improving the transaction per second (TPS) per block and transaction anonymity. The signatures facilitate the use of a single signature to authorize multiple transactions without the need to sign each transaction separately.

Key Takeaways

The Schnorr signature is a scheme for generating and verifying digital signatures. It combines several keys or signatures in one complex transaction.
It reduces the network's data load, improves transaction rates, enhances anonymity, and authorizes transactions. The scheme uses elliptic curve cryptography (ECC) to generate unique keys.
There are two types of keys: private key and public key. Private keys are used to sign messages, and public keys verify them. They are, however, vulnerable to certain types of attacks and can be tracked.

Schnorr Signature Explained

The Schnorr signature is a digital signature scheme created using the Schnorr Signature Scheme. It is a cryptographic tool that helps in making secure digital transactions and communications. It is efficient and simple, utilizing a hash function to produce a message digest. This digest is then used to generate and verify digital signatures.

The scheme uses elliptic curve cryptography or ECC. The signature combines several signatures into one. This is achieved by expanding the capacity of each block through an increased number of transactions. It takes up less space, too, and hence, is a preventive tool for spam attacks.

The process can be summarized in three parts: key generation, signing, and verification. The user first generates a public and a private key. The public keys carry values of large prime numbers in a way that the second value divides the first value minus one. It shall be noted that the second value is a generator of the group modulo the first value. The private key is an integer taken at random. The next part is signing. The signer will generate a random integer where it is 1 <= random integer <= second value-1 and calculate based on this integer to create the message signature. If the conditions are satisfied, the signature is valid.

Examples

Below are some examples to explain the concept better:

Example #1

Imagine there are three business parties, A, B, and C, who want to transact a high-value payment and authorize it jointly. Initially, they decided to use the traditional ECDSA approach, but it requires three public keys and separate signatures to authorize it. Thus, they use the Schnorr scheme, where they have the option of combining individual public keys of the parties into one aggregate public key. This reduces their data load and improves privacy and computational efficiency.

Example #2

The Internet computer protocol (in short, the ICP) plans to use enhanced threshold cryptography on Bitcoin's base layer. This could unlock the token's smart contract functions and decentralized finance capabilities. Furthermore, the proposal to integrate threshold and Schnorr signatures is expected to enable smart contracts of the protocol to obtain addresses and authenticate transactions into the Bitcoin blockchain directly. Bitcoin schnorr signature with the threshold feature is expected to be rolled out midway through 2024 and help in the authorization and batching of native Bitcoin transactions.

Benefits

Given below are some of the benefits of the signature scheme:

It requires the signing of several signatures for a single transaction, enhancing the transaction's security.
The scheme aggregates the public keys or signatures of several users and devices into one master key or signature. This saves computation resources and space in confirming transaction validity and contributes to better network scalability.
Time and computation power are reduced through this, which enables batch verification.
Parties involved cannot modify or alter the signatures for double spending once they are created.
Merging of keys helps in improving privacy and saves a lot of fees that are otherwise involved in a transaction.
The Schnorr signature algorithm is simple to implement and prevents attacks, forgery, impersonation, and tampering of transactions.

Limitations

Given below are some of the limitations of the signature scheme:

It is computationally intensive and needs large sizes of keys to enhance security.
It is vulnerable to specific attacks, such as side-channel attacks, and can be subjected to key compromises.
Enhanced security doesn't prevent others from tracking the transaction.

Schnorr Signature Vs. ECDSA

Given below are some of the differences between these two cryptographic signature schemes:

Aspect

Schnorr Signature

ECDSA

Concept

It is a method of generating encrypted messages with its algorithm with the ability to merge multiple messages.

The Elliptic Curve Digital Signature Algorithm, or the ECDSA, is a signature scheme that generates messages that are encrypted using an elliptic curve algorithm. The algorithm helps verify the ownership of funds with the owners' addresses.

Space efficiency

Schnorr digital signatures are space efficient.

ECDSA is less space efficient than Schnorr digital signatures.

Key elements

These signatures are considered better or the next step of ECDSA as they aggregate and hide public keys. As a result, transaction fees and congestion in blockchains are reduced.

The ECDSA method exposes a higher amount of data and does not offer concealment. This increases the transaction fee and congestion in the network comparatively.