I can provide you with an article on this topic. However, I must clarify that there is no specific discussion or question about breaking 33-byte public keys from Schnorr signatures on Ethereum.
Nevertheless, here is a draft article based on my understanding of the topic:
Ethereum: Why there are no security breaches with 32-byte public keys and Schnorr signatures
Public keys are unique identifiers for digital assets that allow users to securely access cryptographic keys. In Ethereum, public keys are represented as (x, y) coordinates, where x represents the private key and y the associated public key.
Regarding Schnorr signatures, the digital signature used for Ethereum transactions, there is currently a discussion about using 32-byte public keys instead of the standard 33-byte format. In particular, some users ask why security is not achieved when using shorter public keys.
What are Schnorr signatures?
Schnorr signatures are a type of digital signature that allows users to sign messages without revealing their private key. They use a one-way hash function and a secret number called a “secret value” (s) to create a unique identifier for each message. This identifier is then used to create a digital signature that is hashed with the user’s private key.
33-byte format
In Ethereum, public keys are typically represented as (x, y) coordinates, where x represents the private key and y represents the associated public key. The standard format for these coordinates is 32 bytes long, and consists of:
- X coordinate: random 256-bit value
- Y coordinate: random 256-bit value
Consumption
When using Schnorr signatures with shorter public keys (e.g. 31 bytes), some users argue that there is no loss of security because the shortened key is still long enough to generate the required secret values. Shortening the key can actually improve efficiency because it reduces the computational cost associated with generating and verifying a digital signature.
However, this argument assumes that the shorter key is still valid and secure. In reality, a shorter key may not be suitable for all cryptographic operations, such as encryption or signing large messages. Additionally, some users may argue that using a longer key provides more flexibility and reliability for cryptographic operations.
Conclusion
While there are valid arguments on both sides of this debate, there is still no consensus on whether or not using 32-byte public keys for Schnorr signatures on Ethereum is secure. The debate is ongoing, and it is important for users to stay up to date with the latest developments and updates from the Ethereum community.
In conclusion, while using shorter public keys can offer some benefits, such as improved efficiency and flexibility, there is no loss of security when using these shortened keys. However, users should be aware of the potential tradeoffs and risks associated with shortening their public keys before making a decision.
Please note that this article is based on my understanding of the subject, and I am not an expert in cryptography or Ethereum development. If you have specific questions or concerns about Schnorr signatures or 32-byte public keys on Ethereum, feel free to ask!