@Sakura please summarize this article, thanks uwu.
TLDR:
A tutorial on the GKR protocol explains its efficiency in cryptographic proofs, particularly for computations like Poseidon hashes. 
Key Points:
- GKR Protocol: A cryptographic scheme designed for efficient proofs of large computations.
- Efficiency: GKR avoids commitments to intermediate layers, only requiring commitments to inputs and outputs.
- Applications: Particularly useful for proving hashes and neural network computations.
- Sumchecks: A core technique in GKR that simplifies proving polynomial evaluations.
- Performance: GKR shows significant overhead reduction compared to traditional STARKs, making it a promising approach.
In-depth summary:
The GKR (Goldwasser-Kalai-Rothblum) protocol is a cryptographic method that enhances the efficiency of proving large computations, particularly in the realm of zero-knowledge proofs. This tutorial, authored by Vitalik Buterin, delves into the mechanics of GKR, focusing on its application to Poseidon hashes, a type of cryptographic hash function. The GKR protocol is particularly adept at handling computations that are structured in layers, allowing it to process multiple inputs simultaneously without the need for extensive commitments to intermediate results.
One of the standout features of GKR is its use of sumchecks, a technique that reduces the complexity of proving polynomial evaluations across a hypercube. By transforming obligations to prove sums into obligations to prove evaluations at random coordinates, GKR streamlines the proving process. This method not only minimizes the amount of data that needs to be committed but also allows for efficient verification by the prover and verifier alike.
The tutorial also highlights the practical implications of GKR, noting its potential to significantly reduce the overhead associated with traditional proof systems like STARKs. With a theoretical overhead of about 15 times compared to the 100 times seen in traditional methods, GKR presents a compelling option for cryptographic applications, especially in contexts like proving neural network inferences and other complex computations.
ELI5:
The GKR tutorial explains a smart way to prove that big calculations are correct without doing a lot of extra work. It uses a special trick called sumchecks to make this easier and faster. This method is especially good for things like checking hashes, which are important in keeping data safe. Overall, GKR helps save time and effort when proving complex math problems!
Writers main point:
The primary point of the article is to showcase how the GKR protocol efficiently proves large computations, particularly in cryptographic contexts, by minimizing commitments and leveraging sumchecks.