zkMemory: A Game-Changer for Memory Management by Orochi Network

Table of Contents

Zero-knowledge virtual machines (zkVMs) are at the forefront of secure and privacy-focused computation. To further their potential, we introduce zkMemory, a groundbreaking memory management concept. zkMemory is a versatile module that can be seamlessly integrated into various zkVM projects, ensuring secure and efficient memory management.

I. Generalizing Memory for zkVM (zkMemory)

Concept of zkMemory

At the core of zkMemory. It is like a special library for zkVMs, and we're making sure that reading and writing data is safe and reliable while allowing users to customize how they work with data. This is a fundamental building block for secure and efficient computing in zkVM environments.

Memory as a State Machine

Imagine a digital memory system in a computer as a library. In this library, you can read books and write notes in them. However, this isn't just any library; it's designed to work in a special kind of system called zkVM, which stands for zero-knowledge virtual machine.

In zkVM, we want to create a memory system that can be used in different zkVM setups. To do this, we're reimagining how memory works. We're treating memory like a simple state machine with two primary instructions: READ and WRITE. Think of these instructions like reading from a book and writing in a notebook. Additionally, we're making memory configurable, which means you can choose the size of the chunks of data you want to read or write. This chunk size is called WORD_SIZE.

Here's how our zkMemory works:

READ instruction: When you read from memory, you're essentially checking a page in a book. If no one has written on that page, you get a result of zero. Every time you read from the same page, you should get the same value as the last time someone wrote on it.

WRITE instruction: When you write to memory, it's like adding your own notes to a notebook. However, you can only write in certain parts of the notebook; some areas of the notebook are read-only, and you can't make any changes there.

Now, you might be wondering about a few important questions:

- How do we handle memory boundaries?: We need to make sure that we stay within the limits of memory while reading and writing. This is crucial to prevent errors and data corruption.

- Do we need to deal with memory allocation and deallocation?: Memory allocation means setting aside space for your data, and deallocation means releasing that space when you're done with it. In zkMemory, we want to make sure that memory is used efficiently and that there are no memory leaks.

- How do we deal with configurable WORD_SIZE?: We're allowing users to choose the size of the data chunks they work with. This flexibility is important because different applications may need different chunk sizes, and we want to support them all.

II. Introducing the concepts behind of zkMemory

Introduction to KZG Polynomial Commitment

KZG, short for Kate, Zaverucha, and Goldberg Commitments, is a cryptographic concept and polynomial commitment scheme that plays a pivotal role in enhancing the efficiency, security, and privacy aspects of blockchain and distributed ledger technologies.

KZG Commitments enable users to succinctly commit to data and provide proof of values at specific points. They are based on bilinear pairings and hidden order groups, which are algebraic structures with valuable cryptographic properties. These commitments offer various benefits, including succinctness, homomorphism, and the ability to efficiently verify large data sets in blockchain systems. KZG Commitments are fundamental to the development of advanced zero-knowledge proof systems, promoting scalability and privacy in blockchain networks.

Introduction to Verkle Tree

The Verkle tree, introduced by John Kuszmaul, is a k-ary tree with multiple layers. Each node in the Verkle tree has k children, making it distinct from traditional Merkle trees. zkMemory leverages the Verkle tree for efficient and privacy-preserving memory management.

Using KZG Commitment for Verkle Tree and its benefits

The Verkle tree consists of multiple layers, with each node holding commitments to its children. This hierarchical structure simplifies the proof process for memory operations.

zkMemory combines the power of the KZG commitment scheme with the Verkle tree to provide efficient memory commitment. This reduces the overhead of committing and opening memory at arbitrary nodes in the tree.

Utilizing KZG commitment for the Verkle tree offers several advantages, including shorter opening paths and constant-sized opening proofs.

III. First Implementation of zkMemory with Orochi Network

Now, let's talk about putting Orochi plans into action. We're working on creating the first version of zkMemory, and here's what we aim to achieve with it:

Building Memory Trace:

For zkVMs, ensuring the correctness and consistency of memory operations is vital. To achieve this, zkMemory introduces memory tracing. This mechanism keeps a record of every memory access, allowing for verification and proof of the memory's accuracy. Just like a library logbook, we want to document everything that happens in our digital memory.

Memory tracing offers several benefits:

Building Memory Trace: zkMemory builds a comprehensive memory trace, which acts as a historical record of memory operations.

Committing Memory to Verkle Tree: Memory traces are committed to a Verkle tree, providing an efficient way to verify memory integrity.

Providing Witness for Correctness: zkMemory generates a witness after each memory state is committed, enabling the prover to validate the memory's correctness efficiently.

Committing to the Verkle Tree

To ensure the integrity and security of our memory, we employ a special technique called the Verkle tree. This is where things get interesting. Just as a library may use unique codes or labels to manage books and their location, the Verkle tree helps us organize and protect the data in our memory.

The Verkle tree is like a complex digital tree structure, where each piece of data is securely placed. By using the Verkle tree, we can make sure that memory is organized efficiently and that it's not tampered with. It's a bit like arranging books in a library in a way that makes sense and keeps them safe.

Verkle tree was introduced by John Kuszmaul.

The KZG Polynomial Commitment Scheme

In the world of zkVMs, we have what's called a "prover" who needs to prove that the memory is being handled correctly. So, after every memory state is committed (like a library closing its doors at the end of the day), we provide a witness. This witness is like a way to prove that everything in memory is in the right place and hasn't been altered.

This is important for security and trust. If someone wants to check that the library books are all in order, they need evidence, just like in zkVMs, the prover needs a witness to show that the memory actions are accurate and secure.

One of the key tools we use in zkMemory is the KZG polynomial commitment scheme. It's like a special encryption method that ensures that data is kept safe and that we can prove it hasn't been changed.

KZG commitment works in a way that keeps the size of the proof (the evidence that memory is correct) small and the verification process quick. It's like having a small, yet highly effective, security guard for our memory library.

Why Does It All Matters?

Now, you might wonder why we're going through all this effort. The answer is simple: zkVMs are used in various applications where data security and trust are paramount. Just like a library needs to ensure its books are well-maintained and in the right order, zkVMs need to do the same for digital data. It's all about making sure that the memory is accurate, secure, and can be trusted.

IV. Ethereum Foundation Grant

Announcement of Support from Ethereum Foundation

Exciting news! Orochi zkMemory has received support from the Ethereum Foundation. This grant not only validates the significance of zkMemory but also empowers the project to further enhance memory commitment and contribute to privacy-focused technologies within the Ethereum ecosystem.

Implications and Benefits

The Ethereum Foundation's support provides zkMemory with the resources and recognition it needs to thrive. This will ultimately benefit zkVM projects by ensuring more robust and privacy-preserving memory operations.

Conclusion

In conclusion, zkMemory is a groundbreaking module that simplifies memory management for zkVMs. By introducing memory tracing, leveraging the KZG commitment scheme, and utilizing the Verkle tree, zkMemory enhances memory commitment and validation. This easy-to-implement system offers a flexible solution for zkVM projects, contributing to a more secure and efficient virtual machine environment.

About Orochi Network

Orochi Network is a cutting-edge zkOS (An operating system based on zero-knowledge proof) designed to tackle the challenges of computation limitation, data correctness, and data availability in the Web3 industry. With the well-rounded solutions for Web3 Applications, Orochi Network omits the current performance-related barriers and makes ways for more comprehensive dApps hence, becoming the backbone of Web3's infrastructure landscape.

Blog