Can the Generation of Zero-Knowledge Proofs Be Parallelized?

Okay, let's talk about this topic.

Can the Generation Process of Zero-Knowledge Proofs Be Parallelized?

Hey, that's a great question! It directly impacts whether Zero-Knowledge Proofs (ZKPs) can become truly practical, especially in scenarios like blockchain scaling.

The short answer is: Mostly yes, but not 100%.

To help you understand better, let's use an analogy.

Imagine you're organizing a large banquet requiring 100 dishes. The whole process can be broken down into stages:

Designing the Menu (Serial): You first need to decide what dishes to make and create a shopping list. This step is hard to parallelize; you must finalize the menu before moving on.
Shopping and Washing Vegetables (Partially Parallel): You can buy the groceries yourself or have friends split up and go to different markets. Once back, everyone can wash and chop vegetables together. This stage is highly suitable for parallel processing – the more people, the faster it goes.
Cooking (Highly Parallel): With 10 stoves in the kitchen, you can have 10 chefs cooking simultaneously. This is the most efficient parallel stage.
Plating and Serving (Serial): Finally, dishes need to be served one after another in sequence. This stage is serial again.

The generation process of a zero-knowledge proof is very similar to preparing this banquet. It's not a single step but composed of multiple parts. Some parts are inherently suited for "everyone pitching in," while others must be done "in order."

The "Parallel" and "Serial" Parts of ZKP Generation

A typical ZKP generation process (especially for types like zk-SNARKs) can be roughly broken down into these steps:

1. Translating the Problem into Mathematical Language (Arithmetization, Mostly Serial)

What is it? This is the first step, like designing the menu. You need to convert the "program" or "statement" you want to prove (e.g., "I executed a transaction correctly but don't want to reveal the specific amount") into a large set of mathematical constraint equations.
Can it be parallelized? This step usually has strong logical dependencies, similar to needing to define variable A before you can use it in later equations. Therefore, its potential for parallelization is relatively low, much like needing to finalize the menu before shopping.

2. "Intensive Computation" – Core Proof Generation (Highly Parallel)

What is it? This is the most time-consuming and computationally intensive part of the entire process, accounting for over 90% of the time. It mainly involves two "computational beasts":
- Multi-Scalar Multiplication (MSM)
- Fast Fourier Transform (FFT)
Can it be parallelized? Yes, and it's highly suitable! This is the "multiple people washing vegetables and ten chefs cooking" stage of our banquet.
- MSM is like simultaneously computing thousands of independent multiplications and additions like a*P + b*Q + c*R .... These calculations are independent of each other and can be perfectly distributed to different computing units (e.g., multiple CPU cores or thousands of GPU stream processors) for simultaneous processing.
- FFT is a classic "divide-and-conquer" algorithm, naturally divisible into countless smaller subproblems that can be computed independently.
Because these two core computational steps can be highly parallelized, the overall ZKP generation speed has the potential for significant optimization.

3. Packaging into the Final Proof (Mostly Serial)

What is it? Aggregating all the results from the "intensive computation" stage and combining them into a very compact final "proof" file.
Can it be parallelized? This part also has dependencies; it requires waiting for all parallel computations to finish before proceeding, so its parallelization potential is also limited. Fortunately, it usually doesn't take much time.

Why is Parallelization So Important?

Understanding what can be parallelized helps us see why it's such a major research focus.

Speed! Speed! Speed! For a complex proof, a single-core CPU might take hours or even days. But if the most time-consuming MSM and FFT tasks are offloaded to a GPU (graphics card) with thousands of cores, it might be completed in minutes or even seconds. That's the magic of parallel computing.
The Possibility of Hardware Acceleration Precisely because the core computations are parallelizable, specialized hardware for ZKPs has emerged, such as:
- GPUs: Graphics cards are inherently designed for parallel processing of massive data in rendering, making their architecture a perfect fit for ZKP's core computational needs.
- FPGAs / ASICs: For pursuing ultimate performance, specialized chips can be designed (FPGAs are programmable, ASICs are fixed), embedding the MSM and FFT algorithms directly into the hardware for even higher efficiency than general-purpose GPUs. Many leading ZKP projects are currently exploring this direction.

To Summarize

So, back to your question: Can the generation process of zero-knowledge proofs be parallelized?

Yes, and the key bottleneck parts (the computations taking up the vast majority of the time) are highly suitable for parallelization. It's like a large banquet: although designing the menu and the final serving require sequential steps, the most labor-intensive and time-consuming stages of preparation and cooking can be drastically shortened by adding more hands and stoves (i.e., parallel computing).

It is precisely this characteristic that allows zero-knowledge proof technology to leverage the power of modern parallel computing hardware (like GPUs), transforming it from a purely theoretical, slow "academic toy" into something increasingly practical. This remains one of the most exciting development directions in the field!