Understanding Hello Multiply

The Hello Multiply tutorial tells you how to write code that proves you know the factors of a number -- but what is this code doing? What mechanisms does the RISC Zero zkVM use to prove the execution of the source code you provide it?

The complete answer to those questions requires detailed and precise cryptographic arguments. Nevertheless, here we present a short summary of what the zkVM is doing in Hello Multiply, as an overview of the general approach of the RISC Zero zkVM. We hope that this overview helps orient you to the components of the RISC Zero zkVM, and gives a sense of why it might be plausible that code executed in the zkVM could be proven to parties who don't trust the prover.

By reading this post, you should learn, at a high level:

• How RISC Zero can be used to convince someone that code has executed on the zkVM
• How we make programs and variables available to the zkVM guest
• What zkVM guest programs can do to publicly share computation results
• What information the prover would need to transmit to convince a real recipient

This post will not cover:

• A detailed cryptographic analysis of the RISC Zero zkVM (see our proof system explainers and reference materials)
• How to write code using the RISC Zero zkVM (see the Hello Multiply tutorial, or our examples generally)

Overview: A program to multiply two numbers in the zkVM

In the Hello Multiply program, we demonstrate how to multiply two numbers and share their product without revealing what the two factors are. The RISC Zero zkVM provides a cryptographically strong argument that we performed the computation, which is witnessed by a verifiable "receipt." By sharing the receipt, we can convince a skeptical third party that we ran the computation faithfully and that the output is honest.

Differentiating host and guest code

The host driver program runs the guest zkVM. Most code written for the guest zkVM lives in methods/guest/src/main.rs. The main function for our host program code lives in factors/src/main.rs.

When the host code executes, it creates a prover instance that is responsible for all guest zkVM interactions:

    let mut prover = Prover::new(MULTIPLY_ELF).unwrap();

The prover runs an ELF binary of the zkVM guest code. After the guest code has executed, the prover returns a receipt. In our example, these are accomplished with the following line in the factors/src/main.rs host source code:

let receipt = prover.run().unwrap();

Understanding the prover

When a prover runs code on the zkVM, two important things happen:

1. The ELF binary execution produces an execution trace. If valid, the trace generates a cryptographic seal that shows the execution followed RISC-V rules.
2. Any values the guest shares are written to the journal.

A hash of the journal is included in the cryptographic seal so that the recipient will know if it has been altered.

The diagram below shows these components in action:

flowchart LR A(multiply.rs)-->|compiles to an|B(ELF binary) B-->|Whose execution produces an|C(Execution trace) B-->|Whose hash forms a unique|D(Image ID) D-->|That can be compared to the|E(Cryptographic seal) C-->|That, if valid,<br>generates a|E(Cryptographic seal) B-->|Whose operations can include<br>committing values to a|F(Journal) subgraph Together, these form a receipt. E F end subgraph x[The receipt tells us:] E---H(What binary executed in the ZKVM<br>Whether the execution<br>followed expected behavior<br/><br/>Whether the journal or image ID<br/>have changed) F---I(The values of all contents<br>written to the public journal) end style B fill:#3c6464 style x fill:none, stroke:none

For more details on this process, see our zkVM Overview; for maximal detail, see our proof system sequence diagram. In the next section, we'll show how this process is managed from the perspective of the host program, the guest zkVM program, and the prover object that we call from the host.

Interacting with the prover

The process diagram below shows the execution steps relevant to host and guest interactions. To illustrate the responsibility of the prover, we have included it as a separate entity. In practice, this object is instantiated on the host and lives in host memory.

sequenceDiagram participant B as Recipient<br>(recipient) participant H as Host<br>(main program) participant P as Prover<br>(main program object) participant G as Guest zkvm H->>H: create prover object H->>P: share numbers with prover P->>G: add number values to guest-readable memory H->>P: run prover rect rgb(100, 100, 100) note left of G: when the prover runs,<br>it manages these steps. P->>G: run our guest binary rect rgb(60, 100, 100) note left of G: the guest program<br>dictates these steps. G->>G: read prime values G->>G: calculate prime product G->>G: commit prime product<br>to public journal end G->>P: <br>execution trace is complete P->>H: verify trace,<br>return receipt end H->>B: give receipt to recipient B->>B: recipient verifies receipt B->>B: recipient reads prime product<br>from receipt journal

Some of the steps described above are handled by RISC Zero project code (such as the prover.run() function); other steps are performed explicitly by host or guest code. For example, the values shown in the blue box are dictated by guest zkVM code (multiply.rs). Others, like verifying the execution trace and producing a receipt, are a part of our prover object's internally defined behavior.

To get you started, the next section describes which actions must be explicitly included in host and guest code instructions. Read it along with the main.rs and multiply.rs files to get ready to create your own projects.

Writing host and guest programs

The following steps are included in the main.rs host program before the prover is called. Before the host program tells the prover to execute the guest program, it needs to make sure that all relevant methods and values are accessible to the guest.

1. The host creates a Prover object, passing it the ELF path and image ID for multiply.

2. The host makes sure that the guest can read the two numbers being multiplied. The function prover.add_input_u32_slice() sends the host-defined numbers to the guest.

The host then calls the prover's run() method. The prover executes a compiled binary of the guest program, which sets in motion the process of generating a trace and producing a receipt. As the guest binary executes, the zkVM performs the following steps, as dictated by the code in multiply.rs:

1. The two number values are read from guest-accessible memory using env::read().

2. The numbers are multiplied together and the result is saved.

3. To share the computed result, the guest writes them to the journal using the call env::commit().

After the guest program has executed, the prover returns a Receipt object. Recall that this object includes the image ID, journal (with shared results), and a cryptographic seal.

If we send the receipt to someone else, then they can see we ran the expected program (using the image ID); they can also read the computed product from the receipt's journal contents.

A note on practical use

For brevity (and to stay agnostic about use cases), our Hello Multiply example omits a few steps that would typically happen after the prover generates a receipt.

In our example, the receipt is verified from the main.rs host program. However, the value of the receipt is that it can convince another party we ran the multiply.rs program. In a real-world scenario, then, we would want to send the receipt to someone else, most likely by serializing it and passing it over a network.

We would also want to give the source code for the guest program to the recipient. The recipient would generate the image ID of the zkVM program binary on their side and use this to check the receipt's image ID.

If you would like to know more about receipts, we recommend our article Understanding the Password Validity Checker. We'll show you how the computational receipt is created and checked in greater detail as we walk through how RISC Zero projects can allow us to trust user-provided data. We'll look at a slightly (but not much) more involved program that allows a user to check their own password against a set of validity requirements (e.g., the inclusion of uppercase letters) and provide their own password hash.

If you have any questions or are interested in talking about zkVM projects, come find us on Twitter and Discord. We'd love to see what you build using the RISC Zero zkVM!