# Composable Futures-based Batch Verification

In a previous post, we shared details on the new, fully asynchronous network stack we designed for Zebra, the Zcash Foundation’s forthcoming node implementation. In this post, I want to share an idea we’re hoping will help us achieve high performance and high code quality in a different area: cryptographic verification of data on the Zcash blockchain.

The Zcash protocol has undergone several stages of technical development, and now contains many different kinds of cryptographic signatures and zero-knowledge proofs: ECDSA signatures on secp256k1 from Bitcoin, Ed25519 signatures and Sprout-on-BCTV14 proofs from the original Zcash deployment, and RedJubjub signatures, Sprout-on-Groth16 proofs, and Sapling-on-Groth16 proofs from the Sapling upgrade. As a result, verifying Zcash transactions requires verification of heterogeneous data, depending on the transaction version and the contents of the transaction itself.

As an aside, when talking about transaction (or block) verification, it’s useful to distinguish three telescoping levels of verification:

1. Structural Validity, or whether the format and structure of the transaction are valid. For instance, Sprout-on-BCTV14 proofs are not allowed after activation of the Sapling upgrade, and depending on the transaction version, different components must or must not be present.

2. Semantic Validity, or whether all of the signatures and proofs contained in a well-formed transaction verify correctly. In other words, is this transaction valid, when considering it independently of any chain state?

3. Contextual Validity, or whether a semantically valid transaction is valid in the context of a particular chain state. For instance, a transaction that spends a particular note may be semantically valid on its own, but invalid in the context of some chain state where that note has been spent.

We address structural validity in the type system, using algebraic data types to construct a representation of a Transaction that makes structurally invalid transactions impossible to represent internally. The details will be in a future post, but in the meantime, Parse, don’t validate has a great explanation of this approach. And contextual validity is mostly a problem of state management and reconciliation rather than cryptography. Checking semantic validity, however, is the most computationally expensive, because it requires verifying all signatures and zero-knowledge proofs. It’s this step which will be the focus of this post.

## Batch verification and its discontents

A common optimization for cryptographic primitives is batch verification, which asks whether all items in a set are valid in a single all-or-nothing check, rather than performing individual checks for each item. Batch verification can be significantly faster than singleton verification, because computation can be amortized across all elements of the batch rather than performed for each item.

However, conventional batch verification APIs can be cumbersome and difficult to use, especially when verifying heterogeneous data. The core problem is that while batch verification provides all-or-nothing answers about a set of items, the desired information is a per-item answer, and using batch verification requires entangling the validation states of all of the items in the batch.

This problem is especially apparent when attempting to verify heterogeneous data, as in a Zcash transaction. Using conventional batch verification APIs, this would require writing a second set of “transposed” verification logic, scanning through all transactions in a batch, and assembling a set of items for each different data type (Ed25519 signatures, RedJubjub signatures, Sprout-on-Groth16 proofs, Sapling-on-Groth16 proofs, etc) before executing the batch.

This presents the immediate problem of having two implementations of verification logic, which is bad enough, but there’s a second problem, which is that it’s relatively inflexible with respect to the batch size. This matters because different levels of batching are appropriate in different contexts: batching within a transaction is appropriate on receipt of a gossiped transaction, batching within a block is appropriate for block verification, and batching across blocks is appropriate when syncing the chain.

## Futures-based batch verification

To address this problem, we move from a synchronous model for validation to an asynchronous model. Rather than immediately returning a verification result, verification returns a future which will eventually resolve to a verification result. These verification futures can be composed using futures combinators in a way that expresses logical semantics rather than forcing a particular execution order. This allows writing verification logic for each item independently of the other items and even independently of whether the verification is standalone or batched.

To provide a common interface for batch verification, we use Tower, a generic interface and collection of middleware for asynchronous request/response protocols, described in more detail in our previous post. The core abstraction of Tower is the Service trait, and we model verification as a Service whose Request is a signature or proof together with associated data (e.g., for a signature, the public key and message), whose Error type is a validation error, and whose Response is the empty type (). Verification consists of performing a Service call with the request data, and obtaining a Future which resolves to a Result<(), Error>.

In addition to using futures combinators to express semantics of verification results, using the Service trait allows us to use service combinators to arrange more complex request-processing logic, as appropriate for the situation. For example, it’s easy to add tracing diagnostics, or to use a fallback combinator to automatically retry failed requests with a singleton verifier to precisely identify which items failed.

## A first pass at implementing this strategy

Because the primary benefit of this strategy is compositionality, it’s difficult to know exactly how well it will work until there are multiple primitives to compose together. As a first pass, I implemented this strategy in ed25519-zebra, a small library that implements Zcash-flavored Ed25519. Batch verification is provided by a BatchVerifier struct implementing the Service trait. The BatchVerifier maintains a target batch_size and automatically flushes queued verification requests when the batch size is reached. It’s also possible to manually flush the queue by sending a flush request.

Along the way, I noticed a neat optimization for batch signature verification that can take automatically coalesce terms when multiple signatures in the batch are made with the same public key. I haven’t seen this implemented before (although I didn’t look very hard), but in the limiting case where all signatures in the batch are made with the same public key, coalesced batch verification runs twice as fast as ordinary batch verification, illustrated in the graph below. This optimization doesn’t help much with Zcash, where public keys are random, but could be useful in proof-of-stake systems where signatures come from a set of validators.