Adding cross-transaction BLS signature aggregation to ethereum

BLS signature aggregation is a powerful technology that allows many signatures for many messages signed by many keys to be compressed into a single signature, which can be verified against the entire set of (message, pubkey) pairs that it represents simultaneously.

That is, if there are:

  • A set of private keys k_1, k_2 ... k_n (held by different users)
  • The corresponding pubkeys K_1, K_2 ... K_n
  • Messages m_1, m_2 ... m_n, where m_i is signed by the corredponding k_i and the signatures are S_i = k_i * H(K_i, m_i)

Then you can make an aggregate signature S = S_1 + S_2 + ... + S_n, where S has a fixed size (usually 32-96 bytes depending on configuration), and S can be verified against the entire set of pairs [(K_1, m_1), (K_2, m_2) ... (K_n, m_n)] (the messages and the public keys), confirming that S is a valid aggregate of signatures for those key and message combinations.

The challenge when deploying this in a ethereum context, however, is that signature aggregation is at its most powerful when we aggregate many signatures together, and this implies somehow aggregating together signatures across many transactions within a block. Unfortunately, the EVM is not suited to this, because each EVM execution’s scope is limited to being within a particular transaction.

I propose a simple extension to the EVM to alleviate this difficulty. We add a new opcode, EXPECT_BLS_SIGNATURE, which takes two arguments off the stack: (i) a memory slice representing the pubkey (represented on the stack by the starting position in memory, as we know how many bytes a pubkey contains), and (ii) the message (standardized to be a 32 byte hash). The block verification procedure processes this opcode by adding the pair (pubkey, message) to an expected_signatures list (this list starts off empty at the start of every block). We also add to the block header a field bls_aggregate. At the end of block processing, we take the whole expected_signatures = [(K_1, m_1), (K_2, m_2) ... (K_n, m_n)] list, and perform the BLS aggregate signature check:

e(K_1, H(K_1, m_1)) * e(K_2, H(K_2, m_2)) * ... * e(K_n, H(K_n, m_n)) ?= e(S, G_2)

Where S is the bls_aggregate and G_2 is the elliptic curve generator. If the check does not pass, the entire block is invalid.

At network layer, we add a wrapper to the Transaction class, where each transaction can come with a signature that covers the expected signatures during execution. A block proposer (ie. miner) would receive the transaction, attempt to verify it by running the transaction, computing the expected_signatures array just for that transaction, and seeing if the signature provided with the transaction matches that array. If it does, and the transaction passes the other usual validity and fee sufficiency checks, the block proposer incldues the transaction, and adds (using elliptic curve addition) the transaction’s provided BLS signature to the block’s bls_aggregate; if it does not, then the block proposer ignores the transaction.

Note that this breaks the invariant that a transaction cannot be made to be invalid as a result of things that happen during execution (which is important to prevent DoS attacks). Hence, if deployed on the base layer, it should be combined with account abstraction, with the EXPECT_BLS_SIGNATURE opcode only usable before the PAYGAS opcode is called.

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That’s great!

This could be an enabler for plenty of (efficient) schemas, not only related to batching operations but also for novel (authentication) protocols.

It would be nice to see more native instructions for PBC, not only restricted for BLS, e.g IBE.

Pairings are costly in terms of CPU, and each signature aggregation requires one pairing operation. Last time I checked, this cost was approximately 10 times more (in terms of CPU cycles) than validating a ECDSA signature. Therefore your proposal trades space for higher CPU cost.
In 2018 I proposed a hybrid solution to send transactions with both ECDSA and BLS signatures, verifying only ECDSA signatures for some time, and then switching to BLS when the block is sufficiently mature. Therefore only nodes that are synchronizing from zero need to use more CPU cycles, but they benefit from reduced bandwidth and space.

This is ok since most of the times nodes that synchronize from zero can use weak subjectivity to get signed snapshots.

The idea is here:

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