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A sparse Merkle tree is a Merkle tree with fixed height and indexed leavesgiven by a map from indices to leaf values. It allows for both efficientmembership and non-membership proofs. It has been widely used as anauthenticated data structure in various applications, such as layer-2 rollupsfor blockchains. zkSync Lite, a popular Ethereum layer-2 rollup solution, usesa sparse Merkle tree to represent the state of the layer-2 blockchain. Theaccount information is recorded in the leaves of the tree. In this paper, westudy the sparse Merkle tree algorithms presented in zkSync Lite, and proposean efficient batch update algorithm to calculate a new root hash given a listof account (leaf) operations. Using the construction in zkSync Lite as abenchmark, our algorithm 1) improves the account update time from$\mathcal{O}(\log n)$ to $\mathcal{O}(1)$ and 2) reduces the batch update costby half using a one-pass traversal. Empirical analysis of real-world block datashows that our algorithm outperforms the benchmark by at most 14%.

One-Phase Batch Update on Sparse Merkle Trees for Rollups