Merkle trees play a crucial role in blockchain networks in organizing network state. They allow proving a particular value of an entry in the state to a node that maintains only the root of the Merkle trees, a hash-based signature computed over the data in a hierarchical manner. Verification of particular state entries is crucial in reaching a consensus on the execution of a block where state information is required in the processing of its transactions. For instance, a payment transaction should be based on the balance of the two involved accounts. The proof length affects the network communication and is typically logarithmic in the state size. In this paper, we take advantage of typical transaction characteristics for better organizing Merkle trees to improve blockchain network performance. We focus on the common transaction processing where Merkle proofs are jointly provided for multiple accounts. We first provide lower bounds for the communication cost that are based on the distribution of accounts involved in the transactions. We then describe algorithms that consider traffic patterns for significantly reducing it. The algorithms are inspired by various coding methods such as Huffman coding, partition and weight balancing. We also generalize our approach towards the encoding of smart contract transactions that involve an arbitrary number of accounts. Likewise, we rely on real blockchain data to show the savings allowed by our approach. The experimental evaluation is based on transactions from the Ethereum network and demonstrates cost reduction for both payment transactions and smart contract transactions.

The Invertible Bloom Lookup Table (IBLT) is a probabilistic data structure for set representation, with applications in network and traffic monitoring. It is known for its ability to list its elements, an operation that succeeds with high probability for sufficiently large table. However, listing can fail even for relatively small sets. This paper extends recent work on the worst-case analysis of IBLT, which guarantees successful listing for all sets of a certain size, by introducing more general IBLT schemes. These schemes allow for greater freedom in the implementation of the insert, delete, and listing operations and demonstrate that the IBLT memory can be reduced while still maintaining successful listing guarantees. The paper also explores the time-memory trade-off of these schemes, some of which are based on linear codes and Bh-sequences over finite fields.

State sharding is a common solution to the scalability problem in blockchain systems, allowing nodes to hold a partial view of the system state. With sharding, the processing of a transaction might not be completed locally within a node and potentially requires involvement of multiple shards. Such cross-shards transactions have a negative impact on system performance and are frequent with traditional state partition solutions which are often based on a simple mapping of data into shards. By locating together parts of the system state accessed by frequent transactions, the amount of cross-shard transactions can be reduced. On the other hand, the representation of such particular mappings can be memory intensive. In this article, we study traffic-aware sharding that can be described in memory-efficient mappings. We first survey existing mapping schemes in common blockchains. We indicate the tradeoff between the size of the mapping of data to shards and the required transaction processing time and suggest algorithms for finding memory-light sharding of low cross-shard rate. We generalize the approach towards an efficient incremental computation of shards and probabilistic representation of the mapping to shards. We examine the efficiency of the solutions and the required frequency of sharding computation based on real information of the Ethereum network.