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Indexing structures for the PLS blockchain

Alex Shafarenko

TL;DR

This work addresses the data-exchange burden of proofs in a permissioned IoT blockchain by analyzing and redesigning indexing structures for efficient absence and presence proofs. It derives a theoretical path-weight distribution for sparse Merkle trees and introduces a Tunstall-compressed bitmap (Tunstall-Merkle Tree) that enables zero-cost absence proofs from the root while keeping leaf-paths short when present. To decorrelate access patterns and preserve compression effectiveness, the authors propose a lightweight, block-number–dependent pre-randomisation (shuffle-shifter) with avalanche-criterion validation guiding rounds. The resulting framework significantly reduces communication overhead for low-duty-cycle IoT devices and provides a practical path to scalable, provable auditing in PLS; the approach is grounded in analytic MT statistics, bitmap indexing, and efficient on-device decoding, making it suitable for resource-constrained environments. Overall, the paper demonstrates concrete savings in presence/absence verification costs and offers a complete, hardware-conscious implementation path for IoT-focused permissioned ledgers.

Abstract

This paper studies known indexing structures from a new point of view: minimisation of data exchange between an IoT device acting as a blockchain client and the blockchain server running a protocol suite that includes two Guy Fawkes protocols, PLS and SLVP. The PLS blockchain is not a cryptocurrency instrument; it is an immutable ledger offering guaranteed non-repudiation to low-power clients without use of public key crypto. The novelty of the situation is in the fact that every PLS client has to obtain a proof of absence in all blocks of the chain to which its counterparty does not contribute, and we show that it is possible without traversing the block's Merkle tree. We obtain weight statistics of a leaf path on a sparse Merkle tree theoretically, as our ground case. Using the theory we quantify the communication cost of a client interacting with the blockchain. We show that large savings can be achieved by providing a bitmap index of the tree compressed using Tunstall's method. We further show that even in the case of correlated access, as in two IoT devices posting messages for each other in consecutive blocks, it is possible to prevent compression degradation by re-randomising the IDs using a pseudorandom bijective function. We propose a low-cost function of this kind and evaluate its quality by simulation, using the avalanche criterion.

Indexing structures for the PLS blockchain

TL;DR

This work addresses the data-exchange burden of proofs in a permissioned IoT blockchain by analyzing and redesigning indexing structures for efficient absence and presence proofs. It derives a theoretical path-weight distribution for sparse Merkle trees and introduces a Tunstall-compressed bitmap (Tunstall-Merkle Tree) that enables zero-cost absence proofs from the root while keeping leaf-paths short when present. To decorrelate access patterns and preserve compression effectiveness, the authors propose a lightweight, block-number–dependent pre-randomisation (shuffle-shifter) with avalanche-criterion validation guiding rounds. The resulting framework significantly reduces communication overhead for low-duty-cycle IoT devices and provides a practical path to scalable, provable auditing in PLS; the approach is grounded in analytic MT statistics, bitmap indexing, and efficient on-device decoding, making it suitable for resource-constrained environments. Overall, the paper demonstrates concrete savings in presence/absence verification costs and offers a complete, hardware-conscious implementation path for IoT-focused permissioned ledgers.

Abstract

This paper studies known indexing structures from a new point of view: minimisation of data exchange between an IoT device acting as a blockchain client and the blockchain server running a protocol suite that includes two Guy Fawkes protocols, PLS and SLVP. The PLS blockchain is not a cryptocurrency instrument; it is an immutable ledger offering guaranteed non-repudiation to low-power clients without use of public key crypto. The novelty of the situation is in the fact that every PLS client has to obtain a proof of absence in all blocks of the chain to which its counterparty does not contribute, and we show that it is possible without traversing the block's Merkle tree. We obtain weight statistics of a leaf path on a sparse Merkle tree theoretically, as our ground case. Using the theory we quantify the communication cost of a client interacting with the blockchain. We show that large savings can be achieved by providing a bitmap index of the tree compressed using Tunstall's method. We further show that even in the case of correlated access, as in two IoT devices posting messages for each other in consecutive blocks, it is possible to prevent compression degradation by re-randomising the IDs using a pseudorandom bijective function. We propose a low-cost function of this kind and evaluate its quality by simulation, using the avalanche criterion.

Paper Structure

This paper contains 29 sections, 23 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. The main contributions of the paper are as follows:
  3. PLS blockchain: architecture and protocols.
  4. Blocks
  5. Chain.
  6. Transactions.
  7. Operations.
  8. Addresses.
  9. Frequency.
  10. Block structure and optimisation challenge
  11. Immutable dictionary.
  12. Merkle tree.
  13. Blocks represented as Merkle trees.
  14. Mask-controllable sparse MT.
  15. Merkle-Patricia Trie.
  16. ...and 14 more sections

Figures (10)

  • Figure 1: Architecture of a PLS-blockchain system
  • Figure 2: Structure of the PLS protocol
  • Figure 3: Structure of the SLVP protocol. Table on behalf of a single user
  • Figure 4: Merkle Tree.
  • Figure 5: Merkle-Patricia Trie. All unlabelled edges are assumed to have the label '0' if they lean to the left and '1' if they lean to the right.
  • ...and 5 more figures