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A Practical Post-Quantum Distributed Ledger Protocol for Financial Institutions

Yeoh Wei Zhu, Naresh Goud Boddu, Yao Ma, Shaltiel Eloul, Giulio Golinelli, Yash Satsangi, Rob Otter, Kaushik Chakraborty

TL;DR

This work proposes a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability, and builds a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof.

Abstract

Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private protocols for distributed ledger that focus on the Ring-CT model are not suitable for adoption for financial institutions. We propose a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability. The construction leverages various zero-knowledge proof techniques, and introduces a new method for equating two commitment messages, without the capability to open one of the commitment during the re-commitment. Subsequently, we build a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof. We then provide a security analysis of it. The techniques used and the proofs constructed could be of independent interest.

A Practical Post-Quantum Distributed Ledger Protocol for Financial Institutions

TL;DR

This work proposes a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability, and builds a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof.

Abstract

Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private protocols for distributed ledger that focus on the Ring-CT model are not suitable for adoption for financial institutions. We propose a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability. The construction leverages various zero-knowledge proof techniques, and introduces a new method for equating two commitment messages, without the capability to open one of the commitment during the re-commitment. Subsequently, we build a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof. We then provide a security analysis of it. The techniques used and the proofs constructed could be of independent interest.
Paper Structure (76 sections, 42 theorems, 102 equations, 18 figures, 4 tables, 1 algorithm)

This paper contains 76 sections, 42 theorems, 102 equations, 18 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contribution
  3. Related Works
  4. Technical Overview
  5. Encrypted Table-based Ledger (ETL)
  6. Constructing Zero-Knowledge Proofs for various Transaction-related Relations
  7. Zero-Knowledge Proof of Balance
  8. Extracting Commitment with Proof of Consistency
  9. Proof of Asset: Range Proof in the NTT
  10. Bootstrapping the Knowledge of Random Values by Recommitment
  11. Compact Multi-Asset Transaction
  12. Collapsing the Protocol: Security in QROM
  13. Relation to Quantum Proofs of Knowledge.
  14. Preliminaries
  15. Challenge Space
  16. ...and 61 more sections

Key Result

Lemma 3.1

Let $p = p_0 + p_1 X + \cdots + p_{d-1} X^{d-1}$. Then, $\frac{1}{l} \sum_{i=0}^{l-1} \mathrm{NTT}(p)_i = \sum_{i=0}^{d/l-1} p_i X^i.$

Figures (18)

  • Figure 1: Logical Representation of ETL
  • Figure 2: A high-level overview of transaction.
  • Figure 3: ETL Proofs Illustration
  • Figure 4: $\mathsf{PQ-TaDL}$ Proof of Consistency Protocol $\pi_i^C$
  • Figure 5: $\mathcal{V}^C$ verify routine for Protocol \ref{['proto:pi_c']}
  • ...and 13 more figures

Theorems & Definitions (73)

  • Lemma 3.1: ENS20
  • Lemma 3.2: Function Evaluations with Constant CoefficientNguyen22
  • Definition 3.1: Weak Opening of BDLOP Commitment ALS20
  • Definition 3.2: Weak Opening of ABDLOP Commitment LNP22
  • Theorem 4.1
  • Theorem 4.2
  • Remark 4.3
  • Lemma 4.4
  • Theorem 4.5
  • Theorem 4.6
  • ...and 63 more