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Post-Quantum Stealth Address Protocols

Marija Mikic, Mihajlo Srbakoski, Strahinja Praska

TL;DR

This paper introduces three post-quantum stealth address protocols based on LWE, Ring-LWE, and Module-LWE to guard recipient privacy against quantum attacks. Using lattice-based KEMs, notably Kyber for MLWE, the authors demonstrate that Module-LWE SAP achieves the best performance, outperforming ECC-based Curvy protocols in registry scan time. They provide detailed constructions, formal definitions, and implementation results showing substantial efficiency gains and strong quantum resistance. The work highlights practical pathways for integrating PQC into blockchain privacy while outlining trade-offs in key sizes and performance, and suggests that optimizing KEMs can yield significant gains in SAP throughput.

Abstract

The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve Pairing Dual-Key SAP (ECPDKSAP), are based on elliptic curve cryptography, which is vulnerable to quantum attacks. These protocols depend on the elliptic curve discrete logarithm problem, which could be efficiently solved on a sufficiently powerful quantum computer using the Shor algorithm. In this paper three novel post-quantum SAPs based on lattice-based cryptography are presented: LWE SAP, Ring-LWE SAP and Module-LWE SAP. These protocols leverage Learning With Errors (LWE) problem to ensure quantum-resistant privacy. Among them, Module-LWE SAP, which is based on the Kyber key encapsulation mechanism, achieves the best performance and outperforms ECPDKSAP by approximately 66.8% in the scan time of the ephemeral public key registry.

Post-Quantum Stealth Address Protocols

TL;DR

This paper introduces three post-quantum stealth address protocols based on LWE, Ring-LWE, and Module-LWE to guard recipient privacy against quantum attacks. Using lattice-based KEMs, notably Kyber for MLWE, the authors demonstrate that Module-LWE SAP achieves the best performance, outperforming ECC-based Curvy protocols in registry scan time. They provide detailed constructions, formal definitions, and implementation results showing substantial efficiency gains and strong quantum resistance. The work highlights practical pathways for integrating PQC into blockchain privacy while outlining trade-offs in key sizes and performance, and suggests that optimizing KEMs can yield significant gains in SAP throughput.

Abstract

The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve Pairing Dual-Key SAP (ECPDKSAP), are based on elliptic curve cryptography, which is vulnerable to quantum attacks. These protocols depend on the elliptic curve discrete logarithm problem, which could be efficiently solved on a sufficiently powerful quantum computer using the Shor algorithm. In this paper three novel post-quantum SAPs based on lattice-based cryptography are presented: LWE SAP, Ring-LWE SAP and Module-LWE SAP. These protocols leverage Learning With Errors (LWE) problem to ensure quantum-resistant privacy. Among them, Module-LWE SAP, which is based on the Kyber key encapsulation mechanism, achieves the best performance and outperforms ECPDKSAP by approximately 66.8% in the scan time of the ephemeral public key registry.
Paper Structure (23 sections, 2 theorems, 20 equations, 5 figures, 1 table, 5 algorithms)

This paper contains 23 sections, 2 theorems, 20 equations, 5 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Post-Quantum hard problems
  4. Notation and basic definitions
  5. LWE problems
  6. Ring-LWE problems
  7. Module-LWE problems
  8. Stealth Address Protocols
  9. View tag
  10. Viewing key
  11. LWE Stealth Address Protocols
  12. Background
  13. Kyber
  14. Kyber's IND-CPA-secure encryption
  15. CCA-secure KEM
  16. ...and 8 more sections

Key Result

Theorem 1

Let $x \in \mathbb{Z}_{q}$, $d$ and $q$ be positive integers, where $d < \lceil \log_2 q\rceil$. Let Then $x'$ is close to $x$, i.e. $\lvert (x' - x) \bmod^+{q} \rvert \leq \left\lceil \dfrac{q}{2^{d+1}} \right\rfloor.$

Figures (5)

  • Figure 1: Stealth Address Protocol
  • Figure 2: Module-LWE Stealth Address Protocol
  • Figure 3: Performance comparison of Kyber512, NewHope512 and Frodo640
  • Figure 4: Module-LWE SAP - Performance comparison between the full hash($S$) view tag, one byte of hash($S$) and without view tag
  • Figure 5: Performance comparison between MLWE SAP and Curvy protocol

Theorems & Definitions (25)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Definition 10
  • ...and 15 more