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Towards A Post-Quantum Cryptography in Blockchain I: Basic Review on Theoretical Cryptography and Quantum Information Theory

Tatsuru Kikuchi

TL;DR

The paper analyzes the security implications of quantum advances for blockchain cryptography and surveys post-quantum cryptography alongside quantum information theory. It develops a structured overview of cryptographic primitives (encryption, hash functions, symmetric and asymmetric schemes) and their security notions, bridging classical models with quantum considerations. A core focus is on quantum cryptography, especially Quantum Key Distribution via BB84, to illustrate information-theoretic security, and on classical schemes (e.g., Diffie-Hellman, RSA) within a post-quantum context. Collectively, it sets a foundational baseline for designing quantum-resistant ledgers and informs subsequent, deeper exploration of post-quantum blockchain security strategies.

Abstract

Recently, the invention of quantum computers was so revolutionary that they bring transformative challenges in a variety of fields, especially for the traditional cryptographic blockchain, and it may become a real thread for most of the cryptocurrencies in the market. That is, it becomes inevitable to consider to implement a post-quantum cryptography, which is also referred to as quantum-resistant cryptography, for attaining quantum resistance in blockchains.

Towards A Post-Quantum Cryptography in Blockchain I: Basic Review on Theoretical Cryptography and Quantum Information Theory

TL;DR

The paper analyzes the security implications of quantum advances for blockchain cryptography and surveys post-quantum cryptography alongside quantum information theory. It develops a structured overview of cryptographic primitives (encryption, hash functions, symmetric and asymmetric schemes) and their security notions, bridging classical models with quantum considerations. A core focus is on quantum cryptography, especially Quantum Key Distribution via BB84, to illustrate information-theoretic security, and on classical schemes (e.g., Diffie-Hellman, RSA) within a post-quantum context. Collectively, it sets a foundational baseline for designing quantum-resistant ledgers and informs subsequent, deeper exploration of post-quantum blockchain security strategies.

Abstract

Recently, the invention of quantum computers was so revolutionary that they bring transformative challenges in a variety of fields, especially for the traditional cryptographic blockchain, and it may become a real thread for most of the cryptocurrencies in the market. That is, it becomes inevitable to consider to implement a post-quantum cryptography, which is also referred to as quantum-resistant cryptography, for attaining quantum resistance in blockchains.
Paper Structure (18 sections, 8 theorems, 46 equations, 1 table)

This paper contains 18 sections, 8 theorems, 46 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminary --- Cryptographic algorithms
  3. Encryption
  4. Stream cipher
  5. Block cipher
  6. Universal hash function
  7. Public-key encryption
  8. Key-exchange protocol
  9. Quantum Cryptography
  10. Qubits, Entanglement, and Quantum Gates
  11. Quantum Teleportation
  12. Quantum Key Distribution
  13. Cryptographic Algorithms
  14. Cryptographic Hash Algorithms
  15. Symmetric Cryptographic Algorithms
  16. ...and 3 more sections

Key Result

Theorem 2.1

Let ${\mathcal{E}} = ({\mathsf{Gen}}, {\mathsf{Enc}}, {\mathsf{Dec}})$ be perfect secure encryption scheme with a finite size message space ${\mathcal{M}}$ and a key space ${\mathcal{K}}$, then we have $|{\mathcal{K}}| \geq |{\mathcal{M}}|$

Theorems & Definitions (41)

  • Definition 2.1: Encryption scheme
  • Definition 2.2: Perfect secure
  • Theorem 2.1
  • Definition 2.3: One-time Pad
  • Theorem 2.2
  • Theorem 2.3: Shannon's theorem
  • Definition 2.4: Attack Game 1 --- semantic security
  • Definition 2.5: Semantic security
  • Definition 2.6: Attack Game 2 --- message recovery
  • Definition 2.7: Message recovery security
  • ...and 31 more