Offline Digital Euro: a Minimum Viable CBDC using Groth-Sahai proofs

Paper: arXiv 2407.13776

Abstract

Current digital payment solutions are fragile and offer less privacy than traditional cash. Their critical dependency on an online service used to perform and validate transactions makes them void if this service is unreachable. Moreover, no transaction can be executed during server malfunctions or power outages. Due to climate change, the likelihood of extreme weather increases. As extreme weather is a major cause of power outages, the frequency of power outages is expected to increase. The lack of privacy is an inherent result of their account-based design or the use of a public ledger. The critical dependency and lack of privacy can be resolved with a Central Bank Digital Currency that can be used offline. This thesis proposes a design and a first implementation for an offline-first digital euro. The protocol offers complete privacy during transactions using zero-knowledge proofs. Furthermore, transactions can be executed offline without third parties and retroactive double-spending detection is facilitated. To protect the users’ privacy, but also guard against money laundering, we have added the following privacy-guarding mechanism. The bank and trusted third parties for law enforcement must collaborate to decrypt transactions, revealing the digital pseudonym used in the transaction. Importantly, the transaction can be decrypted without decrypting prior transactions attached to the digital euro. The protocol has a working initial implementation showcasing its usability and demonstrating functionality.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper heavily employs advanced cryptography (Groth-Sahai proofs, zero-knowledge proofs) with significant mathematical formalism, but the empirical evidence consists of an initial implementation without backtests, datasets, or statistical metrics.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Offline CBDC with Privacy"] --> B{"Methodology"}
  
  B --> C["Design Offline Protocol<br>using Groth-Sahai Proofs"]
  B --> D["Implement System<br>Prototype"]
  
  C --> E["Zero-Knowledge Proofs<br>for Transaction Privacy"]
  C --> F["Key Recovery Mechanism<br>for Law Enforcement"]
  
  D --> G["Usability Testing<br>Functionality Validation"]
  
  E --> H["Key Findings/Outcomes"]
  F --> H
  G --> H
  
  H --> I["✓ Offline Payments Possible<br>✓ Privacy Preserved<br>✓ Double-spending Detection<br>✓ AML Compliance"]
  
  style A fill:#e1f5fe
  style I fill:#e8f5e8

Cited References (61)

1. Use of cash lower in Euro Area Countries (2022) — link
2. Bitcoin whitepaper (2008)
3. Understanding the social impacts of power outages in North America: a systematic review (2023)
4. Power system resilience: Current practices, challenges, and future directions (2020)
5. Identification of weather patterns and transitions likely to cause power outages in the United Kingdom (2024)
6. Leading causes of outages for transmission elements of the North American bulk power system (2016)
7. Major impacts of weather events on the electrical power delivery system in the United States (2021)
8. Power outages and community health: a narrative review (2020)

0 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.