• Crypto Insights
  • Research on Optimal Bitcoin Threshold Signatures
  • Exploring the Security Limits of Data Embedding in Schnorr Signatures
  • Emoji Mnemonics Proposal: A Visual Approach to Deterministic Keys
  • Lightning++ Berlin Recap
  • Lightning++ Hackathon Winning Projects
  • Quantitative Analysis of Lightning Network Centralization: Less Even Resource Distribution but Ongoing Resilience
  • Marmot Protocol: Extending Nostr’s NIP-EE for Secure Decentralized Messaging
  • NLightning: A Lightning Network Implementation for Corporations
  • BitPriv: A Privacy-Preserving Protocol for DeFi on Bitcoin
  • The Sixty-Four Possible Worlds of Bitcoin

§Crypto Insights

§Research on Optimal Bitcoin Threshold Signatures

Sindura Saraswati published her research on threshold signatures for Bitcoin transactions following the Taproot upgrade, to identify the optimal multisignature scheme. The study explores the parameters of usability and security and their relationship, along with how it affects threshold selection. Through a dynamic model, the research provides a conceptual framework for managing threshold signatures and recommends adaptive strategies that adjust according to changes in the security environment.

Saraswati also examines degrading threshold signatures—starting with a higher threshold that gradually decreases over time. This means that over time, an attacker’s probability of being able to spend the funds increases. She points out that with Taproot, such signatures can leverage taptrees and more complex contracts (including timelocks and multisignatures), potentially enabling new use cases.

More details are available in the project’s GitHub and its paper.

§Exploring the Security Limits of Data Embedding in Schnorr Signatures

Bitcoin developer AdamISZ (waxwing) shared his study on the feasibility of embedding data in Schnorr signatures without exposing the private key. The study shows that embedding data in these tuples would almost inevitably leak private key information, potentially compromising the associated UTXO. Unlike previous works that only noted a “potential risk of data leakage,” AdamISZ’s analysis attempts to demonstrate that no secure method exists to embed data safely. He remarks that while the technical question is intriguing, imagining a world where every on-chain public key is accompanied by a signature for data embedding is unrealistic.

§Emoji Mnemonics Proposal: A Visual Approach to Deterministic Keys

A BIP has been proposed introducing Emoji Seeds for deterministic key management. This proposal defines a complete open standard that maps the 2048 English words in BIP-39 to 2048 pairs of emojis. The project aims to create a universal, language-agnostic, and user-friendly mnemonic system to complement existing word lists while improving cross-cultural accessibility and human memorability.

The full specification, logic description, algorithms, and reference files are available on the project’s GitHub repository.

§Lightning++ Berlin Recap

The first-ever Lightning++ Conference, organized by bitcoin++, took place in Berlin from October 2–4, 2025. It gathered Lightning researchers and developers from around the world to discuss the protocol’s current state, future directions, and the latest research and implementations.

Highlights:

• Rene Pickhardt presented his latest findings on routing reliability and liquidity.
• Peter Todd discussed potential issues related to persistent node logs.
• Fabrice Drouine of Acinq shared their solutions for fund security.
• Matt Corallo warned that Bitcoin is becoming increasingly dependent on custodial solutions.
• Calle showcased the Cashu ecosystem and outlined the next steps for e-cash protocol.
• Zeus’s Evan Kaloudis unveiled their new graduated wallet.
• Dusty Daemon presented Splice Script, a simplified scripting language for increasingly complex splicing operations.
• Allen Farrington introduced Flux, a new Bitcoin-native asset management company.

Replays of Day 1, Day 2, and Day 3.

§Lightning++ Hackathon Winning Projects

Alongside the conference, the Lightning++ Hackathon attracted 14 projects competing for a prize pool exceeding 10 million sats.

Top 3 Winners:

1. Nuts Are Pure Signal: a fork of Signal integrating Cashu for mobile coin payments.
2. Obfusats: a tool that complicates Lightning traffic analysis using Cashu mints and obfuscation.
3. Glacier Wallet: enables users to easily create time-locked transactions with CHECKTIMELOCKVERIFY.

Honorable Mentions:

• REKTBOT9000: Best Design & Best Vibes.
• Satoshibot: Best Beginner Hack & Most Unnecessary Use of OpenTimeStamp.
• Glacier Wallet: Best Electrum Plugin
• Mandel: Best Use of LDK.

§Quantitative Analysis of Lightning Network Centralization: Less Even Resource Distribution but Ongoing Resilience

Concerns about Lightning Network centralization persist, as a small number of highly active nodes can undermine the network’s decentralized nature. A recent study quantitatively analyzes Lightning’s centralization using various metrics — including the Gini Coefficient, Nakamoto Coefficient, Herfindahl-Hirschman Index, Theil Index, and Shannon Entropy. The methodology involved data collection, node clustering into entities, and building an experimental environment.

The results reveal a nuanced picture: over an eight-year period, the Gini coefficient of node capacity distribution increased from 0.85 to 0.97, indicating growing inequality. However, the Nakamoto coefficient fluctuated, suggesting that while resource control is uneven, the network’s overall decentralization might still be stronger than previously expected.

§Marmot Protocol: Extending Nostr’s NIP-EE for Secure Decentralized Messaging

The Marmot Protocol has been officially launched as a secure decentralized messaging framework built on Nostr. It extends the Nostr NIP-EE specification using the Messaging Layer Security (MLS) standard to support advanced use cases like encrypted media, multi-device synchronization, and robust group management.

The team also released the Marmot Development Kit (MDK), a reference implementation written in Rust that fully supports the protocol. A TypeScript version — marmot-ts — is under active early development.

§NLightning: A Lightning Network Implementation for Corporations

NLightning is a new implementation of the Lightning Network adhering to the BOLT specifications. It targets institutional users — such as corporations and banks — looking to operate their own Lightning infrastructure. Written in C#, NLightning leverages a language familiar to major financial institutions (e.g., JPMorgan, Bank of America), easing integration and deployment for enterprise systems.

Developer Nickolas Goline recently demonstrated NLightning’s capability to open channels with LND nodes in real time during the Lightning++ Conference. As of now, roughly 75% of the BOLT spec has been implemented, with BOLT-4, BOLT-5, and BOLT-7 expected to be completed by the end of 2026.

§BitPriv: A Privacy-Preserving Protocol for DeFi on Bitcoin

This research paper introduces BitPriv, a Bitcoin-compatible protocol that enables conditional payments based on secure two-party computation (2PC) results. Its core idea is that both parties lock collateral on-chain while performing computation off-chain via garbled circuits. Misbehavior is deterred using a “cut-and-choose” mechanism, and any deviation can be proven and penalized on-chain through BitVM. The design guarantees security under the rational adversary model, ensuring deviation economically irrational.

The paper also demonstrates new applications enabled by BitPriv and evaluates its performance in a Bitcoin-based privacy-preserving double-blind marketplace. Ideally, settlement requires only two transactions with costs under $3; in case of disputes, costs rise to about $507, depending on the specific BitVM implementation — yet the mere feasibility of on-chain dispute resolution acts as a strong deterrent.

§The Sixty-Four Possible Worlds of Bitcoin

In “Bitcoin Worlds“, the author explores from institutional and economic perspectives how Bitcoin — an asset with absolute scarcity — might shape the future in a world traditionally built on elastic credit.

The paper constructs a framework describing 64 possible Bitcoin worlds, defined by variables such as liquidity, policy clarity, holding concentration, energy stress, trust and information integrity, and credit leverage. Among these, 40 configurations are internally stable, while 24 are prone to collapse. The author compares perspectives from Keynesian, Post-Keynesian, and Austrian schools of economics, finding differing views on Bitcoin’s stability, scarcity, and governance. Two major worldviews emerge:

• Sovereignty-first: resilience derives from decentralization, transparency, and grassroots practice.
• Stability-first: resilience depends on institutional support, deep liquidity, and regulatory integration.

The conclusion emphasizes that Bitcoin’s future will not be determined solely by protocol rules but by governance choices — with implications for fiscal capacity, unit-of-account primacy, and the distribution of monetary authority.