# \#cryptography **URL:** https://delvingbitcoin.org/tag/cryptography/25.md [Latest](https://delvingbitcoin.org/latest.md) · [Categories](https://delvingbitcoin.org/categories.md) · [Tags](https://delvingbitcoin.org/tags.md) --- ## [Towards A K-of-N Lightning Network Node](https://delvingbitcoin.org/t/towards-a-k-of-n-lightning-network-node/2395)
**Author:** [@ZmnSCPxj](https://delvingbitcoin.org/u/ZmnSCPxj)\ **Replies:** 11\ **Last updated:** [November 5, 2026, 12:34am UTC](https://delvingbitcoin.org/t/towards-a-k-of-n-lightning-network-node/2395 "2026-11-05T00:34:27Z")
Subject: Towards A K-of-N Lightning Network Node Z. jxPCSnmZ Introduction With the Nested MuSig2 Paper recently released, we want to consider: can we make a multisig self-custodial wallet with Lightning Network integra… --- ## [Public key recovery for EC leaves in P2MR (BIP-360)](https://delvingbitcoin.org/t/public-key-recovery-for-ec-leaves-in-p2mr-bip-360/2603)
**Author:** [@starius](https://delvingbitcoin.org/u/starius)\ **Replies:** 36\ **Last updated:** [November 4, 2026, 8:50am UTC](https://delvingbitcoin.org/t/public-key-recovery-for-ec-leaves-in-p2mr-bip-360/2603 "2026-11-04T08:50:01Z")
Public key recovery for EC leaves in P2MR This note describes a possible BIP-360 optimization using EC public key recovery. The idea is to have a P2MR output with a cheap EC leaf and an expensive PQ leaf. The EC leaf is… --- ## [Libshrincs: A C implementation with a machine-checked security proof](https://delvingbitcoin.org/t/libshrincs-a-c-implementation-with-a-machine-checked-security-proof/2795)
**Author:** [@jonasnick](https://delvingbitcoin.org/u/jonasnick)\ **Replies:** 2\ **Last updated:** [October 27, 2026, 3:11pm UTC](https://delvingbitcoin.org/t/libshrincs-a-c-implementation-with-a-machine-checked-security-proof/2795 "2026-10-27T15:11:37Z")
Abstract: @remix7531 and I are publishing libshrincs, a proof-of-concept C implementation of WOTS+C with machine-checked proofs of functional correctness and security. WOTS+C is the one-time signature scheme used by SHRI… --- ## [A Novel Post-Quantum Approach: "Proof-Of-Decay" (Cryptographic Half-Life) for Unmigrated Dormant UTXOs](https://delvingbitcoin.org/t/a-novel-post-quantum-approach-proof-of-decay-cryptographic-half-life-for-unmigrated-dormant-utxos/2970)
**Author:** [@bitKingAE](https://delvingbitcoin.org/u/bitKingAE)\ **Replies:** 1\ **Last updated:** [October 23, 2026, 2:21pm UTC](https://delvingbitcoin.org/t/a-novel-post-quantum-approach-proof-of-decay-cryptographic-half-life-for-unmigrated-dormant-utxos/2970 "2026-10-23T14:21:27Z")
\### Context & Problem Statement As the Bitcoin community discusses how to protect the network from future quantum attacks, we are largely stuck between two bad options for old, exposed-key outputs (like early P2PK or lo… --- ## [Block-wide Signature Aggregation via SNARKs](https://delvingbitcoin.org/t/block-wide-signature-aggregation-via-snarks/2875)
**Author:** [@conduition](https://delvingbitcoin.org/u/conduition)\ **Replies:** 9\ **Last updated:** [September 16, 2026, 4:40pm UTC](https://delvingbitcoin.org/t/block-wide-signature-aggregation-via-snarks/2875 "2026-09-16T16:40:16Z")
The core idea is simple: PQ sigs are big but cheap to verify. The huge size slows down block propagation and puts bigger storage/bandwidth costs on archival nodes forever. What if we could compress these signatures with … --- ## [Bitcoin PIPEs v2](https://delvingbitcoin.org/t/bitcoin-pipes-v2/2249)
**Author:** [@nemothenoone](https://delvingbitcoin.org/u/nemothenoone)\ **Replies:** 13\ **Last updated:** [July 27, 2026, 9:37am UTC](https://delvingbitcoin.org/t/bitcoin-pipes-v2/2249 "2026-07-27T09:37:45Z")
Bitcoin PIPEs v2: Covenants and ZKPs on the Bitcoin L1 via Witness Encryption. PIPE v2 \[2\] explores a cryptographic alternative to Bitcoin covenants that operates entirely within existing consensus rules. Instead of ext… --- ## [zkPoH: Zero-Knowledge Proof-of-Hodl](https://delvingbitcoin.org/t/zkpoh-zero-knowledge-proof-of-hodl/2699)
**Author:** [@fabohax](https://delvingbitcoin.org/u/fabohax)\ **Replies:** 7\ **Last updated:** [October 27, 2026, 3:12pm UTC](https://delvingbitcoin.org/t/zkpoh-zero-knowledge-proof-of-hodl/2699 "2026-10-27T15:12:31Z")
I’m sharing a small proof-of-concept for zkPoH, a Zero-Knowledge Proof of Hodl system for Bitcoin. The idea is simple: prove that you control a set of Bitcoin UTXOs whose combined value is at least 1 BTC, without reveal… --- ## [Emulating OP\_RAND](https://delvingbitcoin.org/t/emulating-op-rand/1409)
**Author:** [@olkurbatov](https://delvingbitcoin.org/u/olkurbatov)\ **Replies:** 13\ **Last updated:** [July 3, 2026, 5:59pm UTC](https://delvingbitcoin.org/t/emulating-op-rand/1409 "2026-07-03T17:59:00Z")
We propose a method of emulation of OP\_RAND opcode on Bitcoin through a trustless interactive game between transaction counterparties. The game result is probabilistic and doesn’t allow any party to cheat and increase th… --- ## [SHRINCS: 324-byte stateful post-quantum signatures with static backups](https://delvingbitcoin.org/t/shrincs-324-byte-stateful-post-quantum-signatures-with-static-backups/2158)
**Author:** [@jonasnick](https://delvingbitcoin.org/u/jonasnick)\ **Replies:** 21\ **Last updated:** [July 1, 2026, 2:39am UTC](https://delvingbitcoin.org/t/shrincs-324-byte-stateful-post-quantum-signatures-with-static-backups/2158 "2026-07-01T02:39:06Z")
Abstract: Stateful hash-based signature schemes can be very efficient when the number of signatures generated by a public key is small. One major problem with stateful schemes is that the state needs to be backed up and … --- ## [PQC: Google's result on improving Shor's algorithm reconstructed](https://delvingbitcoin.org/t/pqc-googles-result-on-improving-shors-algorithm-reconstructed/2552)
**Author:** [@nkaretnikov](https://delvingbitcoin.org/u/nkaretnikov)\ **Replies:** 0\ **Last updated:** [June 3, 2026, 3:19pm UTC](https://delvingbitcoin.org/t/pqc-googles-result-on-improving-shors-algorithm-reconstructed/2552 "2026-06-03T15:19:03Z")
From the post linked below: Today, almost exactly two months after we published the ZKPs, André Schrottenloher (a researcher at le Centre Inria de l’Université de Rennes in France) published a preprint showing how to c… --- ## [PQC: Lattice-based signatures](https://delvingbitcoin.org/t/pqc-lattice-based-signatures/2522)
**Author:** [@nkaretnikov](https://delvingbitcoin.org/u/nkaretnikov)\ **Replies:** 2\ **Last updated:** [May 28, 2026, 9:18am UTC](https://delvingbitcoin.org/t/pqc-lattice-based-signatures/2522 "2026-05-28T09:18:17Z")
Dear all, I hate to contribute to the recent flood of PQC posts, but I think it’s an important issue that’s worth discussing. In particular, what I usually see is various competing proposals without a clear winner. So… --- ## [UltrafastSecp256k1 v4.0 — Verification, Performance, and the Cost of Engineering Truth](https://delvingbitcoin.org/t/ultrafastsecp256k1-v4-0-verification-performance-and-the-cost-of-engineering-truth/2508)
**Author:** [@shrec](https://delvingbitcoin.org/u/shrec)\ **Replies:** 0\ **Last updated:** [May 16, 2026, 10:22pm UTC](https://delvingbitcoin.org/t/ultrafastsecp256k1-v4-0-verification-performance-and-the-cost-of-engineering-truth/2508 "2026-05-16T22:22:04Z")
Over the last several months I have been working on a large hardening and restructuring cycle for UltrafastSecp256k1. v4.0 is not just another optimization release. It represents a shift in how I think about cryptograp… --- ## [SHRIMPS: 2.5 KB post-quantum signatures across multiple stateful devices](https://delvingbitcoin.org/t/shrimps-2-5-kb-post-quantum-signatures-across-multiple-stateful-devices/2355)
**Author:** [@jonasnick](https://delvingbitcoin.org/u/jonasnick)\ **Replies:** 6\ **Last updated:** [April 8, 2026, 3:46pm UTC](https://delvingbitcoin.org/t/shrimps-2-5-kb-post-quantum-signatures-across-multiple-stateful-devices/2355 "2026-04-08T15:46:29Z")
Abstract: SHRINCS achieves very small hash-based signatures using a stateful signer while still allowing for static backups. However, its efficient stateful path requires transferring state to any new device, which is er… --- ## [Provable Cryptography for Bitcoin: An Introduction (Workbook)](https://delvingbitcoin.org/t/provable-cryptography-for-bitcoin-an-introduction-workbook/1974)
**Author:** [@jonasnick](https://delvingbitcoin.org/u/jonasnick)\ **Replies:** 1\ **Last updated:** [January 7, 2026, 3:08pm UTC](https://delvingbitcoin.org/t/provable-cryptography-for-bitcoin-an-introduction-workbook/1974 "2026-01-07T15:08:08Z")
I’m excited to share a comprehensive cryptography workbook that we developed for an interactive workshop on Bitcoin cryptography. This workbook contains definitions, propositions, lemmas, theorems, and exercises, along w… --- ## [Vanadium: A Virtualized Secure Enclave for Hardware Signing Devices](https://delvingbitcoin.org/t/vanadium-a-virtualized-secure-enclave-for-hardware-signing-devices/2142)
**Author:** [@salvatoshi](https://delvingbitcoin.org/u/salvatoshi)\ **Replies:** 0\ **Last updated:** [December 3, 2025, 2:19pm UTC](https://delvingbitcoin.org/t/vanadium-a-virtualized-secure-enclave-for-hardware-signing-devices/2142 "2025-12-03T14:19:10Z")
Developing firmware applications for hardware signing devices has always been constrained by the difficulties of embedded development: tiny RAM, tiny flash, vendor-specific SDKs, slow iteration cycles, and painful debugg… --- ## [Flattening Nested 2-of-2 Of a 1-of-1 And a k-of-n](https://delvingbitcoin.org/t/flattening-nested-2-of-2-of-a-1-of-1-and-a-k-of-n/2018)
**Author:** [@ZmnSCPxj](https://delvingbitcoin.org/u/ZmnSCPxj)\ **Replies:** 1\ **Last updated:** [September 29, 2025, 1:00pm UTC](https://delvingbitcoin.org/t/flattening-nested-2-of-2-of-a-1-of-1-and-a-k-of-n/2018 "2025-09-29T13:00:20Z")
Title: Flattening Nested 2-of-2 Of a 1-of-1 And a k-of-n Note It is possible to flatten the below into a single-layer quorum signing group: a 2-of-2 composed of: a normal single signer a k-of-n quorum signer This … --- ## [Implemented Post-Quantum Cryptography (PQC) Feature into Bitcoin Core!](https://delvingbitcoin.org/t/implemented-post-quantum-cryptography-pqc-feature-into-bitcoin-core/1320)
**Author:** [@QbitsCode](https://delvingbitcoin.org/u/QbitsCode)\ **Replies:** 4\ **Last updated:** [April 29, 2025, 11:42pm UTC](https://delvingbitcoin.org/t/implemented-post-quantum-cryptography-pqc-feature-into-bitcoin-core/1320 "2025-04-29T23:42:53Z")
Greetings Bitcoin Developers, We’re glad to share with you a proposed feature ‘Post-Quantum Cryptography’ to permanently eliminate the future quantum advancement threats forever! The acceptance of this issue requires B… --- ## [The path to general computation on Bitcoin (with OP\_CAT)](https://delvingbitcoin.org/t/the-path-to-general-computation-on-bitcoin-with-op-cat/1106)
**Author:** [@victorkstarkware](https://delvingbitcoin.org/u/victorkstarkware)\ **Replies:** 7\ **Last updated:** [April 29, 2025, 11:11am UTC](https://delvingbitcoin.org/t/the-path-to-general-computation-on-bitcoin-with-op-cat/1106 "2025-04-29T11:11:55Z")
1. Introduction In this post, we will discuss the task of achieving general computation on Bitcoin and the various steps it entails. Indeed, the ability to compute arbitrary logic in Bitcoin script is a very compellin… --- ## [Post Quantum Signatures and Scaling Bitcoin with STARKs](https://delvingbitcoin.org/t/post-quantum-signatures-and-scaling-bitcoin-with-starks/1584)
**Author:** [@EthanHeilman](https://delvingbitcoin.org/u/EthanHeilman)\ **Replies:** 0\ **Last updated:** [April 7, 2025, 4:30pm UTC](https://delvingbitcoin.org/t/post-quantum-signatures-and-scaling-bitcoin-with-starks/1584 "2025-04-07T16:30:38Z")
PQ (Post Quantum) signatures present a problem for Bitcoin: We can not ignore them. I strongly believe Bitcoin will need to move to PQ signatures in the near future. The rest of this email is premised on this belief. … --- ## [Non interactive anti-exfil (airgap compatible)](https://delvingbitcoin.org/t/non-interactive-anti-exfil-airgap-compatible/1081)
**Author:** [@moonsettler](https://delvingbitcoin.org/u/moonsettler)\ **Replies:** 16\ **Last updated:** [September 5, 2024, 9:04am UTC](https://delvingbitcoin.org/t/non-interactive-anti-exfil-airgap-compatible/1081 "2024-09-05T09:04:09Z")
An anti-exfil variant for airgaped signing devices using PSBTs that works with the QR code based traditional signing workflow. This proposal is anti-exfil protection level 2. Anti-exfil protection levels (proposed): Le…