Bitcoin Cryptography Study Group

The purpose of the group is to end up doing a deep dive into the cutting edge bitcoin tech, such as MUSIG2, FROST, and BitVM.

The initial plan is to meet every week, discuss a whitepaper, and work out the math behind it.

Resources

Technologies used by Bitcoin

• Taproot and Signature aggregation using MUSIG: https://github.com/bitcoinops/taproot-workshop
• MUSIG2: https://developer.blockchaincommons.com/musig/sequence/
• FROST: https://github.com/BlockchainCommons/Learning-FROST-from-the-Command-Line/blob/main/README.md
• FROST2: https://eprint.iacr.org/2021/1375.pdf
• BitVM: https://bitvm.org/

Foundations

• Provable Cryptography for Bitcoin: https://delvingbitcoin.org/t/provable-cryptography-for-bitcoin-an-introduction-workbook/1974
• Elliptic Curves, ECDSA an Schnorr (by sandipan): https://sandipan.dev/blog/curves-behind-bitcoin
• Programming Bitcoin, by Jimmy Song. Chapters 1-4 include building the ECC layer from scratch. Source code: https://github.com/jimmysong/programmingbitcoin?tab=readme-ov-file. Book: https://www.oreilly.com/library/view/programming-bitcoin/9781492031482/
• Some slides on taproot and schnorr: https://download.wpsoftware.net/bitcoin/wizardry/mw-slides/2017-05-milan-meetup/slides.pdf
• Intro to Zero Knowledge Proofs: https://zkintro.com/
• The RareSkills Book of Zero Knowledge: https://rareskills.io/tutorials/zk-book
• Groth16: https://alinush.github.io/groth16
  • This one has a lot of explainers about digital signatures and other ZKPs
• Arkworks: https://github.com/arkworks-rs/snark
  • BitVM uses arkworks as an inspiration
• For cryptography, in general: https://github.com/sobolevn/awesome-cryptography

Meetings

Whenever possible, we will organize a meeting every week.

How a meeting is organized:

• Choose a topic for that meeting
• Research publicly available materials
• Create an easy to understand summary (preferably in Markdown)
• The meeting lasts for an hour
• First 30-40 minutes are allocated for the presentation, according to the summary
• Last 20-30 minutes are allocated for Q&A and discussion

Roadmap

• Elliptic Curves (20 Feb 2026)
• Schnorr Signatures (6 March 2026)
• MUSIG and MUSIG2
• Zero Knowledge Proofs
• Scriptless scripts
• FROST
• BitVM