MTM22: The Cryptography Workbook (part 1)

Fundamentals.  @Fundamentals21m
Book: https://zeuspay.com/btc-for-institutions
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AverageGary
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Cryptography Wookbook: https://github.com/cryptography-camp/workbook
---- navigate to the current release on the right tab to download the workbook
---- DO NOT LISTEN TO THE EPISODE UNLESS YOU HAVE THE WORKBOOK HANDY

We’re back and recommitting to our North Star: getting comfortable with the math behind Bitcoin-grade cryptography. In this kickoff, we set the stage for a multi‑episode journey through a cryptography “workbook” on discrete‑log‑based multiparty signatures—using it as a scaffold to build real intuition for groups, fields, rigor, and proofs without being intimidated by jargon. We talk prerequisites (Z_p operations, cyclic groups, conditional probability, union bound, proof by contraposition), why rigor matters more than vibes, and how abstraction lets us reason cleanly about things like elliptic‑curve “addition” and key‑tweaking. We also peek at the table of contents we’ll tackle: negligible functions, games and asymptotic security, hash functions and collision resistance, commitments and accumulators (hello, Utreexo), one‑time and Lamport signatures, the discrete log problem, Pedersen commitments, DDH, ElGamal, the random‑oracle model and forking lemma, all the way to Schnorr signatures, key‑tweaks, and interactive aggregate signatures (e.g., DahLIAS). Expect a mix of precise definitions, worked examples, and occasional reinforcements from friends smarter than us—plus some probability detours like Monty Hall and Poisson to keep our statistical muscles warm.

• 'DahLIAS: Discrete Logarithm-Based Interactive Aggregate Signatures': https://eprint.iacr.org/2025/692
• 'BIP-340: Schnorr Signatures for secp256k1': https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
• 'Bitcoin Optech Topic: Schnorr Signatures': https://bitcoinops.org/en/topics/schnorr-signatures/
• 'Taproot (overview)': https://bitcoinops.org/en/topics/taproot/
• 'Utreexo: A dynamic hash-based accumulator optimized for the Bitcoin UTXO set (MIT DCI)': https://www.dci.mit.edu/utreexo
• 'Random Oracle Model (overview)': https://en.wikipedia.org/wiki/Random_oracle
• 'Forking Lemma (cryptography)': https://en.wikipedia.org/wiki/Forking_lemma
• 'Decisional Diffie–Hellman (DDH) assumption': https://en.wikipedia.org/wiki/Decisional_Diffie%E2%80%93Hellman_assumption
• 'Diffie–Hellman key exchange': https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
• 'ElGamal cryptosystem': https://en.wikipedia.org/wiki/ElGamal_encryption
• 'Pedersen commitment': https://en.wikipedia.org/wiki/Pedersen_commitment
• 'Lamport signature': https://en.wikipedia.org/wiki/Lamport_signature
• 'Discrete logarithm (background)': https://en.wikipedia.org/wiki/Discrete_logarithm
• 'Finite field (Z_p basics)': https://en.wikipedia.org/wiki/Finite_field
• 'Cyclic group': https://en.wikipedia.org/wiki/Cyclic_group
• 'Conditional probability': https://en.wikipedia.org/wiki/Conditional_probability
• 'Union bound': https://en.wikipedia.org/wiki/Union_bound
• 'Monty Hall problem': https://en.wikipedia.org/wiki/Monty_Hall_problem
• 'Poisson distribution': https://en.wikipedia.org/wiki/Poisson_distribution
• 'Contraposition (proof technique)': https://en.wikipedia.org/wiki/Contraposition
• 'Riverside (recording platform)': https://riverside.fm
• 'Nostr protocol (reference repo)': https://github.com/nostr-protocol/nostr