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Practical Cryptography and Distributed Ledgers

  • Pablo Deymonnaz
  • Diego Kingston
  • Federico Carrone

The ZK proving systems landscape has exploded. Circle STARKs (Starkware/Stwo) operate over the Mersenne31 field, enabling dramatically faster proof generation by exploiting the structure of circles over finite fields. Binius (Irreducible) works over binary tower fields, achieving the smallest proofs for binary circuits. Jolt/Lasso (a16z) use lookup arguments to verify RISC-V execution without custom circuits -- this is the "lookup singularity" approach where the prover just commits to a trace and proves lookups into predefined tables. Folding schemes (Nova, HyperNova, SuperNova from Microsoft Research) are the other major paradigm shift: instead of proving a computation all at once, you incrementally fold instances together, enabling IVC (Incremental Verifiable Computation) for long-running computations like blockchain state transitions.

Post-quantum cryptography has moved from research to deployment: NIST finalized FIPS 203 (ML-KEM, lattice-based key encapsulation), FIPS 204 (ML-DSA, lattice-based signatures), and FIPS 205 (SLH-DSA, hash-based signatures). Chrome and Signal already ship post-quantum key exchange. The FHE entries (Zama's fhEVM, Concrete ML) show fully homomorphic encryption becoming practical for specific use cases -- encrypted on-chain computation and private ML inference -- though it remains orders of magnitude slower than plaintext for general computation.

Table of Contents

1. Foundations of Cryptography

  • Groups, Rings and Fields
  • Finite Fields
  • Modular Arithmetic
  • Polynomials over a Field
  • P versus NP problem
  • Computationally Hard Problems: Factorization and the Discrete Logarithm
  • Elliptic Curves
  • Elliptic Curves Pairings and Field Extensions

Readings

Exercises

2 Symmetric encryption

  • Stream ciphers and block ciphers
  • AES
  • AES operation modes
  • ChaCha20
  • Security definitions.
  • Attacks on block and stream ciphers.

3. Asymmetric encryption

  • Diffie-Hellman Key Exchange
  • ECDH
  • ElGamal
  • RSA
  • PKCS

Readings

4. Hash Functions, MAC and Signatures

  • Properties of cryptographic hash functions
  • Merkle-Damgard construction
  • MD5
  • SHA1
  • Sponge constructions
  • Keccak - SHA3
  • Message Authentication Codes
  • ECDSA signature
  • Schnor signature
  • BLS signature

Readings

5. What is Money?

6. Introduction to blockchains and cryptocurrencies

  • What is a blockchain?
  • State Machines
  • Consensus
  • Merkle Trees

Readings

Videos

7. Bitcoin

  • Two general's Problem
  • What Is the Byzantine Generals Problem?

Readings

8. Ethereum

  • Solidity
  • ERC20
  • ERC721
  • ERC-1155
  • Merkle Patricia Trie Tree

Readings

9. Wallets, Dapps and DeFi

10. Oracles, Bridges and Rollups

  • Oracles
  • Bridges
  • An Incomplete Guide to Rollups - Vitalik explains how optimistic and ZK rollups scale Ethereum by executing off-chain while posting data on-chain

11. EVM

12. Security

Tools

13. MEV

14. Zcash, SNARKs and Privacy in blockchains

15. Scaling blockchains

  • Data Availability
  • Optimistic versus Zero Knoweledge Rollups
  • Circom, Cairo, Noir

Readings

16. Tendermint, HotStuff and Narwhal

17. Bitcoin: SegWit, Taproot, Lightning Network and Covenants

Books

Blockchain

Cryptography

Abstract Algebra and Number Theory

Courses


Missing topics

  • Light Clients
  • UTXO vs Account model
  • The Blockchain Trilemma
  • PoS vs PoW
  • Soft Forks vs Hard Forks
  • Onchain vs offchain computation
  • Chinese remainder theorem
  • One Time Pad
  • MAC
  • Account Abstraction (argent x)
  • Finality
  • muun, non custodial wallets

Not yet reviewed

These resources were recently found and have not been reviewed yet.

ZK Proofs: New Proving Systems

ZK Proofs: Folding Schemes

MEV (New)

Scaling & Data Availability

Consensus (New)

FHE

ZK Proving Systems (New)

Ethereum: Pectra & Account Abstraction (New)

MEV / PBS (New)

Bitcoin: BitVM & OP_CAT (New)

Consensus Protocols (New)

Post-Quantum (New)

Formal Verification (New)

Cross-Chain (New)

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