Bitcoin and Blockchain Technology, Spring 2020

Department of Mathematics, University of Milano

Please subscribe the course mailing list sending an e-mail to [email protected]; you are also invited to join the 2020-statale channel in the Slack BBT workspace.

Learning objectives

The course is an introduction to bitcoin and the associated blockchain technology.

Starting from a computationally focused approach to elliptic curves over finite fields and presenting the discrete logarithm problem as cornerstone of public-key cryptography, bitcoin is introduced as ingenious breakthrough innovation.

Its game theory, computer science (distributed systems, distributed consensus), and monetary theory elements are examined in the attempt to properly convey the interdisciplinarity of the topic and appreciate its relevance.

Technical and programming elements about digital signatures, blockchain, Merkle tree, addresses, transactions, and timestamping are also provided to assess features and limits of the Bitcoin protocol.


There are no strict prerequisites, even if a computer science mindset and some familiarity with algebra and finance might help to appreciate the course. While a rigorous formal approach is almost impossible in a course touching on so many and so different knowledge areas, intellectual curiosity is stimulated about the interplay between maths, cryptography, economic incentives, technology, monetary theory, and politics.


  • Hash functions, hash pointers, blockchain, Merkle tree
  • Modular arithmetic and algebra of sets
  • Elliptic curves over real numbers and a finite field 𝐹
  • Asymmetric cryptography on elliptic curves
  • Elliptic curve digital signature algorithm
  • Elliptic curve Schnorr signature algorithm: Mu(lti)Sig(nature), threshold signature, batch verification
  • Diffie-Hellman
  • Pedersen commitment
  • Confidential transactions
  • Design of a simplified digital currency
  • Distributed consensus
  • Mining
  • P2P network
  • Protocol governance
  • Addresses and WIFs
  • Hierarchical deterministic wallets: BIP32, BIP43, BIP44
  • Mnemonic phrase: BIP39 and Electrum
  • TxIns, TxOs, UTxO, nLockTime
  • Bitcoin script language
  • Transactions
  • Blocks
  • Wallets and Bitcoin Core
  • Testnet, regtest, and wallet workshop
  • Money and innovation: monetary and token engineering
  • Hayek money and dual asset ledger money
  • Blockchain beyond bitcoin
  • Finance and blockchain
  • Timestamping, notarization, and anchoring
  • Smart contracts
  • Distributed ledger technology

Teaching method

  • Slide based lessons with associated bibliography
  • Python 3 programming assignments and technology assignments
  • Workshop labs on Bitcoin Core, Electrum, and OpenTimestamps

Teaching language

Italian or English, the latter if foreign students are present.

Lessons’ calendar and material

Workshops are with Paolo Mazzocchi, assistant lecturer.

  1. Wednesday 2020-03-16 15:30-17:30
    Bitcoin as Digital Gold slides
  2. Wednesday 2020-03-23 15:30-17:30
    Blockchain, Mining, and Distributed Consensus
  3. Wednesday 2020-03-30 15:30-17:30
    Elliptic Curve Digital Signature Algorithm
  4. Wednesday 2020-04-06 15:30-17:30
    Addresses, Scripts, and Transactions
  5. Wednesday 2020-04-20 15:30-17:30
    Addresses, Scripts, and Transactions (Part 2)
  6. Wednesday 2020-04-27 15:30-17:30
    Deterministic Key Sequences and Wallets
  7. Wednesday 2020-05-04 15:30-17:30
    Deterministic Key Sequences and Wallets (Part 2)
  8. Wednesday 2020-05-11 15:30-17:30
    Beyond Bitcoin: Between Hype and Reality
  9. Wednesday 2020-05-18 15:30-17:30
    The Frontier of Monetary Engineering
    slides, text

In the last lesson anonymous course evaluation forms will be collected

Python library

Python scripts, Excel spreadsheets, and regtest lab material

Introductory reading

  • Ferdinando M. Ametrano,
    “Bitcoin: oro digitale per nuovi standard monetari” (2018),

Technology references

Cryptography references

Monetary theory references

Bitcoin donation address 1FEz167JCVgBvhJBahpzmrsTNewhiwgWVG