1 Introduction: a quantitative stance

What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party.

Satoshi Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System (2008)

1.1 The problem we begin with

Consider a multi-centre clinical trial conducted by five hospitals. Each site enrols participants, assigns them to treatment through a shared randomisation scheme, and records outcome events as they occur. Every site keeps a copy of the growing record, and a regulator will in due course audit it. Suppose now that no site is willing to let any other act as the sole custodian of that record. Perhaps the sponsor has a financial interest in the result; perhaps one site’s data systems have been compromised before; perhaps the institutions operate in different countries under different legal regimes. The question this book begins from is the following: can the five sites maintain a single shared record of trial events, to which entries may be added but never altered, agreed by all and revisable by none, with no central referee to enforce it?

This framing is not a presentational device adopted to make a cryptocurrency course more agreeable to a public-health audience. It is, we shall argue, the same mathematical problem that the Bitcoin system solved in 2008 (Nakamoto, 2008), considered apart from its monetary application. A blockchain is a shared record, added to but never altered, that mutually distrusting parties agree upon without relying on any trusted intermediary. Every mechanism this book studies exists to make some part of that sentence work. Before going further we fix the small vocabulary on which the rest of the book depends, so that the reader need not carry these terms as mysteries.

The core vocabulary, defined once

Six terms recur throughout the book. We define them here and use them consistently thereafter.

Ledger. A record of entries. In this book the record is append-only, meaning that entries may be added but none may afterward be altered or removed.
Hash function. A function that maps an input of any size to a short string of fixed length, called its hash, such that any change to the input, however small, changes the hash beyond recognition. It serves as a digital tamper-evident seal: a record is tamper-evident when any alteration to it can be detected.
Digital signature. A cryptographic mark that only the holder of a private key can produce, and that anyone holding the matching public key can verify. It establishes who authored an entry, so that an entry is attributable.
Consensus protocol. A procedure by which many computers, some of which may fail or act dishonestly, come to agree on one shared ordering of the entries.
Node. A computer that stores a copy of the ledger and checks each new entry against the rules.
Blockchain. An append-only ledger that mutually distrusting parties maintain and agree upon, by means of the tools above, without any trusted intermediary.

With those terms in hand, the sentence resolves. A hash function makes the ledger tamper-evident, digital signatures make its entries attributable, and a consensus protocol makes the parties agree on a single order of entries even though they have no reason to trust one another. The result established by Nakamoto (2008) is that this agreement is achievable even in an open setting, where any party may join, depart, or attempt to deceive.

We shall study these systems as a statistician would wish them studied: as objects of quantitative analysis rather than of advocacy. The central pedagogical claim of the book is that the reader already commands most of the difficult ideas, under other names. The probability that an attacker rewrites confirmed history is a tail probability of a random walk, that is, the small chance that a fluctuating running total strays far from its starting point. The ten-minute interval between blocks is the target of a feedback controller, a rule that nudges a system back toward a desired level, acting on a Poisson process, the standard model for events that arrive at random. The selection of validators in a stake-based system is sampling with probability proportional to size, familiar from the design of complex health surveys. The concentration of holdings on a chain is measured by a Lorenz curve, the same instrument used to quantify inequality in income or in vaccine coverage. The work of the book, chapter by chapter, is to make these translations explicit and then to use the reader’s existing fluency to reach conclusions that most accounts of the subject leave imprecise.

1.2 Why the public-health reader has the advantage

Writing on blockchain divides into two genres, and both fail a quantitative reader. The developer tutorial explains how to operate an interface without explaining why the system is built as it is. The promotional explainer supplies confidence in place of understanding. Neither serves a reader who can fit a survival model, design a sampling plan, or evaluate a probabilistic forecast.

The reader of this book can do something most participants in the field cannot: express a claim as a quantity and test it. That capacity is the single most valuable instrument for navigating a domain in which the typical public statement is promotional. A considerable part of the course consists of taking an assertion that circulates unexamined, writing down the model it presupposes, and computing whether the assertion holds. The reader will find the exercise familiar, for it is the discipline one already applies to a claimed treatment effect or to a surprising signal in disease surveillance.

1.3 Why now: the technology is arriving in health

It is worth stating plainly why a health scientist should undertake this effort now, rather than leave the subject to specialists in computer science. The reason is that the machinery of verifiable data, meaning records whose integrity and origin can be checked by cryptographic means rather than by trust in a custodian, has ceased to be hypothetical in health and has become infrastructure. Cryptographically signed health credentials reached hundreds of millions of people during the COVID-19 pandemic through the SMART Health Cards standard (SMART Health Cards / VCI, 2024), a scheme in which an issuer signs a record and anyone may verify the signature. The World Health Organization now operates a global directory of public keys for verifying such credentials across borders (World Health Organization, 2023). Prescription-drug supply chains in Europe and the United States are being made traceable to the individual package by regulation, and at least one production system serving that mandate is a genuine shared ledger (U.S. Food and Drug Administration, 2023). Estonia has for years anchored the integrity of its national health records to a hash-linked timestamping service, meaning a service that stores a hash of each record so that any later alteration is detectable (Guardtime, 2016). As predictive artificial intelligence enters clinical care, regulators have begun to require a tamper-evident account of the data and models behind a recommendation (U.S. Office of the National Coordinator for Health Information Technology, 2024).

The instructive observation is that most of these successes are built from digital signatures and hash functions, rather than from tradable tokens and the competitive computation known as mining, and that the ventures which insisted on the latter have largely failed. The health professional of the coming decade will be asked, repeatedly, to judge such systems: to say whether a vendor’s claim is a verifiable fact or an unfalsifiable story, whether a shared ledger earns its cost over a well-kept database, and whether an attestation proves what it purports to prove. That judgement, and not the ability to build a chain, is the competence this book develops, and it is the reason the subject belongs in a public-health education now.

1.4 The falsifiability discipline

We maintain a critical stance by construction, not as a matter of attitude. The cryptography at the base of these systems solved a genuine and difficult problem, namely Byzantine agreement, which is the problem of reaching a common decision when some of the participants may behave arbitrarily and even maliciously, in the open-membership setting where any party may join (Lamport et al., 1982). A great deal of what has been built upon that achievement is speculation, and some of it is fraud. Both statements are true at once, and a calibrated analyst holds them together without collapsing into either endorsement or dismissal.

To keep the analysis disciplined, we sort every claim we meet into one of four tiers, and we demote each assertion to its true tier before granting it belief.

The four falsifiability tiers

Protocol fact. A statement verifiable by reading the code, running a node, or checking a proof. Trust it once it has been verified.
Empirical claim. A measurable statement about observed data from a chain or a market. Ask for the data and the method by which it was obtained.
Economic claim. A conditional statement about incentives that holds only under stated assumptions. Ask what those assumptions are and whether they hold.
Narrative. An unfalsifiable or forward-looking story about value or destiny. Treat it as marketing until it has been made into a claim of the second or third kind.

The characteristic failure of the field is tier-slippage: a narrative delivered in the confident cadence of a protocol fact. Naming the tier is the remedy, and we shall ask the reader to do so as a matter of habit. The epidemiologist will recognise the exercise, for it is the same caution one brings to a causal claim drawn from an observational study.

1.5 The running case study

A single application threads the entire book, so that the reader follows one realistic system as it is developed against every layer of the technology.

The trial ledger. The multi-institution clinical-trial data-integrity ledger with which we opened: several hospitals sharing an append-only record of enrolment, randomisation, and outcome events, made tamper-evident and attributable, auditable by a regulator after the fact, with no single party able to rewrite what has been recorded. Every chapter returns to it.
The cold chain. A vaccine cold-chain provenance system serves as a secondary example, where provenance means a verifiable account of an item’s history: here, confirmation that each vial was held within its temperature bounds from manufacture to administration, across custodians who share no common authority.

As each mechanism is introduced, hashing, then the Merkle tree (a hash-based summary that commits to many records at once), then consensus, the account model, the smart contract (a program that executes on the ledger), and the analysis of on-chain data, we shall ask what it contributes to these two systems, and whether it is in fact the right tool. Each such term is defined in full in the chapter that treats it. We should say at the outset that the answer to the question of fitness is frequently no.

When not to use a blockchain

A blockchain provides trust-minimised agreement among parties with no common authority, at a substantial cost in speed, delay, and complexity. If the parties already trust a custodian, or one could be appointed, then a conventional replicated database with cryptographic audit logging delivers tamper-evidence without the overhead of consensus. Most proposals for putting health records ‘on a blockchain’ fail this test, and the book equips the reader to apply it.

1.6 A first computation

The atomic operation of the entire field is the cryptographic hash defined above: a function that maps any input to a fixed-length output and that behaves, for every practical purpose, as though its output were random. We study its statistical properties in Chapter 3. For the present, we invite the reader to observe the two properties that make a ledger tamper-evident. The first is determinism, meaning that the same input always yields the same output. The second is the avalanche effect, meaning that a change of a single character yields an output bearing no resemblance to the original.

library(digest)
h <- function(x) {
  digest(x, algo = 'sha256', serialize = FALSE)
}

h('trial-record: patient 001, arm A, enrolled 2026-02-01')
#> [1] "e41108886d96480faf07fb4438dcfbed3cc340563ca9ad34e5902dce9cf351d2"
h('trial-record: patient 001, arm B, enrolled 2026-02-01')
#> [1] "a7c91464d98cd74bd541ce8602e44c411f3ac61be53878d962994be61855616d"

The two records differ in a single character, the treatment arm, yet their hashes share no visible structure. Were the trial ledger to store the hash of each record, then altering any record after the fact would change its hash and so reveal the tampering. That is the whole of what a tamper-evident log provides, and everything else in the book is, in a sense we shall make precise, an elaboration of this one computation.

1.7 The ten-week map

The book is a ten-week course in four parts, one chapter to each teaching week. The terms named below are each defined in the chapter that introduces them; the map is meant as a signpost, not as a summary to be understood in advance.

Part I, Foundations. The consensus problem in the open-membership setting (Chapter 2), and the cryptographic primitives, the hash function, the Merkle tree, and the digital signature, studied empirically in R (Chapter 3).
Part II, Bitcoin and Nakamoto consensus. Proof-of-work, which secures the ledger by requiring costly computation (Chapter 4); the statistics of mining, treated as a process of random arrivals under feedback control (Chapter 5); and the economics that make an attack unprofitable (Chapter 6).
Part III, Ethereum and programmable state. The account model and the virtual machine that let a ledger run programs (Chapter 7); decentralised finance, treated as applied mathematics (Chapter 8); and the value that the ordering of transactions can be made to yield, known as maximal extractable value (Chapter 9).
Part IV, Proof-of-stake and on-chain data. Consensus secured by capital at risk rather than by computation, and the risks of reusing that capital (Chapter 10); and the statistical analysis of the public record a chain leaves behind, including the study of token economics and of the concentration of holdings (Chapter 11).

1.8 How to use this book

In closing, three habits merit emphasis. First, the reader should consult the primary source before the secondary commentary. For each week the Further reading section names the whitepaper, specification, or paper that constitutes the ground truth, and reading it first prevents a promotional account from installing a misconception before the original has been seen. Second, the reader should execute the code. Every computational result in the book is generated at the time of typesetting from the R code shown beside it, and re-running that code is the most direct route from reading to understanding. Third, the reader should keep a calibrated record of forecasts, introduced in Chapter 11 and scored by the Brier score, a standard measure of how closely probabilistic predictions match the outcomes that follow, so that one’s own scepticism is held to the same account demanded of others.

The reference textbook throughout is Narayanan et al. (2016), whose rigour set the standard this book has tried to meet for a public-health audience.