A private key is a number picked at random, nothing more. From it is derived — through a calculation that is easy in one direction and infeasible in reverse — a public key, and from the public key an address, the string you hand to anyone who wants to pay you. The public key receives; the private key signs and spends. That is how Andreas Antonopoulos and David Harding frame it in Mastering Bitcoin.
Why keys instead of account names?
The chapter opens with a plain scene: Alice wants to pay Bob, and the thousands of full nodes that will verify her transaction do not know who Alice or Bob are — and we want to keep it that way, to protect their privacy. So we need a way to tell the network "these coins are Bob's now" without tying the payment to his real-world identity or to other payments he receives, while ensuring nobody but him can spend them.
That is exactly what asymmetric keys do. A private key applied to a transaction produces a numerical signature that only someone holding that key could produce. Anyone with the public key and the transaction can verify that signature without the private key ever being revealed. So everyone can check every signature on every transaction, while spending stays with the key holder alone. Note that the cryptography here is not used to encrypt transactions; it is used to make signatures that cannot be forged.
What is a private key, and why can't it be guessed?
The book insists on the simplicity: a private key is "just a number." It offers a memorable illustration — you can pick one with a coin, a pencil and paper: toss the coin 256 times and you have the binary digits of a usable key. But it immediately qualifies that: any process that is less than completely random significantly reduces the security of the key and the coins it controls, which is why software uses cryptographically secure random number generators. The book warns explicitly against writing your own randomness code.
The bounds are precise. The key may be any number between 0 and n−1, where n is a constant of roughly 1.1578 × 1077, slightly less than 2256. To convey the scale, the book offers one comparison: about 1077 possible keys, against an estimated 1080 atoms in the visible universe.
Hence two obligations that always travel together. The key must remain secret at all times, because revealing it to a third party is equivalent to handing over the coins. And it must be backed up and protected from accidental loss, because if it is lost it cannot be recovered, and the funds it secures are lost forever with it.
How does a public key become a short address?
The problem is practical. The shortest form of a Bitcoin public key known to early developers was 65 bytes — 130 characters written in hexadecimal. Passing that around by hand is tiring and error-prone.
The answer came from a hash function: a function that takes a potentially large input, scrambles it, and outputs a fixed amount of data. It always produces the same output for the same input, and it is impractical to find a different input producing a previously seen output. That makes the output a commitment to the input — a promise that, in practice, only input x produces output X. The original version of Bitcoin committed to public keys by hashing with SHA256 and then hashing that result with RIPEMD-160, producing a 20-byte commitment.
That is then written in base58check: an alphabet of 58 symbols, letters and digits minus four that are easily confused in some fonts — zero, capital O, lowercase l, and capital I. Four bytes derived from a hash of the data are appended as a checksum, so a mistyped address is rejected by the wallet instead of sending funds into nowhere.
So why did addresses change to "bc1"?
The book lists the complaints against the older format. Its mixed case makes it awkward to read aloud or transcribe by hand. It can detect an error but cannot help you locate it, which can cost several frustrating minutes. And a mixed-case alphabet takes extra space in the QR codes commonly used to share addresses.
So bech32 was designed: an alphabet of 32 symbols in a single letter case, and yet a bech32 address is only slightly longer than the legacy equivalent. More importantly it both detects and helps correct errors: in an address of the expected length it is mathematically guaranteed to detect any error affecting four characters or fewer, and it can tell the user where the errors are so minor transcription mistakes can be fixed quickly.
A real-life example
Picture a glass mailbox in a public square. Its address is written on the front for every passer-by to read, and anyone who wishes can drop an envelope in. The private key is the only key that opens the door. If someone photographs the box and its address and publishes the picture, the owner loses nothing — an address is for receiving, not for spending. But if someone copies the key, they take everything inside, and no authority will bring it back. And here is the real break from an ordinary mailbox: there is no post office to complain to, and no clerk who cuts a replacement key when yours is lost.
Key facts
1077 possible private keys, roughly, against the 1080 atoms estimated in the visible universe — the book's own comparison. 65 bytes was the length of the earliest public keys, or 130 hexadecimal characters. 20 bytes is the commitment after SHA256 then RIPEMD-160. 58 symbols in the base58 alphabet after dropping 4 confusable ones, plus a 4-byte checksum. 32 symbols in the bech32 alphabet, with a guarantee of detecting any error affecting 4 characters or fewer.
What does this have to do with Qist and digital assets?
The chapter's conclusion is that ownership here is not proven by paper or by a ledger held at some institution, but by a signature only the key holder can produce. That is what makes finance without custody possible at all. In Qist on the Base network the client does not hand money to a party that holds it for him; it stays in his wallet and he signs each step of the murabahah with his own key — the approval, the payment, the instalment — so every obligation in the contract becomes a signed fact both parties can read, not a promise written in one party's book. That is what decentralised finance actually means: your key stays in your hand.
The next unit in the series returns to Islamic finance: why Islam treats money as a medium of exchange rather than a commodity traded for its own sake, and what follows from that single rule.
Sources
This unit is based on the ideas of the "Keys and Addresses" chapter of Mastering Bitcoin (third edition) by Andreas M. Antonopoulos and David A. Harding, whose full text is published under CC BY-SA 4.0. The ideas are restated in plain language with explicit attribution to the authors. Educational content, not investment advice.
Frequently Asked Questions
Could anyone guess my private key?
In practice no, as long as it was generated from a secure source of randomness. The book compares the number of possible keys (about 10^77) with the estimated 10^80 atoms in the visible universe. The real risk is weak randomness or a leaked key, not guessing.
What is the difference between an address and a public key?
An address is a shortened, error-checked form built on a hash of the public key with a checksum appended. The public key is longer; the address is what is practical to share between people.
Is sharing my address risky?
An address is for receiving and does not allow spending, so sharing it gives no one access to your funds. But publishing it links your payments together and reduces privacy, which is why modern wallets generate a fresh address per payment.
What happens if the private key is lost?
The book is blunt: a lost key cannot be recovered, and the funds it secures are lost forever. No institution can reissue it, which is why backup is part of ownership rather than an optional extra.
Ilm Noor series index · ← Murabahah: The One Thing That Separates It From an Interest Loan · The Islamic Economy: Why Money Is a Means, Not a Commodity →
Last updated: 2026-08-10