The Cryptography Behind 'Crypto': What's Actually Doing the Securing
Public and private keys, hashing, and digital signatures: the three cryptographic building blocks that make the entire industry possible, explained without the maths.
By Firoz Khan|20 September 2026|Updated 11 October 2026|3 min read
The 'crypto' in cryptocurrency refers to cryptography, not to the industry generically, and it's worth actually knowing what that cryptography is doing, because it's the entire reason the system works without a bank or government standing behind it.
Public and private key pairs
Every wallet is built on a mathematically linked pair of keys: a private key, kept secret, that proves ownership and authorises spending, and a public key, which can be shared freely and is used to receive funds or verify a signature. The mathematical relationship makes it computationally infeasible to derive the private key from the public one with current technology.
Hashing: turning any data into a fixed-size fingerprint
A hash function takes any input, a transaction, a whole block of transactions, and produces a fixed-length output that changes completely and unpredictably if even a single character of the input changes. This is what links each block to the one before it, and what makes tampering with old blockchain history immediately detectable.
Here is a real example. The SHA-256 hash of the text "Pay Ben 10 pounds" starts a9c0cc03a58be156, and the hash of "Pay Ben 11 pounds", which differs by one character, starts 543755ce8060b222. The two outputs look unrelated, and each is 64 characters long in full. A change that small is enough to give a completely different result, which is why altering an old block is so easy to spot.
Digital signatures: proving you authorised something without revealing your key
Signing a transaction with your private key produces a unique signature that anyone can verify against your public key, confirming you authorised it, without ever exposing the private key itself in the process. This is the mechanism that lets a network trust a transaction came from the genuine owner without any central authority vouching for it.
A payment in four steps
- Your wallet builds the transaction: who is paid, how much, and from which funds.
- It signs the transaction with your private key, which never leaves the wallet.
- The network checks the signature against your public key, and checks the hash links.
- If both checks pass, the transaction is included in a block and cannot be quietly altered later.
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What Bitcoin actually uses
The Bitcoin wiki says that Bitcoin currently uses the secp256k1 elliptic curve with the ECDSA signature algorithm. Mining uses SHA-256 as its proof of work algorithm, and SHA-256 is also used in creating Bitcoin addresses. Other chains use different choices, but the idea is the same: a signature proves authorisation, and a hash gives each piece of data a tamper-evident fingerprint.
The quantum question
In theory, a large enough quantum computer could break the signature schemes used by Bitcoin and similar chains. The US standards body NIST has already published its first three post-quantum standards, on 13 August 2024, designed to resist attacks from future quantum computers. Whether and when a chain adopts new signature methods is a decision for its community, not something a holder controls, and this is a theoretical risk to watch, not a present one.
Why this matters beyond the theory
Every meaningful security failure in crypto, a stolen seed phrase, a signed malicious approval, a private key exposed through a compromised device, is a failure at the human or software layer around this cryptography, not a failure of the underlying maths itself, which, as far as current computing allows, still holds up.
Where the money is actually lost
Because the failures are human, the useful protections are practical. The FCA says most crypto activities are not regulated in the UK, so you generally will not have access to the Financial Ombudsman Service, and you will not be protected by the Financial Services Compensation Scheme if a firm fails. The FCA keeps a Warning List of unauthorised firms, and says a firm that is not on it may still be unauthorised or a scam, because such firms often change their names. Scams can be reported to the FCA.
Key terms in one place
- Private key: the secret that authorises spending. Never share it.
- Public key: the value others use to verify your signature.
- Address: a shorter value derived from the public key, used to receive funds.
- Hash: a fixed-length fingerprint of any data.
- Signature: proof, produced with the private key, that you authorised a transaction.
- Seed phrase: the backup from which a wallet's keys can be regenerated. Anyone who has it can spend your funds.
Where to read more
- Does quantum computing threaten Bitcoin?: what is real and what is hype
- The Bitcoin whitepaper, simplified: the original design
- CeFi vs DeFi: who holds the keys to your funds
- DApps explained: what you sign when you connect a wallet
A reminder
The FCA risk warning still applies to higher-risk crypto content. Always assess how much risk you are willing to take before buying.
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