← GlossarySecurity
What Is Public-Key Cryptography? The Basis of Crypto Wallets
Public-key cryptography is a system that uses linked key pairs, a public key that can be shared and a private key kept secret, so people can verify signatures and send data to a key holder without sharing any secret.
Key takeaways
- Every wallet address ultimately depends on a public and private key pair.
- You can share the public key or address freely; the private key must stay secret.
- Signatures made with the private key can be verified by anyone with the public key.
- Security rests on problems that are easy to do forward and infeasible to reverse.
The two keys
Traditional secret-sharing systems use one shared key, which creates the problem of delivering it safely. Public-key cryptography solves this with a pair of mathematically linked keys. The public key can be published to anyone. The private key never leaves its owner. What one key does, only the other can undo or check.
How crypto uses it
In cryptocurrencies, your coins are controlled by a private key. Your address is derived from the matching public key, so people can send you coins using only the address. To spend, you sign the transaction with the private key, and the network verifies the signature with the public key. No password, account or intermediary is involved, which is how non-custodial wallets work.
Why it is safe
The link between the keys relies on a mathematical problem that is easy in one direction and infeasible in the other. Multiplying a point on an elliptic curve is quick, but recovering the number you multiplied by from the result is not feasible with current methods. So publishing the public key does not expose the private key.
What can still go wrong
The mathematics is rarely the weak point. Keys are lost, copied from devices, typed into fake sites or generated with poor randomness. Anyone who obtains the private key owns the coins. That is why wallets protect keys with encryption on the device, why seed phrases must be kept offline and why you should never enter a key or recovery phrase into a website.
Example
Alice publishes her address. Bob sends her coins to it. To spend them, Alice signs a new transaction with her private key. Everyone can verify the signature with her public key, but nobody who sees it can learn the private key.
Put it into practice
Hold your own key pair
Back up the key for each coin you hold in Scrypt Wallet and never share it, because anyone who has a coin's key controls that coin.
Create a free wallet Get Scrypt for AndroidSources and verification
Last reviewed 2026-10-02 by the Scrypt Wallet team. The factual claims on this page, and where each comes from:
- Public-key cryptography uses pairs of keys: public keys that may be shared and private keys that are kept secret. [1]
- Elliptic-curve cryptography bases its security on the difficulty of the elliptic-curve discrete logarithm problem. [2]
Sources
- Public-key cryptography · Wikipedia · secondary source
- Elliptic-curve cryptography · Wikipedia · secondary source
Primary sources are protocol papers, specifications, source code or a project's own documentation; secondary sources are wikis and explainers. We checked each claim against the source text on the review date. Found an error? Tell us and we will correct it.
Frequently asked questions
Is the address the same as the public key?
Not exactly. An address is usually derived from the public key by hashing and encoding, but both are safe to share.
Can quantum computers break it?
Large quantum computers could threaten some current schemes, which is an active research area. No such computer exists today that breaks them.
What if I lose my private key?
Nobody can recover it for you in a non-custodial wallet, so back it up safely.
Written by the Scrypt Wallet team · Updated 2026-10-02. General education, not financial, tax or legal advice.