What is a public key in crypto? Keys, addresses, and signatures explained

A public key is the cryptographic counterpart to a private key. Together they let you prove ownership of cryptocurrency without revealing the secret that controls it.
Summary

• A public key is a large number derived mathematically from a private key using elliptic curve multiplication, a one-way function that is fast to compute forward but practically impossible to reverse.
• Bitcoin and Ethereum both use the secp256k1 elliptic curve, which produces 256-bit private keys and 512-bit uncompressed public keys (or 257-bit compressed public keys).
• A wallet address is not the same as a public key; the address is a shorter, hashed version of the public key designed to be easier to share and more resistant to certain theoretical attacks.
• The private key signs transactions, the public key verifies those signatures, and the address receives funds. Losing the private key means permanent loss of access; sharing the public key or address carries no risk to fund security.
• The July 2026 Coldcard firmware vulnerability, which exposed weak private key generation affecting $116 million in bitcoin, underscores why proper key generation and storage remain the most critical aspects of self-custody.

Public key cryptography is the foundation of every cryptocurrency transaction, yet most users never interact with their public key directly. They see wallet addresses, scan QR codes, and confirm transfers without understanding the mathematical layer that makes trustless ownership possible.

That layer matters because understanding it changes how you think about security. A public key is not a password. It is not a secret. It is a number that you can share with anyone, and from which no one can derive the private key that controls your funds. That asymmetry, easy to go one way but impossible to go back, is what allows strangers on the internet to send each other money without trusting a bank, a government, or each other.

How key pairs work

Every cryptocurrency wallet is built on a key pair: one private key and one public key. The private key is a randomly generated number, typically 256 bits long, which means it is one of roughly 10 to the power of 77 possible values. For context, the estimated number of atoms in the observable universe is around 10 to the power of 80. The keyspace is large enough that guessing a specific private key by brute force is not a practical concern with current or foreseeable technology.

The public key is derived from the private key through elliptic curve multiplication. Bitcoin and Ethereum both use a specific curve called secp256k1. The private key is multiplied by a fixed point on this curve called the generator point, and the result is another point on the curve. That result is the public key.

The critical property is that this multiplication is a one-way function. Given a private key, computing the public key takes a fraction of a second. Given only the public key, computing the private key requires solving the elliptic curve discrete logarithm problem, which has no known efficient solution. This asymmetry is the entire basis of cryptocurrency security.

Public key versus wallet address

A common misconception is that a wallet address and a public key are the same thing. They are not. The address is derived from the public key through one or more rounds of hashing, a process that shortens the output and adds an extra layer of security.

In Bitcoin, the process works as follows. The 512-bit uncompressed public key (or 257-bit compressed public key) is run through SHA-256, then through RIPEMD-160, producing a 160-bit hash. A version byte is prepended, a checksum is appended, and the result is encoded in Base58Check format. The final output is the familiar Bitcoin address starting with 1, 3, or bc1.

In Ethereum, the process is simpler. The 512-bit public key is run through Keccak-256 (a variant of SHA-3), and the last 20 bytes (160 bits) of the hash become the address. A "0x" prefix and an optional EIP-55 checksum are added to produce the familiar Ethereum address.

The reason for hashing the public key into an address is partly practical (shorter strings are easier to share) and partly defensive. If quantum computers ever become capable of breaking elliptic curve cryptography, they would need the public key, not the address, to derive the private key. Addresses that have never been used to send a transaction have never had their public key exposed on-chain, adding a theoretical layer of quantum resistance.
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How digital signatures prove ownership

When you send cryptocurrency, you are not moving coins from one location to another. You are creating a message that says "I authorize the transfer of X amount from my address to this recipient" and signing that message with your private key. The signature proves that the person who created the message controls the private key associated with the sending address, without revealing the private key itself.

The verification process uses the public key. Anyone running a node on the network can take the transaction message, the digital signature, and the sender's public key, and run a mathematical verification that confirms the signature was produced by the corresponding private key. If the verification passes, the transaction is valid. If it fails, the transaction is rejected.

This is why losing a private key is catastrophic. No private key means no ability to produce valid signatures, which means no ability to authorize transactions from that address. The funds remain on the blockchain, visible to everyone, but permanently inaccessible. There is no "forgot password" recovery mechanism because there is no central authority that holds a backup.

The key generation chain

In modern wallets, individual private keys are not generated independently. Instead, a single master seed produces all keys in the wallet through a deterministic process defined by BIP-32 (hierarchical deterministic wallets) and BIP-39 (mnemonic seed phrases).

The process begins with entropy, a source of randomness. The wallet software or hardware device generates a random number, typically 128 or 256 bits. This entropy is encoded as a mnemonic phrase of 12 or 24 words drawn from a standardized list of 2,048 words. The mnemonic phrase, combined with an optional passphrase, is run through a key derivation function (PBKDF2) to produce a 512-bit master seed.

From the master seed, a hierarchical tree of key pairs is derived. Each branch of the tree can generate billions of unique private keys and their corresponding public keys and addresses. This is why a single seed phrase can recover an entire wallet with all its addresses: the seed deterministically regenerates every key pair in the hierarchy.

The security implication is that the seed phrase is the root of all keys. Anyone who obtains the seed phrase can regenerate every private key, every public key, and every address the wallet has ever used or will ever use. Protecting the seed phrase is equivalent to protecting every key pair in the wallet simultaneously.

Compressed versus uncompressed public keys

Early Bitcoin software used uncompressed public keys, which include both the x and y coordinates of the point on the elliptic curve. An uncompressed public key is 65 bytes: a 1-byte prefix (0x04) followed by 32 bytes for the x coordinate and 32 bytes for the y coordinate.

Because the elliptic curve equation means that for any given x coordinate there are only two possible y values (one even, one odd), it is sufficient to store just the x coordinate and a single bit indicating whether y is even or odd. This produces a compressed public key of 33 bytes: a 1-byte prefix (0x02 for even y, 0x03 for odd y) followed by 32 bytes for the x coordinate.

Compressed keys save space in transactions, which reduces fees. Since 2012, most Bitcoin software defaults to compressed public keys. Ethereum uses uncompressed public keys internally but strips the prefix byte in address derivation, using only the 64-byte x and y values.

The distinction matters for compatibility. A compressed and uncompressed public key derived from the same private key produce different addresses in Bitcoin. Importing a private key into a wallet that uses a different compression format than the original wallet will generate a different address, which can cause confusion if funds were sent to the other format's address.

Real world key security failures

The theory behind public key cryptography is sound, but implementation failures have caused significant losses.

In July 2026, researchers discovered that the Coldcard hardware wallet had been generating weak private keys for five years. A build flag in the firmware told the device to skip its dedicated hardware randomness chip, resulting in predictable entropy. An attacker reverse-engineered the weakness and began draining wallets on July 30, emptying approximately $116 million in bitcoin before the vulnerability was publicly disclosed.

The lesson is that the security of a key pair depends entirely on the quality of the randomness used to generate the private key. A theoretically unbreakable 256-bit key is worthless if the random number generator is flawed, biased, or predictable. This is why reputable hardware wallets use dedicated true random number generators and allow users to add their own entropy (such as dice rolls) as an additional safeguard.

Other historical incidents include the 2013 Android SecureRandom vulnerability, which caused multiple Bitcoin wallets to generate duplicate random numbers, allowing attackers to compute private keys from transaction signatures. The Profanity vanity address generator was exploited in September 2022 when researchers discovered that its key generation used a 32-bit seed, reducing the effective keyspace from 2 to the power of 256 down to 2 to the power of 32, roughly 4 billion possibilities that could be brute-forced in minutes.

Public keys and smart contracts

On smart contract platforms like Ethereum, public key cryptography serves a dual purpose. It secures externally owned accounts (EOAs), the standard user wallets controlled by private keys, and it authenticates messages signed by those accounts when they interact with smart contracts.

When a user calls a function on a smart contract, the transaction includes the digital signature produced by the user's private key. The Ethereum Virtual Machine verifies this signature against the sender's public key before executing the function. This is how a smart contract knows that the person calling "transfer 100 USDC to address X" is actually the owner of the tokens being transferred.

Smart contract wallets (account abstraction wallets introduced by ERC-4337) can modify this model. Instead of relying solely on a single private key, a smart contract wallet can require multiple signatures, biometric authentication, social recovery, or spending limits enforced by code. The public key remains part of the system, but the rules governing what constitutes a valid authorization become programmable.

Custodial versus self-custodial key management

On a centralized exchange, the exchange holds the private keys and users access their funds through traditional authentication (username, password, two-factor codes). The user never sees a public key or private key. The exchange signs transactions on the user's behalf.

In self-custody, the user holds the private key (or the seed phrase that generates it) and is solely responsible for its security. The public key and address are derived locally, and no third party has access to the signing capability.

The tradeoff is clear. Custodial solutions are convenient but introduce counterparty risk: if the exchange is hacked, insolvent, or freezes withdrawals, the user's funds are at risk. Self-custody eliminates counterparty risk but introduces operational risk: if the user loses the seed phrase, misstores it, or falls victim to phishing, the funds are gone permanently.

Multisignature setups split the difference by distributing key management across multiple parties or devices. A 2-of-3 multisig requires any two of three private keys to sign a transaction, so losing one key does not result in permanent loss and compromising one key does not give an attacker control.

What this article does not cover

This article does not cover post-quantum cryptography schemes such as lattice-based signatures, which are being researched as replacements for elliptic curve cryptography in the event that large-scale quantum computers become viable. It does not cover the mathematics of elliptic curves beyond the conceptual level. It does not cover specific wallet setup guides, as those vary by product and change frequently.

Practical checks for protecting your keys

Never share your private key or seed phrase. No legitimate service, support agent, or airdrop will ever ask for them. Any request for these credentials is a scam without exception.

Verify address format before sending. Clipboard malware can replace a copied address with an attacker's address. Always visually confirm the first and last several characters of an address after pasting it.

Use hardware wallets for significant holdings. Hardware wallets generate and store private keys on a dedicated chip that never exposes them to the internet-connected device. Research the manufacturer's track record with entropy generation before purchasing.

Add your own entropy when possible. Some hardware wallets allow users to supplement the device's random number generator with manually entered randomness such as coin flips or dice rolls. This mitigates the risk of a flawed hardware random number generator.

Keep seed phrase backups in multiple secure locations. A single copy stored in one location is vulnerable to fire, flood, or theft. Metal seed phrase backups resist environmental damage better than paper.
Read more: What is a seed phrase?

What is a public key in cryptocurrency? {#faq-1}

A public key is a large number derived from a private key using elliptic curve multiplication. It serves as the cryptographic identity that verifies transaction signatures without revealing the private key. Anyone can see a public key, and sharing it does not compromise fund security.

Is a public key the same as a wallet address? {#faq-2}

No. A wallet address is derived from the public key through one or more rounds of cryptographic hashing. The address is shorter and easier to share. In Bitcoin, the same private key can produce different addresses depending on whether compressed or uncompressed public keys are used.

Can someone steal my crypto if they know my public key? {#faq-3}

No. The public key is designed to be shared. Deriving the private key from the public key requires solving the elliptic curve discrete logarithm problem, which has no known efficient solution with current computing technology.

What happens if I lose my private key? {#faq-4}

The funds associated with that key become permanently inaccessible. There is no recovery mechanism because cryptocurrency networks have no central authority that stores backups. This is why seed phrase backups are critical for self-custody wallets.

What is the difference between a public key and a private key? {#faq-5}

The private key is a randomly generated secret number used to sign transactions. The public key is derived from the private key and is used to verify signatures. The private key must remain secret; the public key can be shared freely.

How does a seed phrase relate to public and private keys? {#faq-6}

A seed phrase (12 or 24 words) encodes the master entropy from which all private keys in a wallet are deterministically derived. Each private key produces a corresponding public key and address. Protecting the seed phrase protects every key pair the wallet will ever generate.

What elliptic curve do Bitcoin and Ethereum use? {#faq-7}

Both Bitcoin and Ethereum use the secp256k1 elliptic curve. It produces 256-bit private keys and 512-bit uncompressed public keys (or 257-bit compressed public keys). The curve was chosen for its efficiency and well-understood security properties.

Could quantum computers break public key cryptography? {#faq-8}

Theoretically, a sufficiently powerful quantum computer running Shor's algorithm could derive a private key from a public key. However, no such quantum computer exists as of 2026. Addresses that have never been used to send transactions have not exposed their public key on-chain, adding a layer of protection. Post-quantum signature schemes are being researched as future replacements.

Disclaimer: This article is for informational purposes only and does not constitute financial, investment, or security advice. Cryptocurrency self-custody carries inherent risks. Always conduct your own research and follow current security best practices. Published August 24, 2026.