Bitcoin doesn’t use passwords. It doesn’t rely on banks to verify who owns what. Instead, it uses something far more powerful: public key cryptography. This system is what makes Bitcoin work without a central authority. If you understand how public and private keys interact, you understand Bitcoin’s core security model.
What Are Public and Private Keys in Bitcoin?
Every Bitcoin user has two keys: a private key and a public key. Think of the private key like the password to your safe. It’s a randomly generated 256-bit number - that’s a number with 78 digits. Only you should ever know it. If someone gets it, they can spend your Bitcoin.
The public key is derived from the private key using math. It’s like a lock you can give out to anyone. You don’t need to hide it. In Bitcoin, the public key is used to create your Bitcoin address - but not directly. First, your public key is hashed (using SHA-256 and RIPEMD-160) to make a shorter, more secure version called a Bitcoin address. That’s why your address looks like 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa - it’s not your public key, it’s a hash of it.
When you send Bitcoin, you sign the transaction with your private key. Everyone on the network can use your public key to check that the signature is valid - without ever seeing your private key. This is the magic of asymmetric cryptography: verification without exposure.
Why Elliptic Curve Cryptography (secp256k1)?
Bitcoin doesn’t use RSA or other older systems. It uses elliptic curve cryptography, specifically the secp256k1 curve. This curve was chosen for three reasons: speed, security, and efficiency.
With RSA, you’d need a 3072-bit key to match the security of a 256-bit elliptic curve key. That means bigger files, slower processing, and more bandwidth - all bad for a peer-to-peer network like Bitcoin. secp256k1 gives the same level of security with much smaller data. A Bitcoin signature is about 72 bytes. An equivalent RSA signature would be over 300 bytes.
The curve’s equation is simple: y² = x³ + 7, calculated over a finite field. The base point G is fixed. To generate a public key, you multiply the private key (a number) by G. This math is easy one way - hard the other. That’s the whole point. Even with today’s fastest computers, it would take trillions of years to guess a private key from a public key. The math isn’t just theoretical - it’s been tested for over 14 years.
How Digital Signatures Work in Bitcoin
Bitcoin uses the ECDSA algorithm (Elliptic Curve Digital Signature Algorithm) to sign transactions. Here’s how it works in practice:
- You want to send 0.5 BTC to someone.
- Your wallet creates a transaction message with inputs, outputs, and amounts.
- Your wallet hashes that message with SHA-256.
- It uses your private key and the hash to generate a digital signature - a pair of numbers (r and s).
- You broadcast the transaction, including the signature and your public key.
- Miners and nodes use your public key to verify the signature matches the transaction hash.
If the math checks out, the transaction is valid. No one needs to trust you. The network just checks the math.
Verification takes about 5-10 milliseconds on standard hardware. That’s slow compared to symmetric encryption - but it’s fine. Bitcoin only processes about 7 transactions per second anyway. Speed isn’t the goal. Security and decentralization are.
Compressed vs Uncompressed Public Keys
Early Bitcoin wallets used uncompressed public keys - 65 bytes long, starting with 0x04, followed by 32 bytes of x and 32 bytes of y coordinates.
But that wasted space. In 2012, Bitcoin adopted compressed keys through BIP12. A compressed key is only 33 bytes. It starts with 0x02 (if y is even) or 0x03 (if y is odd), then just the x coordinate. The y coordinate can be mathematically recovered from the curve equation.
Today, nearly all wallets use compressed keys. If you’re using an old wallet or importing a private key from 2009, you might see uncompressed keys. But they’re rare now. Mixing them can cause problems - like sending funds to the wrong address if your wallet doesn’t handle format correctly.
Why Schnorr Signatures Changed Everything
For years, Bitcoin’s ECDSA had a flaw: malleability. A third party could slightly alter a transaction’s signature without invalidating it. This broke some advanced features like the Lightning Network.
In November 2021, the Taproot upgrade activated Schnorr signatures (BIP340). Unlike ECDSA, Schnorr signatures are linear. That means multiple signatures can be combined into one. A 2-of-3 multisig transaction that used to take 500+ bytes now fits in under 400.
This isn’t just about saving space. It improves privacy. All transactions start to look the same - whether it’s a simple send or a complex smart contract. It also makes signature verification faster and more predictable. And unlike ECDSA, Schnorr has a formal mathematical proof of security under standard assumptions.
Taproot didn’t break anything. It upgraded Bitcoin quietly - a soft fork. That’s the beauty of Bitcoin’s design: security improvements can be added without forcing everyone to upgrade at once.
What Can Go Wrong? User Mistakes and Risks
The cryptography itself is solid. But humans mess it up.
Common mistakes:
- Writing down a private key but not knowing if it’s compressed or uncompressed.
- Using the same private key on multiple wallets or networks (like Bitcoin and Bitcoin Cash), leading to theft.
- Confusing a wallet backup phrase (12-24 words) with a private key. The phrase generates keys - it’s not the key itself.
- Not verifying the Bitcoin address before sending. A single typo can send funds to a stranger.
On Reddit and Bitcoin forums, hundreds of stories exist of people losing thousands because they didn’t understand key formats or didn’t test their backups. One user lost 0.5 BTC because they copied their private key from an old wallet that used uncompressed format, but their new wallet assumed compressed. The keys didn’t match. The funds are gone forever.
The lesson? Test your recovery. Send a small amount to your wallet, then restore it from your backup. Do it before you hold real value.
Quantum Computing: A Future Threat?
Yes, quantum computers could break ECDSA. Shor’s algorithm could derive a private key from a public key in hours, not millennia. But here’s the catch: you have to see the public key to attack it.
In Bitcoin, public keys are only revealed when you spend. Before that, only the address (the hash) is on the blockchain. Hashes are safe from Shor’s algorithm. So if you never spend from an address, your funds are still protected.
But if you reuse addresses - and many people do - you’re exposing your public key. That’s why best practice is to use a new address for every transaction.
Even if quantum computers arrive, Bitcoin can upgrade. NIST is already working on post-quantum signature schemes. Bitcoin’s soft fork mechanism means it can adopt new cryptography without breaking the network. The system is designed to evolve.
Why This Matters Beyond Bitcoin
Bitcoin’s use of public key cryptography proved it could work at scale - without central control. Today, over 90% of top cryptocurrencies use similar elliptic curve systems. Ethereum, Litecoin, Dogecoin - they all follow the same model.
Regulators now treat private keys as legal assets. The U.S. SEC says losing a private key is a material event for institutional investors. The EU’s MiCA law requires hardware security modules for custodians - meaning private keys must be stored in certified, tamper-proof devices.
Bitcoin didn’t invent public key cryptography. But it showed how to use it to build a trustless financial system. That’s why it’s not just a currency. It’s a new kind of infrastructure - built on math, not middlemen.
Final Thoughts
Public key cryptography is the invisible engine of Bitcoin. It’s why you can send money to someone across the world without asking permission. It’s why no one can steal your coins unless they get your private key. And it’s why, after 14 years and over 750 million transactions, no one has ever broken the math.
You don’t need to understand the math to use Bitcoin. But if you want to truly own it - not just hold it in an app - you need to understand the keys. Treat them like your life’s most important secret. Because in Bitcoin, they are.
Hannah Kleyn
15 11 25 / 06:14 AMSo the private key is like your soul and the public key is your shadow? You can see the shadow but you can't touch the soul. And if someone steals your soul... well you're just a ghost with a bank account now. I love how math became the new religion and we're all just praying to elliptic curves.
Also why does every Bitcoin post sound like a TED Talk written by a cryptographer who just got off a 12-hour caffeine bender?
gary buena
16 11 25 / 16:41 PMtypo in the post? 'secp256k1' looks like a sneeze on a keyboard but somehow it's the backbone of global finance. wild.
also why do we still call it 'public key' when it's actually a hash of a hash? like calling your house 'the thing with the door' instead of 'home'.
Vanshika Bahiya
17 11 25 / 18:47 PMFor anyone new to this: your private key is NOT your seed phrase. Your seed phrase GENERATES your private key. Think of it like your birth certificate vs your actual DNA. Mess up the certificate and you can get a new one. Mess up the DNA? You're stuck.
Test your backup with 0.001 BTC before you deposit your rent money. I've seen people lose 50k because they trusted their memory. Don't be that person.
And yes compressed keys are the norm now. If your wallet says 'uncompressed' it's probably from 2011 and you're one typo away from losing everything.
Albert Melkonian
18 11 25 / 06:44 AMIt is a remarkable testament to the elegance of mathematical abstraction that a system founded on number theory can achieve global scalability without centralized governance. The fact that asymmetric cryptography enables verifiable ownership without identity disclosure represents a paradigm shift in trust architecture.
One must not underestimate the significance of the secp256k1 curve’s computational efficiency in enabling peer-to-peer consensus at scale. The reduction in signature size from over 300 bytes to 72 bytes is not merely an optimization-it is a foundational enabler of decentralization.
Kelly McSwiggan
19 11 25 / 02:57 AMSo we're trusting the security of trillions of dollars to a curve equation that was invented in 1985 and has never been formally proven secure?
Also 'trillions of years to crack' is just math theater. We're not even close to quantum-ready and already half the wallets on this planet are stored on phones with malware.
Also who wrote this? A grad student who thinks 'elliptic' is a yoga pose?
Byron Kelleher
20 11 25 / 21:01 PMJust want to say this is one of the clearest explanations I've ever read. No fluff, no hype, just math that works.
And yeah, the Schnorr upgrade was quiet but massive. Like upgrading the engine of a car without changing the body. People didn't even notice... until their Lightning payments started working better.
Bitcoin's real magic isn't the tech-it's that it lets you be your own bank without being a crypto nerd.
Cherbey Gift
21 11 25 / 13:55 PMPublic keys? Private keys? Sounds like emotional baggage with encryption.
Man, we're all just digital ghosts dancing on a blockchain graveyard, hoping the math doesn't get bored and delete us.
And don't even get me started on 'compressed keys'-like your soul got a haircut and now it's awkward at parties.
Also why does Bitcoin feel like a cult where the priest is a math equation and the sermon is written in hexadecimal?
Anthony Forsythe
22 11 25 / 01:22 AMImagine a world where your identity isn't tied to a social security number or a credit card, but to a 256-bit number you keep locked in a vault made of silence.
That's what Bitcoin gives us-not just money, but autonomy. A digital soul that no government, no bank, no algorithm can take away unless you hand it over.
And yet, we're still the same humans who forget passwords, write keys on napkins, and send funds to the wrong address because we were distracted by a cat video.
The math is flawless. The humans? We're the bug in the system. The glitch in the divine algorithm.
And somehow... that's the most beautiful part.
Kandice Dondona
22 11 25 / 02:51 AMYESSSS this is why I love Bitcoin 😍
Math > banks 🤖❤️
And Schnorr signatures?? SOOOOO elegant!! Like a digital ballet 💃
Also please everyone test your backups!! I cried when my friend lost 3 BTC because he thought his 12 words were his key 😭
Use a metal backup. Don't be lazy. Your future self will hug you 💪✨
Becky Shea Cafouros
22 11 25 / 22:36 PMInteresting. The technical depth is adequate. However, the tone is overly celebratory. One might argue that reliance on elliptic curve cryptography introduces a single point of failure in the event of algorithmic compromise. The article does not sufficiently address regulatory risks associated with private key ownership as asset class.
Also, 'trustless' is a misnomer. It's merely mistrust of institutions, not absence of trust.
Drew Monrad
24 11 25 / 01:57 AMOh wow. So we're all just trusting that some guy named 'secp256k1' didn't just make up the math? What if it's a backdoor planted by the NSA? What if the curve was designed to fail in 2030?
And don't tell me 'it's been tested for 14 years'-the same thing was said about MD5. And look where that got us.
Also, compressed keys? That's just crypto-hipster nonsense. Real men use uncompressed keys. And I'll die on this hill.
Cody Leach
25 11 25 / 11:23 AMBiggest takeaway: your private key is your responsibility. No one else can fix it for you.
And if you're using a custodial wallet and calling it 'Bitcoin', you're just renting money. The real thing lives on your own device.
Also, Schnorr is a quiet hero. Nobody talks about it but it made multisig actually usable. Respect.
sandeep honey
26 11 25 / 10:58 AMEveryone here talks like they understand this but I bet half of you don't even know what hashing means. Let me explain: SHA-256 is like a blender. You put in your public key, it spins, out comes a weird string. You can't un-blend it. That's why your address is safe.
And yes, compressed keys are better. Stop using old wallets. Your coins are not safe if you're still on uncompressed format. I've seen it happen. People lose everything because they're too lazy to update.
Mandy Hunt
28 11 25 / 05:48 AMQuantum computers will break Bitcoin and then the government will come and take your keys anyway so why even bother
Also I think the whole thing is a CIA project to control the world through math
They use elliptic curves because they can hide backdoors in the math no one understands
And why does every wallet look the same? Coincidence? I think not
My neighbor's cat has more privacy than my Bitcoin wallet
They're watching us through the blockchain
Don't trust the math
Trust nothing
anthony silva
29 11 25 / 02:52 AMWow. So we're trusting the entire global economy to a curve that looks like a doodle on a napkin.
And the fact that you need to be a crypto wizard just to not lose your money? That's not innovation. That's a bug.
Also 'test your backup' - yeah right. Who's gonna do that? I'm not spending my weekend playing crypto detective.
David Cameron
30 11 25 / 03:06 AMThe math doesn't care if you believe in it.
It just works.
And that's the quiet revolution.
Not the price.
Not the hype.
Just the fact that a number, hidden in silence, can own value without permission.
That's the real miracle.
Everything else is noise.
Sara Lindsey
30 11 25 / 08:43 AMOkay but real talk-Schnorr signatures are the unsung hero of Bitcoin. No one talks about them but they made multisig actually usable and private. Like, finally we can have fancy smart contracts without everyone knowing it's a fancy smart contract.
Also if you're still using uncompressed keys in 2025 you're basically driving a horse and cart to a Tesla factory.
Update your wallet. Please. For the love of math.
alex piner
1 12 25 / 03:46 AMJust learned all this from this post and honestly I feel smarter now.
Also I used to think my seed phrase WAS my private key. So I wrote it on a sticky note. Oops.
Now I use a metal plate and hide it in a book. Still scared I'll forget where though 😅
Thanks for the clear breakdown. Bitcoin isn't magic. It's just really good math.
Gavin Jones
1 12 25 / 09:51 AMIt is of considerable significance that Bitcoin's architectural design leverages cryptographic primitives in a manner that is both scalable and permissionless. The adoption of compressed public keys under BIP12 represents a pragmatic evolution in blockchain efficiency, reducing on-chain bloat without compromising security.
Furthermore, the transition to Schnorr signatures via Taproot exemplifies the protocol's capacity for non-disruptive innovation-a hallmark of mature decentralized systems.
One must, however, remain cognizant that technological robustness does not absolve human fallibility. The greatest vulnerability remains the user who fails to secure their private key with due diligence.
ratheesh chandran
2 12 25 / 12:28 PMso if i lose my private key... is that like losing my soul? or just my car keys? i mean if my soul is gone... do i still exist? or am i just a ghost with a bank account? also i think the math is a lie. i think the blockchain is just a big computer game where the devs are the gods and we're the npcs. i wrote my key on a napkin and lost it. now i cry every night. also i think bitcoin is a cult. i love it. i hate it. i don't know. help.
ps: i think the curve is called secp256k1 because someone sneezed while typing it. and now we're all stuck with it.