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A Brief Introduction to Private Keys
You may think of your public and private key like your house and house key. Your house is a public object with an address that anyone can find. Anyone can see your house (and it's contents if they get close enough), but they cannot enter it or change anything about its contents. Now, if someone has your house key, they could enter it and do as they please with it's contents, so you never want to give someone your house key! Your assets on a blockchain operate much like this. Your public key has an address and a private key to access the contents of that address on the blockchain. In truth your public key can derive many addresses, but we'll keep it simple for now.
Your Lattice1 hardware wallet, and all other crypto wallets for that matter, do not store cryptocurrencies and other digital assets directly, instead it stores your private keys which enable you to use the assets you own on the blockchain. Anyone can send cryptocurrency to any address, but only the owner of the corresponding private keys can ever move assets from that address. If private keys are ever lost, the assets can never be accessed again.
Public-key cryptography makes blockchain technology possible. Cryptocurrency wallets store your public and private key pair; your public key is used to verify your signed transactions and your private key is used to generate signatures and transactions.
Your private keys enable complete access to your holdings - it's of paramount importance that you keep your private keys safe and secure. That's where your Lattice1 and SafeCards come into the picture.
Never share your private keys or seed phrase with anyone. Period.
A user who wishes to send coins initiates a transaction (commonly abbreviated to "tx") which is then broadcast to everyone on the network to be validated and executed.
Users who add a transaction to the blockchain include a signature to the transaction that only they can produce with their unique private key. A transaction signed in this way shows everyone else in the network that the transaction could have only originated from the transactor's address and that they intended to create the transaction, much like how you sign a check or contract.
A digital cryptographic signature is even more secure than an ordinary written signature, because there is no analogue for forging a digital signature. Nobody could forge a transaction from a wallet they do not own, since they cannot create the unique signature.
What's a Seed Phrase?
The problem with seed phrases is that their proper storage creates an additional set of security considerations, because anyone that can access this list of words can access all of your holdings.
Is There A Risk of Two People Generating the Same Private Keys?
The odds of generating an Ethereum private key that corresponds to someone else's is approximately 1 in 2^160. That's approximately 1 in 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976.
There are more public/private key pairs than there are atoms in the observable universe!