A brain wallet is a standard wallet that generates its address by hashing a passphrase to create a private key and therefore a public key and resultant address.
Seeing as a Bitcoin or a Litecoin address is usually a 256 bit string – the SHA-256 algorithm is usually used – although various levels of complexity can be added to this.
So if I wanted to generate a private address using the passphrase cryptocompareisamazing for litecoin I could go to liteaddress.org and generate the private and public litecoin key pair shown below.
Brain Wallets have a significant disadvantage that means they have a higher probability of being hacked. That is that us humans are pretty predictable in what we use as a passphrase and password, and hacking technology has got a lot better through the use of rainbow tables and dictionary attacks. Also a few large databases of passwords have been leaked meaning so it is quite easy to hash all these passwords and then see if their corresponding address exists as an active address on the blockchain – if so you have the private key and therefore access to the funds.
A simple technique is using a hashing functions number of times over so that the hacker will have to guess both the hashing function and the number of times it was applied to a particular password. This is called key stretching.
Some tests have been done where simple passwords have been used and deposited with funds – they have been quickly stolen – also, reportedly, one Bitcoin user lost 4 BTC from his wallet after using a brain wallet private key generated from an unknown Afrikaans poem – proving that the complexity of some rainbow tables and dictionary attack programs are extremely sophisticated.
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