-By Milly Bitcoin - November 2, 2013.
Recently the US Federal Bureau of investigations (FBI) seized bitcoins from the alleged Silk Road operator. There is also discussion that the FBI has a wallet file that is encrypted. Around the same time there has been speculation that the US National Security Agency (NSA) worked with the US National Institute of Standards and Technology (NIST) to recommend weak cryptography methods that could be broken. Some recent articles and commenters have confused these concepts.
Breaking Encryption - A Bitcoin wallet is a collection of Bitcoin addresses and their associated private keys. The private key is the “password” that allows the coins to be spent. Anyone who has this private key can spend the funds so for security it is encrypted while it is stored on your hard drive. That way, even if someone gets the wallet file they cannot read the private keys without knowing the password needed to decrypt the wallet file. This password has nothing to do with the public Bitcoin address in the wallet and the FBI needs a copy of the wallet file if they wish to try to break the encryption. Usually a wallet will contain multiple Bitcoin addresses and multiple private keys. The Bitcoin protocol itself does not use encryption, it uses cryptography. Encryption is something used to secure the private keys.
Breaking Cryptography - In order to create a Bitcoin address a private key is generated and then a Bitcoin address is calculated using a 9-step process. There is no known way to go backwards from a public address to the private key other than to try to go through all possible keys and there are just too many. There has been speculation that the NSA has some sort of back door to find the private key from the public Bitcoin address. This is pure speculation at this point and there is no evidence this is the case. If this were true then the private address could be determined from the public Bitcoin address. The wallet file would not be needed and it would not matter if the wallet file was encrypted. All funds could be taken from the information contained in the Bitcoin blockchain ledger.
How to create Bitcoin Address: https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
Click this image for a discussion of brute forcing addresses: