In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.
Transactions
We need a way for the payee to know that the previous owners did not sign any earlier transactions.
In the mint based model, the mint was aware of all transactions and decided which arrived first.
To accomplish this without a trusted party, transactions must be publicly announced [1], and we need a system for participants to agree on a single history of the order in which they were received.
We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.
我们定义，一枚电子货币（an electronic coin）是这样的一串数字签名：每一位所有者通过对前一次交易和下一位拥有者的公钥(Public key) 签署一个随机散列的数字签名，并将这个签名附加在这枚电子货币的末尾，电子货币就发送给了下一位所有者。而收款人通过对签名进行检验，就能够验证该链条的所有者。
Timestamp Server
A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post.The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.
时间戳服务器通过对以区块(block)形式存在的一组数据实施随机散列而加上时间戳，并将该随机散列进行广播，就像在新闻或世界性新闻组网络（Usenet）的发帖一样。能够证实特定数据必然于某特定时间是的确存在的，因为只有在该时刻存在了才能获取相应的随机散列值。每个时间戳应当将前一个时间戳纳入其随机散列值中，每一个随后的时间戳都对之前的一个时间戳进行增强(reinforcing)，这样就形成了一个链条（Chain）。
https://bitcoin.org/bitcoin.pdf
http://www.8btc.com/wiki/bitcoin-a-peer-to-peer-electronic-cash-system