Just given all the news about this topic lately (Android security flaw), I'm curious about WHERE and WHY the random number is used during the signing of a transaction.
I always thought a transaction was signed by just hashing the prev_out** and then encrypting that hash with the private key, so when it is published along side the public key it can be verified by other nodes.
**(maybe I need more clarity here too: is the ENTIRE previous transaction hashed at this point, or just one the input being used in the prev_out?)