# Gavin Andresen
# 2013-02-08 03:38:03
# https://bitcointalk.org/index.php?topic=141879.msg1511465#msg1511465

@s{quotedtext}
@s{quotedtext}
 @p{brk}
The magic of public key crypto is that you can give somebody your public key, some data, and a signature, and they can be certain that: @p{par}

a) that particular signature could only have been created by somebody that has the private key that corresponds to the public key @p{brk}
b) the data hasn't been changed in any way @p{par}

They don't need to know the private key@p{--} you keep it secret. @p{par}

The "hash over..." bit is the way digital signatures work@p{--} you sign a hash of the data, and not the data itself, because the hash is much smaller. @p{par}

The "...simplified version of the transaction" bit is complicated. The data signed is the transaction minus all it's scriptSig signatures, plus (almost always) the previous transaction's scriptPubKey. See the OP_CHECKSIG page on the wiki for all the gory details. @p{brk}