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There is a standard mechanism for doing that called deterministic
signatures and is described in RFC 6979. It uses the private key and
the HMAC construction to generate a ECDSA k value.

On 01/03/2014 10:16 AM, Tier Nolan wrote:
> The random number that the buyer uses could be generated from a
> root key too.
> 
> This would allow them to regenerate all random numbers that they
> used and recreate their receipts.  The master root would have to be
> stored on your computer though.
> 
> The payment protocol is supposed to do something like this already
> though.
> 
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