Shamir Secret Sharing Implementation Query
 From: Jason <tntcoder4@xxxxxxxxxxx>
 Date: Wed, 16 Jun 2010 13:10:32 0700 (PDT)
Hi,
Say my secret is an nbit number, under Shamir's scheme I need a
prime, the first prime larger than the secret, then I work in GF(p).
(Think that's correct)
Now in terms of a practical implementation, lets say im secret sharing
arbitrarily long data in 64bit blocks. I have to assume my secret
could be all 64 bits, which means I will need a 65bit prime.
What im trying to understand is what is the most efficient way to
share arbitrarily long data in small broken down blocks. i.e if I use
64bit blocks then how big should my prime be to avoid bitwasting.
Will 64bit blocks with a 65bit prime work ok? Or should I use 63bit
blocks with a 64bit prime. Because im working with 8bit ASCII
secrets, it's obviously easier to work with 64bit data blocks.
Please could someone give me some pointers on how to do this
correctly, ideally I want to hardcode a prime for my application
rather than searching for one bigger than the secret on each block.
Additionally how complex is it to compute shares in GF(p) from a
programming perspective? Will I have to use lookup tables? Any help
here is much appreciated, I'm not a mathematician and don't have
access to any fieldcalculation libraries for this project, so have to
do the calculations manually from the ground up.
Thanks for any help.
.
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