I think it deserves to be mentioned that you can do conditional
statements on secret values in some cases. A simple case is easy to
implement with the other primitives, but then of course you can be
annoying and start nesting them.
Citat af Sigurd Torkel Meldgaard <s...@cs.au.dk>:
Other nice 2. order operations are bitsplitting (and also
recombination of the bits) and multiplicative inverse (works only if
you can guarantee a non-zero element)
And when you have the bits you would also like logic negation, xor,
and and or.
- Sigurd
On Tue, Aug 25, 2009 at 9:22 AM, Tord Ingolf
Reistad<to...@stud.ntnu.no> wrote:
If you boil down VIFF, or any MPC program you can boil it down to 5
primitives.
These primitives are
x + y = z Addition
x * y = z Multiplication
-x = z Negation
z = Share(x) Secret sharing
z = Reveal(x) Revealing of a secret sharing
My question is now: What are the second order primitives?
What are the basic features that, make a programmers life easy but not
essential. I would propose the following 5:
z = f(x,y) Function calls
for(0 to n) A for call with a fixed number of iterations.
z = Rand(x) Generating random values in Zp
x = y Equation
x < y Comparison
while( x ) A while loop on x, where x is a revealed value
The first 2 primitives are easy since they are already implemented using the
underlying programming language.
Should creating random values be on this list? Or should it maybe be among
the first order primitives, a basic building block of MPC.
Equation and comparison are obvious second order primitives and has been my
research topic for many years.
The last on the list is the while loop, I have included it because I have
seen many times that you want to compute some function, open a variable,
check some information and then redo the function if the revealed value was
false. This can be found when creating random values less than some
threshold, creating RSA primes, and many other algorithms. Also it is not
trivial to program if you want it to be efficient.
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