`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

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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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