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Secure protocols with the dynamic programming solution concept?

cd flag

Suppose that we have the usual problem of secure communication, where each of the $I$ agents have a private signal $s_1,s_2,\dots,I$ and they wish to compute any function $f(s_1,s_1,...,s_I)=(x_1,x_2,...,x_I)$ in such a way that no party learns more than their input $s_i$ and output $x_i$.

Although I have seen many cryptographic protocols designed to be secure and in order to solve the problem they use linear programming, I haven't seen any paper using dynamic programming and the Hamilton - Jacobi - Bellman equation. Why is this so? Isn't this possible to designed? Has anybody any paper in mind that uses dynamic programming?

fgrieu avatar
ng flag
I don't think it's proper to say the article linked to _uses_ linear programming. It solves a [linear programming](https://en.wikipedia.org/wiki/Linear_programming) problem with privacy constraints. Also, opposing linear programming to dynamic programming is odd: _programming_ has different meanings in the two. In linear programming, it's in the sense of deciding things for the future, in a sense that predates computers and does not imply them. In the second, it's about organizing instructions for a computer.
kelalaka avatar
in flag
[Cross-posted with Math.SE](https://math.stackexchange.com/q/4311424/338051). Maintain only one copy; see [Is cross-posting a question on multiple Stack Exchange sites permitted if the question is on-topic for each site?](https://meta.stackexchange.com/questions/64068/is-cross-posting-a-question-on-multiple-stack-exchange-sites-permitted-if-the-qu)
Nav89 avatar
cd flag
@fgrieu what do you mean organizing instructions for a computer?
Nav89 avatar
cd flag
And let me re-define my question then...could I consider a problem with dynamic programming where a protocol of communication is secure?
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