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Questions tagged [circuit]

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Efficient fields over arithmetic circuits

What sort of fields is efficient over an arithmetic circuit? Efficient meaning that given a field $\mathbb{F}_p$, reduction (modulo) does not require many multiplications and preferably inversion was ...
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1answer
37 views

How would I convert an arithmetic circuit into a system of bilinear equations?

Given an arithmetic circuit, are there any examples of turning it into a system of bilinear equations, with the end goal of turning it into a matrix?
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1answer
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What is a rank-1 constraint system?

Why not rank-2 constraint system or rank-3 constraint system? How do rank-1 constraint systems link to circuits?
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65 views

In constraint systems for ZK proofs, why are multiplications counted but are additions not?

For example, If I wanted to prove that: $$x^2 + x^3 = 45$$ This cost of this would be calculated by counting the number of multiplications that need to be done, and not the addition of $x$ squared ...
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1answer
247 views

Representing a function as FHE circuit

I am actually trying to study homomorphic encryption (on lattices) but I'm facing a problem. Every paper that I have read so far talk about writing the function to evaluate on ciphertexts as a circuit,...
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3answers
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How to determine the layers of a circuit?

In many cryptographic applications like Multiparty Computation (MPC) or Fully Homomorphic Encryption (FHE), you consider a function $f$ described by a circuit over some algebraic structure, typically ...
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zkSNARK and definition of Quadratic Span Program

In zkSNARKs in a Nutshell, page 12, what exactly are $I_{free}$ and $V_{free}$? Why do we have $V_{free}$ but not $W_{free}$?
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Can any one explain why circuit privacy is needed on homomorphic encryption?

I know some works have been done in the context of cirrcuit privacy on homomorphic encryption, where from an output ciphertext it does not allow someone to distinguish what function is computed. I ...