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Cryptography Stack Exchange

Questions tagged [arithmetic-circuit]

14 questions
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Arithmetic Circuits to R1CS. Do we consider addition gates or not?

Here is Ariel Gabizon's Blog for the process of converting Arithmetic Circuits into R1CS - https://electriccoin.co/blog/snark-explain5/ Here, he writes We assume multiplication gates have exactly two input wires, which we call the left wire and…
user93353
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Why do SNARKs operate on arithmetic circuits?

I'm currently writing my bachelor thesis about zero-knowledge proofs. Right now I'm working on introducing SNARK's and in my approach I'm following this course that's available on youtube. In the course they first define what arithmetic circuits are…
Niko Wolf
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How to perform bitwise XOR by rational function modulo $2^n$?

Does there exist a rational function modulo $2^n$? This is a function of the form $$f(a,b)\pmod{2^n},$$ such that $$\forall\;a,b\in \{0,1,\ldots,2^n-1\},\quad a\oplus b=\frac{g(a,b)}{h(a,b)}\pmod{2^n},$$ where $g$ and $h$ are polynomials. It's…
max_herman
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How to convert exponents and group operations to gates in arithmetic circuit

I am following Vitalik Buterin's article to study zk-SNARKs recently. I can understand the main procedure of zk-SNARKs when given example equation x**3 + x + 5 == 35. However, in cryptography, most equations contain exponents. For example, the…
Z. Chen
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Can a 3-coloring for a graph be represented as a circuit?

I was looking at a layman explanation for zero-knowledge proofs in zk-SNARKs here. The idea there is that if one knows a solution (3) to a question (find a value of x satisfying x^3 + x + 5 = 0), then one can prove this using a circuit to represent…
user1936752
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How to compare two field elements in Arithmetic Circuit?

Given two field elements as input of Arithmetic Circuit (consists of adding gates and multiplicating gates only), how could I output the bigger one? Or, how to place the gates in order to distinguish which one is bigger (using Arithmetic Circuit)?…
Yiyi
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Information conservation with random bitstrings and full addition circuitry

I've been interested in studying information content in the context of algorithms, especially PRNGs. Originally inspired by the entropy extracting properties of the XOR gate, I wanted to simulate arithmetic operators on bitstrings to look at how…
Doddy
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Bootstrapping of BV11 (2-nd Gen FHE): bootstrapping with arithmetic circuit

The bootstrapping technique, using the arithmetic circuit of the decryption algorithm presented in BV11, is questionable. The authors say, “Checking if the result is in Z_p can be done with depth O(log(k) + log log (p)) arithmetic circuit." However,…
Gulan Tayghan
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Matrix multiplication circuit

I am trying to understand which operations are computable by an $\texttt{NC}^1$ circuit. However, I am struggling to understand whether there is such a circuit for multiplying a matrix with a vector or if the circuit will necessarily be in…
Mjf T
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How to compute the absolute value of a float number using only addition and multiplication (or using an and-xor circuit)?

Hi I am trying to calculate the abs or a float number $x$, however, I want to apply this operation when $x$ is under fully homomorphic encryption (typically CKKS Scheme). So I come up with the idea that if we can use only addition and multiplication…
itabline
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Are polynomial hash functions over prime order fields ZK-friendly?

"Traditional" hash functions such as SHA2/SHA3 are not considered ZK-friendly because their translation in the native prime fields of the ZK-proof system leads to a large number of multiplications, resulting in highly inefficient prover…
Raoul722
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Conditional Boolean circuits

I have two questions I couldn't find straightforward answers to after many searches. (1) We can perform 2-party MPC over arbitrary functions using Garbled Circuit. To do that, we first need to convert a function to a boolean circuit and then garble…
taserghar
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How are arbitrary boolean gates constructed in homomorphic encryption using only addition and multplication?

I've recently become interested in homomorphic encryption, specifically how boolean gates are constructed to do arbitrary circuit arithmatic on the encrypted data without decrypting it. I have heard that all you need are arbitrary addition and…
August H
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reason of using $y=0$ result in ABE for arithmetic circuits

In Boneh et. al.'s ABE scheme (https://eprint.iacr.org/2013/669.pdf, https://link.springer.com/content/pdf/10.1007/978-3-642-55220-5_30.pdf), the result value for the arithmetic function is selected and fixed to zero. In other words, if the…
Mahdi Mahdavi
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