Questions tagged [commitments]

A commitment scheme is a protocol where one party commits themselves to a secret value without revealing it. At a later point, the value can be revealed.

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Is the BFV homomorphic encryption scheme a commitment scheme?

The BFV scheme can be described as: Public Key: $(p_0, p_1)$ To encrypt a plaintext $m$, the ciphertext is : $(c_0, c_1) , c_0= up_0+\Delta m + e_0, c_1=up_1 + e_1$
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What's the difference among Vector Commitment, Zero-knowledge Set, Zero-knowledge Accumulator, and Zero-knowledge Elementary Database?

Vector commitment allows one to commit to an ordered sequence of $q$ value ($m_1,\cdots,m_q$) in such a way that one can later open the commitment at specific positions(e.g., prove that $m_i$ is the $...
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Why is the proof on the commitment correct?

In the paper "Efficient Zero-Knowledge Proofs for Commitments from Learning with Errors over Rings", they gave a commitment from Ring-LWE: to commit to a polynomial $m$ in $Rq(Zq[x]/(x^n+1))$...
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29 views

Difference between a Polynomial Opening & a Polynomial Commitment

Going through the literature led me to think I understood the difference between these two things, but thinking about I am not actually certain. Could you help me correct my definitions of these two ...
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Hash as encryption used by Monero

Monero uses a Pedersen commitment $yG + bH$ to obfuscate the value of a transaction, where $b$ is the value and $y$ is the blinding factor. For the receiver to know both variables, it uses a Diffie-...
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41 views

All fully homomorphic encryptions (FHE) are converted into homomorphic commitments?

The GSW one of the FHE scheme is widely used as a homomorphic commitment scheme to build lattice based ABE, homomorphic signatures and NIZK and so on. But I cannot find other FHE schemes to be ...
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Does resuing pederson commitment preserve the hiding property?

Assume you have a pedersen commitment scheme where the commitment is: $$\mathcal C_1 =C(m,r)=g^m\cdot h^r$$ with $g,h$ being public generators in a public group $(G,\cdot)$ in which the discrete ...
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Question about hiding commitment scheme for integers

Given a generic group $\mathbb{G}$ of an unknown order (such as a $3000$-bit RSA group) and a randomly generated element $g \in \mathbb{G}$, is the commitment scheme $\mathrm{Com}(x)= g^x$ not ...
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64 views

Constructing a commitment scheme from two (possibly defective) commitment schemes

If we have two commitment schemes Com1 and Com2, which are possibly defective (in the sense of not satisfying hiding or binding properties), is it possible to construct a commitment scheme which does ...
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Can I prove in zero knowledge that the public key corresponding to a secret that I committed is in the Accumulator?

I have a set of users in my system, each having a private/public keypair of a digital signature scheme. I also have an accumulator in my system, where all the public keys of the users are accumulated. ...
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A card game (for mental poker or any other card game)

I thought of a way to produce trustless card game in a flexible way. One feature that I want is it should be flexible (It should work for any type of card game, though I indeed started it as a ...
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102 views

How can a public-key encryption scheme be used to construct a commitment scheme in the CRS model?

For a PKE scheme $(Gen, Enc, Dec)$, the most 'obvious' idea is to commit to an encryption of a bit and in the reveal phase maybe send $r_g$, $r_e$ where $r_g$ is the randomness of $Gen$ and $r_e$ is ...
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Multiplication of a Pedersen commitment 10 times

Suppose I have a Pedersen Commitment $cm(x,r) = g^xh^r$ where $g,h$ are generators of group $G$ of prime order $p$. Based on $cm$, I want to create a commitment $cm' = (10\cdot x,r')$, without of ...
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Is there a concept of Pedersen commitment “in the base”?

This question Can Elgamal be made additively homomorphic and how could it be used for E-voting? says ElGamal can be made homomorphic over multiplication. So you can have $(g^r, h^r g^m)$ (i.e., ...
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Notation for commitment schemes

I was reading this set of lecture notes on commitment schemes, where they define a commitment scheme $\text{Com}(b, r) = f(r), h(r) \oplus b$ as a secure commitment scheme. In this case, $f : \{0,1\}^...
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Non-interactive zero-knowledge proof system for a language undecidable in polynomial time

I am studying through some material in an online course, and there is an exercise which I could not figure out. The problem is this: Let $L$ be a language that is not decidable in polynomial time (...
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Understanding anonymous credentials. Does someone understand how it works?

After reading a series of papers CL01 CL02 CL04, I feel like I understand the intuition behind the anonymous credential framework but I don't understand some details the mathematics behind it. I ...
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How to change the following commitment scheme to Pedersen commitment?

In my question here Zero knowledge set membership protocol The suggested solution allows a prover to choose a commitment $C$. Then, A trusted third party ($T$) can validate if $C$ is valid or not. ...
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116 views

Constant size commitment to a bivariate polynomial

In this paper by Kate et al, a constant size polynomial commitment scheme is described. The commitment scheme assumes a public reference string: \begin{align*} \Big\{ \{ g^{ \tau^i }, g^{ \alpha \...
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How to prove in zero-knowledge that the attributes of Pointcheval Sanders signature is the opening of a commitment?

In anonymous credentials schemes, it is possible to anonymously prove knowledge of a signature. Proposals for anonymous credentials with attributes also include a method for proving statements about ...
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How to show that Cx is a commitment to a integer of length lm

With reference to Jan Camenisch and Anna Lysyanskaya's paper A Signature Scheme with Efficient Protocols, in proceedings of SCN 2002, I need some help to understand How to verify that $C_x$ is a ...
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regarding usage of hashing

I have a question regarding pitfalls of using only encryption. Suppose Bob and Alice want to flip a coin over a network. Alice proposes the following protocol. Alice randomly selects a value X ∈ {0,1}...
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How to achieve identity authentication without revealing credentials

I am looking at a scenario where I would like to claim to an authority (call it A) that I am indeed me without revealing my identity documents. I am guessing some zero knowledge protocol has to be ...
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Zero Knowledge Set Membership proof

ZK set membership: I am trying to create my own zero knowledge set membership proof for a commitment to an element in the set for small sets. I am a beginner in such works, so can someone help me find ...
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Sigma proofs for Pedersen commitments arithmetic under different bases

I was wondering if it's possible to prove an equality of openings between $3$ Pedersen commitments $P\cdot Q$ and $R$ when $P, Q, R$ have different commitment keys. Suppose that commitment $R$ commits ...
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Subset-sum Problem & Commitment Schemes

In this question I asked about a subset sum hash. Would it be possible to adapt that into a commitment scheme by keeping M private and revealing it at a later time? Would this be secure for some size ...
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Computationally binding commitment

A Computationally Binding commitment scheme is defined as a tuple of protocols $(\mathsf{Keygen}, \mathsf{Com}, \mathsf{Open})$, that along with correctness guarantees that for all PPT algorithms the ...
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41 views

Constant size commitment to a membership of a fixed size of elements

Suppose there is a global set of $n$ elements, out of which I want to commit to $2n/3$ elements, i.e., anyone can take my commitment and test what $2n/3$ of the possible $n$ elements I committed to. ...
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Sigma-Protocol to prove a commitment to a commitment

Let $Com$ be a pedersen commitment function with publicly known $g$, $h$, and $p$ values s.t. $Com(x,r)$ is a commitment on $x$ with random number $r$. Is there a $\Sigma$-protocol to prove $ZKPoK\{ (...
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Can Pedersen commitment be used in pairing groups?

For bilinear groups: $(p,\mathbb{G}_1,\mathbb{G_2},\mathbb{G}_T,e,g_1,h_1,g_2,h_2)$, where $\mathbb{G}_1,\mathbb{G_2},\mathbb{G}_T$ are groups of prime oder $p$. $g_1,h_1$ are generators of $\mathbb{G}...
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Question of proving the opening of Pedersen Commitment

Given an opening $(m, r)$ of a Pedersen commitment $c = g^m h^r$, where $g, h$ are the generators of a group $G$ with prime order $q$ (public), a PPT prover wants to prove to a verifier the opening of ...
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Computational Binding of Pedersen Commitment

Let us assume that Alice and Bob are playing a game. Alice first commits her value chosen from $\{0,1\}$ via Pedersen commitment scheme and sends the commitment to Bob. Then Bob sends his value chosen ...
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Does Schnorr identification protocol using commitment scheme?

In schnorr identification protocol, a prover needs to choose a random,let's say $r$ at the beginning, then commit to this randomness as $g^r\bmod p$. When we say "commit", does it really mean we are ...
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Verify commitment C commits to the same value that E encrypts

Given the following (using additive notation): $G$ - generator of an elliptic curve group of order $q$ $s$ - secret drawn uniformly from the distribution $1..q$ $k$ and $K$ - a private public keypair ...
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Is the random oracle commitment scheme secure against PPT active adversaries?

The probability that a probabilistic polynomial adversary corrupting the sender can finds two pairs $(m,r)$ such that the output of the random oracle $c$ is the same (break the binding property) is ...
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What is a Pedersen commitment?

I couldn't find any answer providing a high-level overview on what Pedersen commitments are or what they are used for.
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Computational binding implies Perfect hiding?

Given a commitment scheme which is computationally binding (based on some conjectured hard problem, say), does it also imply that the scheme is unconditionally hiding? My idea was: Since the scheme ...
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Using Pedersen commitment for a vector

I'm reading Bootle/Groth. I'm trying to understand how they are committing to a vector using Pedersen commitment. Here's my understanding of Pedersen commitment in the context of this paper: We have ...
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Range Proofs based on Polynomial Commitment Scheme (PCS)

I have been trying to implement the PCS-based Range Proofs as described here. My code is in a public repository. I am not able to understand this part: This w_cap is a linear combination of f and ...
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Multilinear trapdoor commitments secure against concurrent man-in-the-middle attacks

I am trying to understand how to apply a multi-trapdoor commitment described by Gennaro and what makes them secure against a concurrent MiM attack. There are two ways to construct a multi-trapdoor ...
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Is it possible I can open pedersen commitments without revealing r?

With setup $p$ and $q$ where $p = 2q + 1$, and $g$ and $h$ is the generator with order $q$. In Pedersen commitment, I commit the value m with $c=g^m h^r \bmod p$, then de-commit by revealing $(m, r)$....
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What does the “x” operator stands for in cryptography?

I am studying commitment scheme and in of the notes from the class this statement comes up. I'd like to know exactly what the X = M x R mean, since I don't seem to understand how the "x" operator ...
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65 views

Is the hash-based commitment IND-CPA?

As we know the well-known hash-based commitment is as follows: Prover: given a message $m$, it: (1) picks a fresh random value $r$ (2) computes $H(r||m)=c$. Verifier: given $c$ and the commitment ...
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Is it correct using Sigma Protocol to do the knowledge proof?

For this background, the prover knows a secret $x$ for $h=gx$. Prove to the verifier that he knows $x$. (I know $h=gx$ is not a NP problem, I just want to practice the Sigma Protocol) Step 1 : $P \...
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Is Commitment Scheme with hash function is a perfectly hiding scheme?

If I use a hash function to construct the commitment scheme, can I say it is perfectly hiding? $m$ is the message $r$ is a random value In commit stage, $$ c = C(m, r)$$ In reveal stage, by ...
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How to securely and noninteractively generate a blinding factor in MimbleWimble Pedersen commitment?

I'm working on a prototype which will use MimbleWimble Confidential Assets transaction protocol using Cosmos as the blockchain layer. In my prototype a user is always sending a whole amount to ...
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209 views

Sigma protocol with Pedersen commitment and Hash function

Suppose I construct a Pedersen commitment as $g^m h^r$. I could pick the randomness in a "pseudo-random" fashion, such that $r = H(m)$. My questions are as follows: Given that $H$ is collision-...
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Statistically Binding Commitments

Is it possible to ever have a commitment scheme that is statistically binding but not perfectly binding? The sender would be computationally unbounded, hence could always computationally trudge ...
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Zero knowledge proof that ElGamal ciphertext encrypts the opening of Pedersen commitment

Given ElGamal ciphertext for a message $m$ with a random $r$ as $(c_1,c_2) \gets (g^r, g^my^r)$ for a public key $y$, and a Pedersen commitment $C \gets g^xh^r$, I have been able to create a proof ...
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How to authenticate indivisual value after applying homomorphic encryption using Paillier homomorphic

Assuming I have three parties in a system: Alice, Bob, and a Server. Alice and Bob needs to aggregate some messages $m1$ for Alice, and $m2$ for Bob. And send the aggregate $m1+m2$ to the Server. I ...