Cryptography

Questions tagged [commitments]

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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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Are there batched vector/polynomial commitment proofs with sublinear proof size for Verkle Trees?

High level goal: a Verkle tree (Merkle tree using algebraic vector commitments at each level rather than hashes) with depth d where I can prove the existence of <...
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Why the Kate Commitment and the Algebraic Group Model is used a lot in zk-SNARKs proving system since 2019？

I am engaged in the research of zk-SNARKs. After I read some papers about zk-SNARKs, I realize the Kate Commitment and the Algebraic Group Model is used a lot since 2019. They are used in Sonic, Plonk,...
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How such so called Merkle pre image are computed?

I’ve just encountered the following source code which is used as an authentication mechanism where the bytes32 leaf is the hashed action to authenticate : ...
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What does it mean for g and h to be indendent in pedersen commitments?

I'm looking at a research paper about the insecurity of a specific (wrong) usage of Pedersen commitments. First, I'll go through the steps of Pedersen commitments, so that it can be shown if I have a ...
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MuSig: could the rogue key attack be mitigated by using commitments instead of key transformations?

Background MuSig is an extension of/derivation from Schnorr signatures using cyclic groups on elliptic curves. In the original paper, the authors point out that naive multi-Schnorr is vulnerable to a ...
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Efficient proof for Cartesian product

I am trying to find some efficient zero-knowledge arguments that could prove the vector ${\bf v}$ is the Cartesian product of two vectors ${\bf x}$ and ${\bf y}$. I know there are efficient inner ...
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Pedersen Commitment and Computational Zero Knowledge

I am curious at how "good" is computational zero knowledge? Consider Pedersen Commitment $z = g^x h^y$. There exists perfect ZK protocol (based on Schnorr's) to prove that one knows the ...
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Difference between a key value commitment and authenticated dictionary

I was wondering about the difference between an authenticated dictionary and a key value commitment scheme like KVac. Are they the same thing or they have different model or definitions? Thanks
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Gennaro & Goldfeder Key Generation Protocol

As I am going through the “Fast Multiparty Threshold ECDSA with Fast Trustless Setup” paper by Gennaro & Goldfeder, 2018, I am stumbled by the key generation protocol (Sect. 4.1, p.10): In Phase ...
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Commitment scheme for a possible unordered growing collection of elements

Merkle trees can be used for vector commitment scheme. In particular given two sequences S, S' with the same elements in the same order the merkle root for S will be the same as the one for S'. What ...
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55 views

Zero-knowledge proof of committed value

I am considering the following questions and would appreciate any help. Problem formulation: Suppose Alice holds a secret value $x$ and there is a public Boolean predicate function $\texttt{Pred}$ ...
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Coin tosses in the context of commitment schemes

I was reading the “Fast Multiparty Threshold ECDSA with Fast Trustless Setup” paper by Gennaro & Goldfeder, 2018 and I encountered this portion (Sect. 2.4, p.6): This excerpt leaves me slightly ...
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134 views

How can I prove "single-use authorization" from multiple parties without revealing identity?

I've been trying to create a distributed authorization protocol where identities are not revealed. Let me explain with an example. Let's assume we have 4 actors, Alice, Bob, Charlie, and Dan. Alice is ...
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Why must s be kept secret in pedersen commitments?

I was reading up on Pedersen commitment over at this website: https://asecuritysite.com/encryption/ped, where they calculate $h=g^s \bmod p$, and they say that $s$ must be a secret. I wonder why this ...
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179 views

Finding an elliptic curve of specific order

I wish to use elliptic curves for cryptographic operations like commitments etc. I see that most standard elliptic curves like $\operatorname{secp256k1, sect571r1}$ have a certain specific and fixed ...
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Solution to Discrete Log as a Commitment

Is the solution to a discrete logarithm a reasonable commitment scheme? By my analysis, the following scheme is a reasonable commitment scheme: Let $p$ and $q$ be large primes such that $q∣(p−1)$, let ...
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Does there exist a provably correct and recipient hiding encryption scheme?

I am looking for an encryption scheme $E$ and a commitment scheme $C$ which allow encrypting the message $m$ for the public key $y$ as $e = E_y(m)$, so that the ciphertext $e$ does not reveal any ...
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Proving statistically hiding for a simple commitment scheme in the ROM

It is well known that one can construct a simple commitment scheme in the random oracle model (ROM) by setting $\mathsf{Commit}(m;r) = H(r||m)$, where $m \in \{0,1\}^k$, $r \in \{0,1\}^{2k}$ and $H: \{...
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Dishonest verifier running a concurrent zero-knowledge protocol

Suppose Alice and Bob are engaged in the graph 3-colorability Zero-knowledge protocol in which Alice permutes a coloring $\varphi:V\rightarrow \{1,2,3\}$ for a graph $G(V,E)$, and then sends a ...
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Commitment schemes for arbitrarily large integers

My question is about commitment schemes for arbitrarily large integers. One scheme I know uses groups of unknown order (RSA or class group) and depends on the strong-RSA assumption. You chose a random ...
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Intuition Behind Commitment-Challenge-Response a.k.a. Sigma Protocols

In How To Prove Yourself: Practical Solutions to Identification and Signature Problems, Fiat and Shamir introduce a zero-knowledge identification scheme where The prover sends a commitment to the ...
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Zero-knowledge proof of knowledge of a plaintext in exponential ElGamal

Consider the exponential ElGamal cryptosystem over some group $G$ with generator $g$. Let $m$ be a plaintext, and $(R, C) = (g^r, g^m \cdot y^r)$ an encryption thereof for some public key $y$. Assume ...
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UC-secure commitment in the ROM

Looking at the question Is this a UC-secure commitment scheme in the ROM?, I was wondering, is the commitment scheme proposed in the answer (which uses $H(M||r)$ as commit) secure in the UC-model, ...
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Why are the fully homomorphic encryption algorithms the commitment?

Is there some references about the commitment scheme based on FHE ? Why could the BFV, CKKS, BGV algorithm be convert to commitment? How ?
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How does the rejection sampling lemma work in the proof of HVZK?

In this protocol, Q1: how does the commitment work? What if the prover sends $\textbf{t}$ directly, and then sends $s_m,s_r,s_{\textbf{e}}$? Q2: How does the rejection sampling lemma work? refer to ...
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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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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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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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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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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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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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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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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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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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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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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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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 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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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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