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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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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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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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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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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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-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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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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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 ...
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Commitment based on authencticated encryption

Let $(E,D)$ be the encryption/decryption of an authenticated encryption scheme. Consider the following commitment scheme. Generate a random key $k$. Commit to $m$ by sending $c=E_k(m)$. Reveal $m$ by ...
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Orthogonal generators of a group in Lelantus protocol

In the Lelantus Paper, the authors mentionned this: In our case, the commitment key ck specifies a prime-order group G and three orthogonal group generators $g, h_1$ and $h_2$. G is mentioned in ...
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Prove knowledge of signature on committed value

Assume that a prover $P$, has previously obtained a signature $\sigma$ on a value $x$ from a verifier $V$. At a later stage, $P$ produces a Pedersen commitment $C$, to this value: $C = g^x h^r$ I'm ...
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Verifiable Encryption of a Pedersen Commitment

Can the Verifiable Encryption of a Discrete Logarithm scheme of the paper https://www.shoup.net/papers/verenc.pdf (page 19) be used to verify that a ciphertext encrypts the same value committed in a ...
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Which groups to use for Pedersen Commitments

I have been reading about Pedersen Commitments, and have come across some contradictory examples, which is confusing. Just focusing on simple commitment of scalars (not EC points or vectors), then I ...
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Zero-knowledge voting with hidden weights

Assume a voting with delegates, where each delegate's vote $v_i \in \{-1,1\}$ has a certain weight $w_i$ depending on the number of people who elected the delegate. Is there a way to calculate the ...
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Commitment to a degree of a polynomial

Is there a way to commit to a degree of a polynomial without committing to every single one of its coefficients? The problem I am trying to solve is to prove that two polynomials are the same in a ...
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Zero knowledge proof for opening of Pedersen commit and discrete logarithm

I am looking for a proof of knowledge as such: $PK\{ (x,r) : C = g^xh^r \land V = g^x\}$ Where $C, V, g$ and $h$ are public information and $x$ and $r$ is known only to the prover. I.e. I have a ...
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What is the reason of using Pedersen Commitment scheme over HMAC?

I want to implement non-interactive Bit Commitment scheme for messages of arbitrary length. And I am curious, what is the reason of using Pedersen Commitment scheme over Salted Hash (in other words ...
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Commitment to a polynomial

$A(x) \bmod B(x) = C(x)$ and $A(x) \bmod D(x) = E(x)$: A dealer knows $A(x)$ polynomial, which is a secret. He distributes $C(x)$ and $E(x)$ privately to $X$ and $Y$, respectively. $B(x)$ and $D(x)$ ...
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Overview of relations between cryptographic primitives?

Is there a web page that gives a graphical (or, alternatively, a textual) overview of known implications and separations between cryptographic primitives? More specifically, I am looking for ...
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Selectively opening only a few commitments

I have k messages $m_1,m_2...m_k$ and I want to commit to all of them but open only a few of them -- as asked by Bob. Each message is of $n$ bits. Show how one can commit to all the $k$ messages and ...
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How to sign comitted group elements?

I'm actually searching some particular primitive compatible with Groth Sahai commitment. I would like to know a signature scheme (on group elements), such that there exists an algorithm $\mathtt{...
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What does “constant rate” mean in universal composable commitment scheme?

I'm wondering what does the "constant rate" mean in universal composable commitment scheme? I have known the rate of a commitment scheme is message length divided by the communication complexity of ...
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How to determine r' in pederson commitment?

Can someone help me with that question? Assuming that someone knows $log_g(h)$ so that he can calculate any message $m'$ for commitment $c$, how to determine $r'$ in?