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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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 ā {0,1}...
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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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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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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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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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71 views
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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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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164 views
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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63 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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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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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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201 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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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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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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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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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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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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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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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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261 views
Simple commitment scheme using secure hash function
Can I create a simple commitment scheme using a secure hash function?
If so, is concatenation with a random secret enough to preserve hiding? (i.e. $C = H( random\_string || message)$)
Thank you
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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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111 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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262 views
What is wrong with encryption-based / hash-based commitment schemes?
In the slides to my information security class it is stated without explanation that a encryption-based commitment scheme defined as follows is broken:
Commit: P outputs c = Enck(m)
Reveal: P sends k ...
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Efficient protocols for set membership proofs with private sets
I found the paper on Efficient Protocols for Set Membership and Range Proofs in which
efficient protocols for the following problem are discussed:
Given a commitment $C_v$ to a value $v$ we want show ...
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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?
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Are Fujisaki commitments binding if the factorization of the group is known?
If I understand correctly, a Fujisaki commitment is as follows: $g^m \cdot h^r $ mod $n$, where $m$ is a message, $r$ is a random number, there exists $a$ such that $h^a = g$, and $n$ is an RSA ...
