# 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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### 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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### 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 ...
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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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### Gennaro multi trapdoor commitment scheme

In the Scheme Based on the SDH Assumption (page 11 of the paper https://link.springer.com/content/pdf/10.1007%2F978-3-540-28628-8_14.pdf), how does the commitment get revealed with the master trapdoor ...
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### What information does $g^x$ reveal about $x$?

Let $p$ be a large prime number. Let $G$ be a subgroup of $\mathbb{Z}_p^*$ with order $q$ - again a large prime. Let $g$ be a generator of $G$. Consider the following standard protocol for ...
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### Pedersen commitments in bulletproofs

In Bulletproofs range proof, Pedersen commitments look like $C=aG+bH$ If I need to proof several values' range proof and keep G as constant, do I need to change H everytime? I have found it doesn't ...
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### Zero Knowledge for Low Entropy Witness

For any PPT prover ($p$) and verifier ($v$), imagine I have a low entropy witness, say smaller than $2^8$. Now, let us say I have a dlog statement in the form of $y = g^w$. Theory says I could use a ...
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### Disjunctive zero knowledge proof of equality of committed values

I have read on ZK proof of equality of committed values, that is for $g^xh^y$ and $g^{x'}h^{y'}$, prove in ZK that $x = x'$ (can also be generalized if generators are different using sigma-protocols). ...
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### Can 2 bit commitment protocols be secure when sent together with the same bit

Suppose I have 2 bit commitment schemes, C1 and C2 which are computationally hiding.Suppose I commit the same bit using both and send them to an adversary who knows that the same bit was committed. Is ...
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### trapdoor commitment from lattice-based assumptions?

I'm wondering that is there any equivocal commitment scheme (i.e., trapdoor commitment) can be constructed from lattice-based assumptions? I know there are a lot of commitment schemes from lattices as ...
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### Simple reduction of commitments to one way functions

I am looking for an explicit and simple reduction of commitments to one way functions. I don't care about the number of rounds, only simplicity. I am aware of the simple reductions you can find in ...
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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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### Pedersen commitment in elliptic curves

I try to understand Pedersen commitment in elliptic curves over finite fields. I could use some clarification. Let's say we have two generators $G$ and $H$. Is that required that $G$ and $H$ are ...
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### How do I create a cryptographic signature and commitment scheme with accountable evidence?

This is a weird one... I am looking for a method which I don't even know how to call, nor whether it actually exists! Given a pair of asymmetric keys $s_{k}/P_{k}$ and defining $Sig_{k} \dagger B_{i}$...
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### Zero knowledge set membership protocol

I read that paper Efficient Protocols for Set Membership and Range Proofs of Camenisch et. al that describes the zero knowledge range proof. The paper applications looks interesting like if you want ...