# 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 prove secret value in Pedersen commitment is equal to secret value in Fujisaki commitment?

We have Pedersen commitment C to the secret value x, and Fujisake commitment C' to the secret value x. How can we make a zero-knowledge proof of equality for x value in the commitments?
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### Coin flipping with limited communication between participants

Alice and Bob want to play a coin flipping game. Alice wins if the coin flips head. They choose to trust a independent third party that generates a random beacon (such as NIST). There is no ...
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### How to prove knowledge of discrete logarithm in a product?

Definitions Suppose I have two large safe primes $p$ and $q$, and a composite number $N=pq$. I have $G$, a large cyclic subgroup of $\mathbb{Z}^{*}_{N}$; $g$ and $h$ are generators of $G$. I commit ...
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### How to prove that a commitment hides the decryption of an ElGamal ciphertext?

I've decided to remove a previous unanswered question of mine and break it down into smaller pieces so it's not such a loaded question. For this question I need to prove that I've committed to a ...
510 views

### Number generation for Fujisaki-Okamoto commitment scheme parameters

I need to implement the Fujisaki-Okamoto commitment scheme for a project such that I can demonstrate performance of various zero-knowledge proofs in relation to one another, for example Boudot's "...
255 views

### Is authenticated encryption basically a lockable box?

I recently used a custom construction as a commitment scheme, which was taken from the standard picture you give people while explaining commitment schemes. Basically commitment schemes can be ...
67 views

### Commitment scheme to share money

I have such problem: party $X$ has an amount of money $M$, which it needs to share with $n$ other parties. Every week the amount of money is different. Let say not, that I am a party A, which is one ...
1k views

### Mutual verification of shared secret

Is it possible to develop a scheme where two parties, unsure if they have the same secret, can verify that the other does or does not share the same secret, without one party being able to cheat and ...
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### Generating shared secret random permutation

There are three blind card game players. Each player does not trust any other, even prejudicing other two players may not be blind, or there may be others in the room, peeking at their cards. In ...
1k views

### Rock-paper-scissors over network, how to protect from cheating server?

I'm trying to design cryptographic protocol to play Rock-Paper-Scissors with two parties, neither trusting each other, nor trusting server they use for communication, so game is 'provably fair'. So ...
200 views

### Proving a decision was randomly made [duplicate]

Alice and Bob want to agree on a bit $0$ or $1$. Both know it would be fair to pick that at random, but there's no way they could meet to throw a dice and no third party they could trust. Are there ...
1k views

### How to prove that a ciphertext is encrypting multiplication of two values?

Zero-knowledge proofs with soundness, completness and zero-knowledge enable a prover to convince a verifier that a witness validates successfully a predicate without giving any information about the ...
1k views

### What are the pros/cons of using symmetric crypto vs. hash in a commitment scheme?

In a commitment scheme, are there any differences on using a symmetric cipher versus using a hash? If at the "opening", I have to reveal $r$ (a random number concatenated with the messaged at the ...
5k views

### Difference between Pedersen commitment and commitment based on ElGamal

Does any of you know what is the difference between the Pedersen commitment and the commitment that uses the ElGamal encryption scheme? For the sake of completeness, I recall what both of them look ...
788 views

### Bit commitment with 1-out-of-2 oblivious transfer

I know a protocol for bit commitment using regular OT (Bob has 1/2 chance of learning the bit Alice transferred to him) which goes like this: COMMITMENT PHASE Alice chooses a bit $b$ For $i=0$...
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### Decrypting without using the private key

Let $g$ be a generator of a multiplicative group $G$ of order $q$, $x$ be a private key, and $h=g^x$ be a public key of an exponential ElGamal cryptosystem. Given a ciphertext $c$ produced as the ...
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### Why is the Pedersen commitment computationally binding?

This is how the Pedersen commitment seems to work: Let $p$ and $q$ be large primes such that $q \mid (p-1)$, let $g$ be a generator of the order-$q$ subgroup of $Z_p^{\star}$. Let $a$ be a random ...
3k views

### Have I understood pedersen commitment correctly?

I want to do a one-sided integer commitment scheme. I.e. the whole process must be non-interactive where I at one point first publicly reveal some data and then at a later time reveal the committed ...
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### Proving item association without revealing one of the associated items

I'm a total noob when it comes to cryptography but I believe this falls under the "zero knowledge" category. I have two associated pieces of information: tag — known by both parties. Unique per ...
879 views

### What type of hash functions provides non-malleability of hash digests?

I want to use a hash function for commitments. I don't want an attacker to construct a commitment related to a previously published (but still unopened) commitment. A simple deterministic commitment ...