# Questions tagged [commutative-encryption]

A commutative encryption system allows a message encrypted with two different keys to be decrypted using the keys in either order.

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### Are there any strong or well established commutative encryption algorithms?

I am looking for an encryption algorithm that's secure and commutative. This means that if N parties encrypt their data in any order, it could be decrypted in any other order.
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### Has AES some keys which are related to each other? e.g. $\forall m: AES(AES(m,k1),k2)=AES(AES(m,k2),k1)$ or $AES^n(m,k1)=AES(m,k2)$. How to find them?

Do $\exists$ keys $k_1, k_2$ which given any (128-bit) message $m$ are related to each other by being commutative to each other with $AES(AES(m,k_1),k_2)=AES(AES(m,k_2),k_1)$ $\forall m$ and ...
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### Same hash for subsets of a set? [closed]

Suppose I have a set $S$ containing $n$ bit strings, where $n$ is on the order of about 10. Consider $$\mathfrak{S} = \{ R : R \subseteq S, |R| \geq 2 \},$$ the collection of subsets of $S$ with two ...
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### Coppersmith attack on NTRU and non-commutativity

In this paper, Coppersmith and Shamir used lattice reduction to attack NTRU. At the very end of the paper, they note that developing non-commutative variants of NTRU would be wise, in light of their ...
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### Can I use RSA as hash function?

My end goal is to have an encryption function $e$ and a hash function $H$ such that for all m we have: $$H(e(m)) = e(H(m))$$ This would work if we use RSA encryption along with RSA "hash", ...
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### Are there any hash functions that are commutative yet secure for ordered lists?

I'm looking for a hashing function that can combine random numbers together in any order yet still find the same value. But it needs to be secure against hackers. The idea is if I'm hashing together: ...
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### One-way Functions for Floating Points

Are there any commutative one-way functions for floating points? I tried to explain why I need these functions. First, I describe the problem on a high level and then I further formalize it; There ...
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1 vote
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### Looking for commutative asymmetric cipher for data matching

I need some crypto operation for matching data privately between two peers (let say Alice and Bob). Alice should be able to encrypt her data with Alice and Bob public keys and pass the cipher text to ...
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### Are commutative digital signature possible?

Say we have a message $m$. Signer $S^1$ will sign this message using his digital signature to produce: $$\operatorname{Sign}_{S^1}(m)$$ Now, say another signer $S^2$ wants to sign the output of the ...
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### A hash function for sets that from a hash of a set and a subset of it doesn't reveal the hash of the remaining elements in the set

I'm looking for a function to compute a hash of a set. It needs to satisfy two properties: If someone published a hash $h(S)$ of a set $S$ and a hash $h(S')$ of some subset $S' \subset S$ of it, I ...
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### Can multiplication of two primes be seen as a strong cipher?

If we were define such a cipher: A reversible function that would accept a message $M$ and an initialization vector $\text{IV}_1$ $\operatorname{map}(\text{IV}_1, M)$ which can map an input $M$ to a ...
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### Are there transitive ciphers (either symmetric and asymmetric)

Say Alice has information that's already encrypted with Bob's key. She wants Bob to decrypt it without knowing what he just decrypted. So she encrypts it with her key and sends it to him, he decrypts ...
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### Is there a mental poker algorithm that does not rely on commutative encryption?

The algorithm for mental poker that I saw on Wikipedia and everywhere else relies on an encryption algorithm such that $E_k(E_j(P)) = E_j(E_k(P))$, but I can't find a modern and secure algorithm for ...
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### Crypto libary with Commutative Encryption

I want to implement Mental Poker in JavaScript as a toy program and lead in to a larger serious project so I did my research and found Massey-Omura cryptosystem and the Shamir three-pass protocol ...
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### Decrypting an encrypted text out of order

Does there exist a cipher that can be encrypted twice with two different keys and then decrypted twice using either key first? For example: ...
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### Commutative Encryption with RSA scheme?

I wanted to know how I could manage to do what I'm going to tell you next, with the RSA encryption/decryption scheme. So Alice and Bob each have a public key $(n, e)$ and a private key $(p, q, d)$; ...
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