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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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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 ...
shuvalov's user avatar
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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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Can we use Pohlig-Hellman Exponentiation Cipher with a PRG to achieve an oblivious PRF

The Commutative Cipher Setup Alice and Bob agree on a 2048-bit safe-prime $p$, where $(p-1)/2$ is also a prime. Both parties have an encryption exponent $e$ in the range $(1, p-1)$ with $gcd(e, p-1) =...
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How can Alice enable Bob to look-up values in a private map

I think this problem is similar to private set intersection, yet distinct in a way where: Alice has an extensive Mapping of say id to name id1 -> John Doe id2 -> Jane Doe id3 -> Edgar Poe ...
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Is it safe to publicly announce the prime number in Shamir three-pass protocol

So say, I want to use a prime number p for anyone that wants to communicate with me using Shamir's Three Pass Protocol. I will be maintaining my secret keypair (encryption exponent, decryption ...
zetaprime's user avatar
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Commutative homomorphic encryption for zero-knowledge transfers

I am trying to design a scheme that would allow the following: Alice has a number $a$ which she wants to keep secret Bob has a number $b$ which he wants to keep secret Alice can "transfer" a number ...
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Authentication scheme to protect against fake devices

I want two embedded devices (call them master and slave) to communicate with each other. For intellectual property protection, the master must reject fake slave devices (the other way around is a pre ...
Mark Jeronimus's user avatar
13 votes
1 answer
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Is Pohlig-Hellman Cipher the only option?

I am looking for a cipher which would allow something like this: E(E(M, a), b) = E(M, ab), where a and b are encryption keys, and ab is a combination of the keys that is impractical to separate into a ...
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Information sharing using interactive zero-knowledge system

I am trying to build a system that would allow information sharing in a kind of zero-knowledge way. Here is the set up: Let's say there is a trusted third party that has Alice's sensitive info M (e.g....
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Is there a cryptographic way (a la mental poker) two people can determine if they both Like each other, without revealing their personal preferences?

Specifically: Alice and Bob want to know if they like each other, but won't admit it if the other person doesn't reciprocate. (They're teenagers, or physicists.) They don't trust anyone else, so want ...
doctorofphysics's user avatar
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1 answer
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Are there encryption systems that are both homomorphic and commutative?

If so, which ones are? If not, is it known whether or not these are mutually exclusive? Is there a page that exhaustively lists encryption systems and properties such as these? I could not find a ...
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Is there a system where multiple people can encrypt a message and then decrypt it in any order? [duplicate]

For example, A encrypts a message. B encrypts that. C encrypts that. Then B decrypts, followed by A then C. Are there systems that allow this? Does such a property have a name?
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Commuting hash and encryption function?

I wonder if there are secure cryptographic hash function $H$ and encryption function $E$ such that: $H(E(m)) = E(H(m))$ for all $m$. Do such functions exist?
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2way cryptography

Imagine Alice sending Bob a message. They act like this: Alice encrypts a message with her key and sends it to Bob. Bob encrypts the message again with his key and sends it back to Alice. Alice ...
christostz's user avatar
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1 answer
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Is there an encryption method where the order of decryption is irrelevant to the order of encryption?

With most encryption methods, if a message is encrypted first using key $k_1$ and then using $k_2$, to decrypt it you have to use first $k_2$ and then $k_1$. I was wondering if there are any ...
user avatar
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1 answer
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Commutative Hash Function for Password Challenge?

I had an idea. Could anyone tell me if this is a thing, if they see any problems with it, and if they know of a commutative hash function that would make it work? Suppose you had a pair of ...
Edward Peters's user avatar
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2 answers
1k views

Public key crypto without modular arithmetic?

This comment from Reddit math, in response to a statement about how people can communicate secrets to each other with a third party listening, has a very small, simple example of public key ...
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1 answer
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Are any public key algos commutative?

Are there any public key encryption algorithms that allows for arbitrary ordering of crypto operations (commutative). That is, given a plaintext $\text{message}_1$, the following operations work to ...
Mike Janzen's user avatar
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3 answers
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Is there a way to prove equality of plaintext that was encrypted using different public keys?

Imagine if Alice encrypts message to Bob (using public key $P_{bob}$) and then Bob encrypts the same message to Carol (using $P_{carol}$). Is there a way for Bob to prove that: $P_{carol}$ was indeed ...
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Can CFB mode of block cipher be used as a commutative encryption?

Can CFB mode of block cipher be used as a commutative encryption? Is it possible to use CFB mode of AES block cipher to create commutative encryption? With CTR it is possible but not secure.
user1563721's user avatar
2 votes
2 answers
299 views

Is this commutative encryption protocol secure?

My assumptions are: encryption must be commutative man-in-the-middle is not an issue I would like to implement the following scheme between 2 parties ($A$ and $B$) to exchange a key: Lets $C = P \...
user1563721's user avatar
4 votes
4 answers
1k views

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 ...
Nati Keidar's user avatar
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1 answer
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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 ...
Daffy's user avatar
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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 ...
xanth's user avatar
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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 $(p, q, d)$; ...
Desura's user avatar
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Can a commutative block cipher be indistinguishable from a random one, assuming a random permutation of keyspace?

Define a commutative block cipher with keyspace the finite set $K$, and message space the finite set $S$, to be an application $$\begin{align} E:K\times S&\mapsto S\\ (k,x)&\mapsto E(k,x)\text{...
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Can a commutative block cipher be indistinguishable from a random permutation, for fixed key?

Define a commutative block cipher with keyspace the finite set $K$, and data space the finite set $S$, to be an application $$\begin{align} E:K\times S&\mapsto S\\ (k,x)&\mapsto E(k,x)\text{ ...
fgrieu's user avatar
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Can we decrypt in this order when the message is encrypted twice?

If we encrypt a message twice with symmetric key $k_1$ first and then $k_2$ like $E_{k2}\{E_{k1}\{m\}\}$ , ideally we should decrypt with $k_2$ first and then $k_1$ but is it possible to decrypt with $...
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Are there any secure commutative ciphers?

This answer lists two commutative cipher algorithms - Pohlig-Hellman and SRA. However, they don't appear to be too secure. My question is, here there any commutative ciphers out there that are secure ...
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Transparent cipher

I'm trying to implement this protocol: Alice has her permanent key $K_1$. She computes $E(K_1, P)$. She wants to share $P$ with Bob, Carol and Dave. For each of them she: 2.1. Generates $K_2$. 2.2. ...
Kirill Morarenko's user avatar
9 votes
5 answers
4k views

Software implementation of a commutative cipher?

I've got an application (detailed below) that calls for the use of a cipher that is commutative. I've been doing some googling & reading, and there are two algorithms that seem to get mentioned ...
Roy Pardee's user avatar