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Questions tagged [elgamal-encryption]

ElGamal is a public key encryption scheme with security based on the discrete logarithm problem.

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ElGamal encryption and signature using same keys

In ElGamal scheme we have message $M$; $p$, $g$ and $y=g^x \bmod p$ as public key where $x$ is unknown private key. Encrypted message $(c,d)$, where $c=g^k \bmod p$ and $d=M \cdot y^k \bmod p$. ...
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An MPC protocol from Elgamal is a good solution a homomorphic multiplication?

I want to compute a multiplication between many secret values and then distribute the result to everyone involved. For this, I thought about an MPC protocol built from Threshold Homomorphic Elgamal. ...
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Use of randomness in an Elgamal like encryption

Suppose I have the following encryption scheme: for a message $m\in\mathbb{F}_p^*$, I generate the ciphertext = $(g^r,f^mh^r)$ where $g$ is the generator of a cyclic group $G$ of unknown order $n$ and ...
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Indistinguishability vs fixed bit-length

Suppose there is a cyclic group $\mathbb{G}$ of prime order $q$ of elements in $Z^{∗}_p$ with a generator $g$ and values $a,b,c,d \in Z_q$. There is also an equation $g^{ab} = g^{cd}$, where $a,b,c$ ...
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Proof of knowledge of exponentiations

I am reading a paper of Furukawa and Sako, "An efficient scheme for proving a shuffle" from 2001. This paper writes a protocol for verifiable shuffling in mixnets. Their protocol make use of ...
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El-Gamal and Lines on Planes

I've been thinking about a geometric picture for El-Gamal. The idea is to understand the set $\{(my^{x},g^x) \mid x \in Z_p\}$ (the set of encryption of $m$ for fixed $g$ and $y$) by taking the $\...
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El-Gamal like encryption, how can i guess the key?

There is $p$ (large prime number), $g$ (generator of $p$), and $x_a$, $x_b$, $r$ (which are between $1$ and $p-1$). I know $g^{x_a}$, $g^{x_b}$, $g^r$, $g^{x_a\cdot x_b\cdot r} \bmod p$. How can I ...
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Chinese Remainder Theorem and Elgamal

I am studying an encryption scheme which is Elgamal-like where I think CRT can help optimise the encryption and decryption but I am not sure if I am applying CRT the correct way. I have a cyclic ...
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Is EC El Gamal the only option?

This question is related to the question I asked here. I'm looking for encryption scheme with the following properties: Given $m$ is a 256-bit value, $pub_a$ and $pub_b$ are public keys, and $priv_a$ ...
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Understanding ElGamal encryption for a Mental Poker Case

I am looking to understand ElGamal encryption as it is used in a specic context described below. I am interested in creating a practical form of Mental Poker for games other than poker developed by ...
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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 ...
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Is it possible to re-cipher with Paillier?

I know that with ElGamal we can re-cipher and get a second ciphertext equal to the first. Is it possible with Paillier too? When saying "re-cipher", I mean "A sends me a message, that is encrypted ...
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Can I overcome ElGamal malleability with AES preprocessing?

So textbook ElGamal is known to be vulnerable to CPA, and although there are several proposals (DHAES/EIES) for modifications none of those are formally accepted or standardized. My question is ...
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ElGamal: Why is reusing the same $k$ not secure?

I have a question on the encryption process of ElGamal: $$ Y = g ^ a \bmod p \\ C = g ^ k \bmod p \quad\text{($k$ is chosen randomly)} \\ D = m \cdot y ^ k \bmod p \\ \text{Decryption:}\...
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ElGamal signatures systems

Let $p$ prime number $q/p-1$ prime and $g\in (Z/pZ)^*$ element of order $q$.Also $a\in \{1,...,q-1\}$ the private key and $y\equiv g^a\pmod p$ the correspoding public key.For each of the following ...
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How represent message in Menezes–Vanstone elliptic curve cryptography

I ask about represent message in Menezes–Vanstone elliptic curve cryptography I now encrypt function as follow $C_1 = (M_1 * K_1) mod\ P$ $C_2=(M2 * k_2) mod\ P$ My question is about how much the ...
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El Gamal encryption scheme and symmetric encryption scheme

Consider the El Gamal encryption scheme, a symmetric encryption scheme (KG,E,D), and the following hybrid encryption scheme having an encryption algorithm that, on input a public key (G,q,g,h), where ...
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About Elliptic Curve ElGamal, 3 simple problems I have trouble with

In Elliptic Curve ElGamal, why are a=b=1 always legal for primes whose lengths are no shorter than 11(2) bits long? Is there any reason why the Point at Infinity can always be encoded as (0,0)? ...
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How compared encryption algorithm in terms of efficiency

I want to compare two cryptographic algorithms. The first algorithm is RSA, and second algorithm is ElGamal elliptic curve cryptography. Now, I’m looking for a way to compare the speed of the two ...
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Beginners question regarding ElGamal

How to motivate, that in ElGamal Alice the recipient keeps her keys fixed, while Bob the sender changes the key each time - why not both of them change their keys each time?
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ElGamal re-encrypts data

I try to learn ElGamal re-encrypts scheme and I have a question about the example: How is a re-encryption done with elGamal?. The $g$ value of Alice must be the same as $g$ value of Bob or not? And ...
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I2P Tunnel Creation Build on Request Record Question en(de)cryption method

Not sure if anyone here can help, but if so, sure would appreciate the help. If we read the https://geti2p.net/spec/tunnel-creation documentation page on how I2P creates a tunnel, we can read on the ...
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How to decrypt plain text x using man in the middle attack

Suppose Alice want to share a plain text $x = 5$ to Bob; using RSA, DHKE, and El-Gamal. My question is if Man-in-the-middle attack is applied then weather oscar can compute/decrypt plain text in all ...
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Batch ElGamal Scheme

I know about ElGamal scheme and its key generation, encryption, and decryption methods. I'm not sure about what is meant by batch ElGamal. Can someone please clarify it. How it differs from ElGamal ...