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

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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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Ephemeral key is held constant in ElGamal

Is there a known algorithm to recover the sender's messages in ElGamal $\mathbb{F}_p^*$ if the ephemeral key is held constant in two or more transmissions, assuming the messages are always distinct? ...
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ElGamal and Paillier key sizes for short messages

I am using ElGamal and Paillier schemes to encrypt a large number of short messages: typical 4-byte integers. I do this for the homomorphic properties of these schemes. However, the way the ...
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Brute forcing the secret key in Elgamal encryption

Crypto noob here, I am attempting to do this programming challenge. I do not have the secret key that is used to decrypt the message. However, the key is small enough for a brute force approach. I am ...
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Is ElGamal IND-CCA1?

We all know that textbook ElGamal falls due to chosen ciphertext attacks, because of its multiplicative homomorphic property ($E(A)*E(B)=E(AB)$). However these attacks require the ciphertext ($E(A)$ ...
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ElGamal against chosen ciphertext attacks

In Hoffstein, Pipher, and Silverman's book An Introduction to Mathematical Cryptography, the authors make the following remark: An attack in which Eve has access to an oracle that decrypts ...
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ElGamal scheme attack when one message is known and ciphertexts are intercepted

Let $G$ be a finite cyclic group of order $p$ and let $pk = (g, h=g^a)$ and $sk=(g,a)$ be Bob's ElGamal public/secret key pair in $G$. To encrypt a message $m$, a random number $r$ is selected and a ...
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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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Why is the re-encryption algorithm in Universal Re-encryption for Mixnets more complicated than apparently necessary?

This is the paper. On page 6, the paper describes a variant of El Gamal and a way of re-encrypting ciphertexts. I thought an easier way to do encryption is to output $(m(g^x)^y,g^y)$, and universal ...
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ElGamal Generator g problem

Having an ElGamal encryption scheme with p=19 which value can not be assigned to g? The answers were : 1,7,11,2 I think you can't assign value 1 to g.
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Break El-Gamal Algorithm by knowing the value of the random k

In El-Gamal Algorithm, the public key is $(p, g, A)$, and the secret key is $(a)$, in order to encrypt some data, the sender generate a random $k$, where: $(C_1, C_2) = (m.A^{k} \pmod{p}, g^{k} ...
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How to perform homomorphic multiplication in ElGamal?

How can I compute homomorphic multiplication in ElGamal? That is: Given two ciphertexts $(R_1,c_1)$ and $(R_2,c_2)$ corresponding to plaintexts $m_1$ and $m_2$ under some public key; how can I compute ...
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What does L_n is the bit length of the group order n states need for my calculation in ECDSA algorithm?

I am doing the program of implementing ECDSA for which I am trying to solve the equation scenario. In ECDSA that signature generation algorithm which states as hash value from the SHA-1 and where $l$ ...
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Secure ElGamal with OAEP

Is it possible to make ElGamal IND-CCA2 using OAEP or OAEP+? (OAEP+ from: "OAEP Reconsiderd" by Shoup) The reason I ask is that I recently answered this question and it came to my mind that OAEP or ...
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Zero knowledge proof relation + number is binary

I want to develop a ZKPK for the following problem: $$Y=g_0^{r_Y} \prod_{i=1}^n g_i^{s_i}$$ and $$Z=h_0^{r_Z} \prod_{i=1}^n h_i^{s_i}$$ I want to proof knowledge of $r_Y,r_Z$ and $s_i$ which I have ...
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Can the same random number be used in encryption and signing?

In several public key algorithms, the person running the algorithm must generate a random number (that's separate from the key). Can this random number be the same for an encryption and a signature? ...
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Reusing the random exponent for ElGamal encryption with different plaintexts

In the basic ElGamal encryption scheme, we encrypt a message $m$ as $(g^r, h^r m)$, where $g$ is the group generator and $h$ is the public key of the recipient. If the sender has another message $m'$ ...
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Drawback of ElGamal encryption

I am trying to find out some disadvantages of ElGamal cryptography but I'm not able to figure out what's wrong with the algorithm. The only one I found is that a known-plain text attack is possible in ...
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Check if this cryptosystem is safe

Let $G$ be any group where group operations, as well as finding the inverse of an element, can be performed quickly, but the discrete log problem is difficult. Consider the following cryptosystem: ...
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Usage of GF(p^m) fields, where p != 2

$GF(2^m)$ Galois fields are widely used in different cryptographic algorithms, for example, in Rijndael. However, $GF(p^m)$ fields are possible with any prime $p$, not only 2, but $GF(2^m)$ fields ...
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Converting a number to a member of a multiplicative cyclic group

I am currently trying to make an implementation of the ElGamal encryption for educational purposes. As I understand it, when using the encryption with multiplicative cyclic groups, one generates a ...
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ElGamal and Schnorr groups

As I gather, a normal practice for choosing a cyclic group for ElGamal key generation is to find a safe prime $p$ and use a multiplicative cyclic group with modulus $p$ and order $q = (p-1)/2$. ...
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Which multiplicatively homomorphic encryption scheme supports encryption of 0?

I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). I also want the multiplication to be operated on the ciphertext of 0, i.e., if ...
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How to use ElGamal to encrypt zero?

ElGamal encryption algorithm is as follows: To encrypt a value $m$, it chooses a random value $r$, and calculates $c_1=g^r$ $mod$ $q$ $c_2=m*h^r$ $mod$ $q$ where $g$ is the group generator, $x$ is ...
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How to implement homomorphic multiplication for Elgamal?

I want to add the homomorphic property to Elgamal in libgcrypt. This is the core code I added to the library. ...
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ECC - ElGamal with Montgomery or Edwards type curves (curve25519, ed25519) - possible?

I know the usual way of using getting shared secrets for encryption with ECC is DH, however, this only works with two keypairs of exactly the same kind, for example two curve25519- or two ...
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how to represent message as an integer between $1$ and $n-1$ [closed]

I am trying to implement simple El-Gamal cryptosystem. And I can't understand how to represent message as an integer between $1$ and $n-1$. The only thing that comes to my mind is: if $n$ bit length ...
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El gamal correctness

I tried to find online for the correctness of El-Gamal, but I couldn't find any good resource that will teach me how to show the correctness of El-Gamal, could any body show me how is it done?
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Proving correctness of a decryption of a homomorphically summed ciphertext?

I would like to take some additively homomorphic cryptosystem - don't care much which one for now - and encrypt a series of numbers with it. I would then like to (in public) take these numbers, add ...
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How many characters per block in an El Gamal ECC cryptosystem?

Looking for the number of characters that can be encrypted using the The elliptic curve ElGamal cryptosystem of each block, I found these lines. But I cannot understand them: Actually in our case ...
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How does chosen ciphertext attack on Elgamal work?

Can it be proven that attacker can obtain the full message if he knows some plain-ciphertext pairs?
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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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Use of ElGamal encryption for signature generation

If RSA (textbook RSA that is) generates a digital signature by using the sender's private key, couldn't any cryptosystem (the only two that come to mind are RSA and ElGamal) capable of asymmetric ...
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How do RSA and ElGamal key sizes compare?

I have a rather silly question regarding the comparison of RSA with ElGamal over integers. If you want to compare their performance in the same level of security, does the modulus of both of them need ...
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What does OIW stand for

There seem to be many OID's that have been put in the ASN.1 tree that have the following ISO identified organization: OIW. One example is SHA-1 (ElGamal seems to be another): ...
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Why are we not using multiple ciphers per message?

I am aware of at least rsa, elgamal-encryption, and variations of elliptic-curves relying on different problems and that those problems are considered hard. However, if someone figures out a way to ...
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Prevent MITM attack while encrypting data by using ElGamal ECC?

I am using ElGamal ECC to encrypt my plain text data. I want to ensure that my data is safe from a Man-In-The-Middle attack. What methodology I can adopt to achieve this goal? How can we prevent a ...
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Homomorphic Encryption: how does the equality test on ciphertexts work?

Let's suppose we have a asymmetric crypto-system $H$ which is homomorphic with respect to some function $F$. Alice encrypts a message $m$ with her private key $e$ in the crypto-system $H$ and ...
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Known plaintext attack on ElGamal encryption

Assume that Alice uses Bob’s ElGamal public key ( = 2, Yb = 8) to send two messages $M = 17$ and $M' = 37$ using the same random integer $k = 9$. Eve intercepts the ciphertext and somehow she finds ...
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How to calculate complexity of ElGamal cryptosystem?

How to calculate time and space complexity of ElGamal encryption and decryption as there are two exponentiation operation during encryption and one during decryption? Here is my code for encryption: ...
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Use ElGamal to solve Diffie-Hellman problem

Say we are able to decrypt a Elgamal ciphertext $c$ using only the public key. Apparantly it is now possible to solve the Diffie-Hellman problem (given $g^a, g^b$ calculate $g^{ab}$). How? I know how ...
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Condensed ElGamal + AES

In normal ElGamal encryption, the encrypted message is a pair (gb, gabM) - that is, the actual "encryption" is simply multiplication by the shared secret ...
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How to prove NIZK proof of knowledge?

Assuming we have an El-Gamal pk tuple $(G,q,g,g^s)$. Someone, knows only the first three parameters. In round $i$, I send him $X_i=(g^s)^{t_i}$ (the $t_i$ values are chosen randomly for each round), ...
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What differences between Menezes–Vanstone ECC and ElGamal ECC?

After researching ECC encryption, I found that we can use ElGamal cryptosystem with elliptic curve and can we use Menezes-Vanstone cryptosystem with elliptic curve. What is the essential difference ...
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Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
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weaknesses in ElGamal with public key of small order

Suppose $p=29$, $\alpha = 2 \in F_p^*$ is a generator of $F_p^*$. Bob picks $d \in \{2,...,27\}$ such that $\beta = \alpha ^d=28 \pmod{29}$. He then sends his $(p,\alpha ,\beta)$ to Alice who herself ...
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How can one encrypt with RSA (or ElGamal) without revealing whom the ciphertext is intended for?

Imagine Alice wants to encrypt for Bob and post this encryption publicly, so that only Bob can decrypt but no one can other than Alice or Bob tell that the message was encrypted for Bob. The naive ...
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Is the private key static or variable key in the elgamal algorithm?

I read about elgamal algorithm it work like the follow steps Bashir chooses a large random prime p and a primitive root α modulo p. Bashir then chooses a random integer a with 2 ≤ a < p - 1 and ...
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Why is ElGamalEngine in bouncy castle restricting input data to be less than the length of the group parameter p?

I am currently using the ElGamalEngine of bouncy castle to implement exponential ElGamal for the purpose of making ElGamal additively homomorphic. To do this i raise the message to be encrypted to the ...
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Size of p in ElGamal cryptosystem?

In the ElGamal cryptosystem, I was wondering whether the $m$ (message) should be less than $p$ (large prime). Because on decryption, we are getting $m \bmod p$. For $m \bmod p$ to be equal to $m$, ...