# Questions tagged [elgamal-encryption]

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

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### ElGamal, message > p

Assume that we have: p = 89 g = 5 public key: 17 private key: 73 If we try to encrypt message M = 53 (M < p), then we get (c1, c2) == (55, 67) and further ...
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### Decrypting a ciphertext in ElGamal's cryptosystem

I am a student in computer science currently working on a problem set in cryptography (practical problem but stuck on the math part). Basically, suppose we receive a message that has been encrypted ...
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### Understanding Practical Differences Between ElGamal and Diffie-Hellman

I've been tasked with building a Web Assembly site that implements E2EE. I was thinking of using ElGamal Encryption to encrypt the message and Diffie-Hellman to establish the key. After doing further ...
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### What is the quadratic character of the field over which elliptic curve is defined?

I'm trying to understand the injective encoding of a message to an elliptic curve point (from this paper). However, I'm not sure what do they mean by the quadratic character of the field. Do you know ...
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### How to prove lifted ElGamal encryption with square root communication?

I'm looking for a more efficient solution to prove the correctness of multiple ciphertexts sent to different parties are correct. The background is that $P_i$ uses lifted ElGamal encryption to encrypt ...
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### Decryption of ElGamal ciphertext

If someone says that the decryption of an ElGamal ciphertext is "x", how can I be sure that the real value is "x" and not "y", even if he is the owner of the respective ...
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### Group Signature by Camenisch and Stadler

Page 8, Paper: "Efficient Group Signature Schemes for Large Groups" by Camenisch and Stadler (1) I was trying to understand membership certificate part. I am have only basic knowledge of ...
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### malleability of the Elgamal cryptosystem

In bidding for a contract, a company might outbid its competitor by simply multiplying its rival company’s encrypted bid by 0.9, without even knowing the bid. Now Suppose we are given the ciphertext c ...
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### Short randomness in ElGamal and Paillier

In the Paillier cryptosystem the encryption of $m \in \mathbb{Z}_N$ with randomness $r \in \mathbb{Z}_n^*$ is $c = g^m r^n \bmod{n^2}$. My question is, what if short (E.g. 512bits) $r$ is used? ...
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### Can I use a certificate authority with Elgamal encryption?

Can I use a certificate authority with Elgamal encryption? Is this type of keys in CA?
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### Asymmetric encryption scheme with the shortest output for encrypting 1 byte of information

Imagine that one needs to periodically encrypt very short messages (i.e., a boolean Yes/No, a single byte, or 3-4 bytes in the worst case). We assume that there is no session, and we just need to ...
169 views

### How to calculate the n in n-bit security of a crypto algorithm?

I think I'm likely missing the term because searching for this is coming up with not so precise results. I'm looking to calculate the n-bit security of say Paillier vs ElGamal vs EC ElGamal, when I ...
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### Paillier versus Lifted ElGamal for homomorphic addition for e-voting

I'm looking to create an anonymous e-Voting system which will assign a certain number of bits to each candidate during a vote, e.g. 010000 for Alice, 000100 for Bob, and 000001 for Charlie. It works ...
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### How are the points computed in the ElGamal elliptic curve encryption algorithm?

I was looking at an example of the ElGamal encryption operation here (page 24), but I can't seem to understand why: $$\beta = 3(10, 3) = (10, 8)$$
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### ElGamal and Pailler combined

currently I am working on some secure accounting application. I have few requirements: Application should store items which can be searched by name. Every item has price and tax. Every invoice ...
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### Is it possible to apply the El Gamal encryption/decryption technique using Edwards curve in Montgomery form

I've been trying to understand the ElGamal encryption/decryption technique. I plan to use it for sending a private message to the server. That is: Alice needs to send $Pm$ (private message encoded via ...
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### Difficult to guess the targeted receiver

The protocol is defined as : Bob want to send message to one of his friends say $k$ friends , he does not want his others friends (except one whom he want to send message ) to tell who is targeted ...
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### Can you obtain private key d and compute plaintext from El-Gamal?

Given an Elgamal encryption scheme with public parameters $k_{pub}=(p,\alpha,\beta)$ and an unknown private key $k_{pr}=d$. Due to an erroneous implementation of the random number generator of the ...
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### Zero-knowledge proof of knowledge of a plaintext in exponential ElGamal

Consider the exponential ElGamal cryptosystem over some group $G$ with generator $g$. Let $m$ be a plaintext, and $(R, C) = (g^r, g^m \cdot y^r)$ an encryption thereof for some public key $y$. Assume ...
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### Zero Knowledge Proof: Prove correct ElGamal encryption without leaking message

I know it is possible to prove zero knowledge that a given ElGamal ciphertext $(c,d)$ encrypts a plaintext belonging to some set ($\{0,1\}$ is frequently used for electronic voting applications). Next ...
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### Modified ElGamal encryption (ElGamal encryption with messages in the exponent ) is implemented in a pairing friendly elliptic curve. Is it secure?

In my scenario, I need to distinguish if the encrypted message is 0 or not. The message is encrypted by Elgamal encryption but with the message in the exponent. i.e. $(C,R)=(g^my^r,g^r)$ where $y$ is ...
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### ElGamal Encryption over a Subgroup

Say for instance we are encrypting over a subgroup of ($Z_{67}^*, \bmod 67$). To perform a round of El Gamal's encryption scheme we should: Choose a subgroup of ($Z_{67}^*, \bmod 67$), of prime order....
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### Given ciphertexts C1, C2 of different messages P1 and P2; how can we prove that both C1 and C2 were encrypted using public keys of the same pair?

I vaguely recall reading about a scheme that accomplished this but am not able to figure out which one it was. For the sake of brevity I'm gonna omit any nonces. Let's say we have an asymmetric ...
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### Request for a zero-knowledge proof (or hint)

I want to design a zero-knowledge proof (ideally a NIZK, but could be a sigma protocol) so that Alice can prove that a certain encryption contains a value that has been signed by a certain key. More ...
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### ElGamal encryption of concatenated messages

Suppose an encrypter separately produces three ElGamal ciphertexts $c_1 = E(m_1)$, $c_2 = E(m_2)$ and $c_3 = E(m_3)$, which encrypt the messages $m_1$, $m_2$ and $m_3$, respectively. Is it possible ...
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### ElGamal variant Encryption scheme

I was asked about the following variant of $ElGamal$ Encryption Scheme (Preparing for exam): Instead of encrypting $(g^r,h^r*m)$, encrypt $(g^r,h^r+m)$. And the question is whether the new variant CPA ...
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### Python library that implements additive homomorphism of Elgamal Encryption on the Elliptic curve i.e X25519 or P-256

I'm trying to find a Python library that implements Elgamal Encryption on the Elliptic curve i.e X25519 or P-256. My purpose is to use the additive homomorphic property of Elgamal. I'm using https://...
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### ElGamal encryption security

Assume we have 2 prime numbers in form p = 2q + 1. Is it safe to use the cyclic group of order p-1 instead of one with order <...
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### Attack on ElGamal Encryption

Bob is holding a secret-bid auction using ElGamal encryption. He chooses a “safe” prime $p$ of sufficient size, a generator $g$ in $\operatorname{QR}(\mathbb Z_p)$ and a value $b$ in $[1, p]$. He then ...
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### Is there an Elgamal implementation in javascript?

Does anyone know a good, well known implementation of ElGamal encryption and decryption in JavaScript? I was told that Stanford Javascript Crypto Library https://github.com/bitwiseshiftleft/sjcl/ ...
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### Why Bellare-Micali Oblivious Transfer Construction requires ElGamal with hashed key?

The idea of the Bellare-Micali Oblivious Transfer Constructions is the following: Informally, the receiver is required to generate two public keys $y_b$, $y_{b-1}$ such that it knows only the secret ...
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### How to determine if ElGamal message was a quadratic residue?

Consider the following ElGamal encryption (using a generator of $\mathbb Z^*_p$): Key gen: find a big prime $p$ and $g$ a generator of $\mathbb Z^*_p$. choose $a\in \mathbb Z_{p-1}$ randomly and ...
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### Breaking Elgamal private key

I have been given a task to explain if - given a public key and a portion of a private key (over 300bits) with a remain unknown of 80 bits - the private key can be broken with an algorithm faster than ...
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### Is there a concept of Pedersen commitment "in the base"?

This question Can Elgamal be made additively homomorphic and how could it be used for E-voting? says ElGamal can be made homomorphic over multiplication. So you can have $(g^r, h^r g^m)$ (i.e., ...
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### ElGamal with massage hashed ind-cca secure?

It is well known that text book ElGamal is not IND-CCA secure, because an attacker can just have $$(Y,W)\leftarrow E_{x}(LR(M1,M2,b))$$ where M1, and M2 can be any message in the group, and than just ...
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### Secure asymmetric encryption with 32byte ciphertext

I need securely asymmetrically encrypt the up to 16 bytes plaintext and receive up to 32 bytes ciphertext. I found that ElGamal produces ciphertext that is 2 times keysize. So I would need to use ...
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### How can breaking the ElGamal encryption scheme break the Diffie-helman protocol?

I have been studying how ElGamal is a public-key algorithm built on top of the Diffie-Hellman key exchange but I got confused. How exactly could an attacker break the Diffie-Hellman protocol (i.e. ...