Questions tagged [elgamal-encryption]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
57 views

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 ...
0
votes
1answer
81 views

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 ...
0
votes
1answer
62 views

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 ...
2
votes
1answer
58 views

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 ...
0
votes
0answers
20 views

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 ...
0
votes
1answer
42 views

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 ...
0
votes
0answers
18 views

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 ...
0
votes
1answer
54 views

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 ...
1
vote
1answer
34 views

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? ...
0
votes
1answer
41 views

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?
3
votes
1answer
103 views

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 ...
3
votes
3answers
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 ...
2
votes
1answer
53 views

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 ...
1
vote
1answer
27 views

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: $$\beta = 3(10, 3) = (10, 8)$$
0
votes
2answers
74 views

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 ...
1
vote
0answers
44 views

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 ...
0
votes
0answers
35 views

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 ...
0
votes
0answers
61 views

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 ...
1
vote
0answers
126 views

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 ...
0
votes
0answers
78 views

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 ...
0
votes
1answer
60 views

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 ...
1
vote
1answer
79 views

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....
0
votes
2answers
150 views

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 ...
0
votes
0answers
80 views

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 ...
1
vote
1answer
198 views

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 ...
0
votes
0answers
54 views

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 ...
2
votes
1answer
292 views

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://...
2
votes
2answers
116 views

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 <...
0
votes
0answers
50 views

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 ...
0
votes
0answers
76 views

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/ ...
0
votes
1answer
77 views

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 ...
0
votes
0answers
54 views

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 ...
-1
votes
1answer
111 views

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 ...
0
votes
0answers
60 views

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., ...
0
votes
0answers
73 views

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 ...
0
votes
1answer
71 views

ElGamal Decryption variant

I am trying to do some ElGamal encryption but having a different encryption formula. For that I doing the following steps: The key generator: Choosing value $p = 107$ and $a = 2$ Random number $d = ...
0
votes
1answer
87 views

Elgamal Encryption: Why does Bob get to reuse his keypair while Alice has to generate a new one for every message?

From Christof Paar's book The protocol consists of two phases, the classical DHKE (Steps a–f) which is followed by the message encryption and decryption (Steps g and h, respectively). Bob computes ...
2
votes
0answers
40 views

Why is confusion & diffusion not required PKI encryption schemes like Elgamal encryption?

The Elgamal encryption scheme is a Multiplicative Mask with the shared key. It doesn't seem to have any confusion or diffusion. So why is it not necessary here as compared to Block Ciphers?
2
votes
1answer
105 views

Questions about Symmetric Encryption part of TLS

In TLS, we use DHKE for establishing the session key & then encrypt the actual communication with session key using symmetric encryption. While reading about DHKE, I learnt that you could use the ...
1
vote
0answers
102 views

Breaking vulnerable ElGamal encryption

In a ctf, I encountered this problem: ...
0
votes
1answer
91 views

Is there a way to confirm that a homomorphic division (multiplication with inverse) using ElGamal produced the correct result?

By running some tests I observed that if I perform a homomorphic division (multiplication with the multiplicative inverse) between two values using the ElGamal scheme, I get the correct result when ...
1
vote
2answers
291 views

Adversary for attack on one variant of ElGamal

I came by the following question: Consider the following variant of ElGamal encryption. Let $p= 2q+ 1$, let $G$ be the group of squares modulo $p$ so $G$ is a subgroup of $Z_p^*$ of order $q$, and ...
3
votes
1answer
111 views

How do I encrypt a long message using ElGamal encryption correctly?

According to ElGamal encryption, in order to encrypt a message I need to generate a shared secret s and after that I am to calculate ...
2
votes
1answer
241 views

Negative numbers with additive ElGamal

I'm trying to implement Private Set Intersection using the additive ElGamal public key encryption system. The code I've written can encrypt and decrypt numbers using the ElGamal system, so far so good....
0
votes
1answer
169 views

Number of operations for Elgamal cryptosystem

In page 408 of Hoffstein, Piper, and Silverman's Introduction to Mathematical Cryptography, it says "Roughly speaking, in order to achieve $k$ bits of security, encryption and decryption for ...
2
votes
1answer
169 views

Can Eve break this public key cryptosystem if she can solve DLP or DHP?

The PKC is in this way: Alice and Bob fix a publicly known prime $p$, and all of the other numbers used are private (unless sent). Alice takes her message $m$, chooses a random exponent $a$, and ...
0
votes
0answers
43 views

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 ...
0
votes
0answers
162 views

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. ...
2
votes
1answer
83 views

Standard for asymmetric encryption based on elliptic curves

Most parts of public key cryptography has established standards which are in turn used in a large amount of real world applications. There is PKCS#1 for RSA based encryption and signatures and there ...
1
vote
0answers
48 views

Two ElGamal ciphertexts equivalence

Is there a way to prove that two ElGamal ciphertexts encrypt the same message with different public keys without knowing the private keys? The prover is the producer of both ciphertexts.

1
2 3 4 5
7