# Questions tagged [elgamal-encryption]

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

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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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### How to verify if g is a generator for p?

For learning purpose, supposed I have a 16-digit prime which is 2685735182215187, how do I verify if g is a generator? (p is supposedly a special kind of prime)
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### El Gamal Cryptosystem Proof, Step-by-Step Explanation Needed. I feel like I don't understand what I have on this proof

Can someone provide a good and thorough explanation of the El Gamal proof? Basically, I need a step-by-step breakdown of what is happening at each important part in the algorithm. I haven't been able ...
534 views

### Diffie-Hellman private key recover with non-prime modulus

Say we have a classic Diffie-Hellman key exchange. We have the following parameters of a public key: p,g,y Where $p$ is the modulus, $g$ is the base, $y$ is the ...
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### Usefulness of OAEP with ECC

Does OAEP make sense for use in an ECC ElGamal cryptosystem? The way I see it, OAEP makes questionable sense even for RSA because even though it's a "all or nothing" transformation, many RSA ...
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### Given paramaters of an Edward's curve and x, determine a y value if it exists

I'm making a demonstration cryptosystem using ECC ElGamal. I've currently got a working implementation of Edward's Curve operations and a basic ElGamal implementation (Encrypts only points on the ...
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### How to securely map messages to points on an elliptic curve

I'm implementing a demonstration hybrid cryptosystem in Python (FinCrypt, I know the name is bad) and I'm migrating over from my Weierstrass curve implementation, which was based off of this, to one ...
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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 this problem still as hard as discrete logarithm (modified ElGamal)?

I am trying to find a vulnerability or proof for the following problem: ElGamal part. Given $g\in\mathbb Z_p$ where $g$ generates $\mathbb Z_p^\star$, select randomly $k\in\mathbb Z_p$ and calculate ...
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### For ElGamal-based key encapsulation, is it necessary to hash before using as AES key?

I'm working with SJCL, specifically using ElGamal to encrypt messages. Behind the scenes, this is doing something similar to what's described in this SO post (emphasis mine): Regardless how big ...
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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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### What is an example of elgamal homomorphic double encryption?

I am looking for such an cipher algorithm that is based on assymetric cryptography where the order of encrypting is irrelevant. For example: There is a message "x", Bob encrypt that message with his ...
356 views

### Zero-knowledge transfer of value protocol inspired by EC El Gamal

This is a follow up on the question I asked here. I designed a scheme that allows the following: Alice has a value $a$ which she wants to keep secret Bob has a value $b$ which he wants to keep secret ...
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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 $priv_a$ ...
239 views

### 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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### How to encode messages in $\Bbb Z_p^*$ to be encrypted with ElGamal scheme?

In ElGamal encryption scheme, in order to achieve IND-CPA security, one must use a group where the DDH problem is assumed to be hard. As this answer suggests, one way to achieve that is the following: ...
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### ElGamal ciphertext lenght

I'm studying for an exam and answering practice questions and I would love clarification on something. Apologies if it seems really simple. My lecture notes indicate that for ElGamal: the ...
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### Non interactive ZKP that encrypted additive elgamal message is in set of valid messages

This is taken from Anonymous voting by two-round public discussion by F. Hao P.Y.A. Ryan P. Zielinski Votes are encrypted using the additive variant of ElGamal. I am also using ECElgamal. The idea is ...
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### Implementing commitments and challenges for a distributed ElGamal encryption scheme

I am trying to implement a distributed encryption system by having as a main source of information this book (Introduction to Cryptography by Delfs and Knebl) and this Internet article (More Mix than ...