Tagged Questions

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

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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?

While I look for how many characters that can be encrypted using the The elliptic curve ElGamal cryptosystem. of each block found for these lines. But I can not understand Actually in our case we ...
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49 views

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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1answer
48 views

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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143 views

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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70 views

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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141 views

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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179 views

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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137 views

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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101 views

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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107 views

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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49 views

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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127 views

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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136 views

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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158 views

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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1answer
34 views

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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101 views

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 $m$, ...
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Undefined $E_y(1,r_{i,j,1})$ notation in cryptography paper, suspect ElGamal-like

I'm trying to understand a paper that uses the notation $E_y(1,r_{i,j,1})$ (full text available in link, used just once on Page #35, 6th page of pdf, Section 3.3, Step 1c) in the context of an ...
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In Pedersen Key Distribution, can the public key be persistent?

I am implementing a key distribution protocol described by Torben Pedersen in A Threshold Cryptosystem without a Trusted Party (EUROCRYPT'91). In the protocol, the $n$ parties distribute a public key ...
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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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Zero Knowledge Proof for Correctness of the product of additive ElGamal Ciphers [duplicate]

Suppose we use Additive ElGamal defined as follows: Let $(K,E,D)$ be a triple. The key-generator $K$ outputs the description of a finite multiplicative group $G$ of prime order $q$, with three ...
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1answer
403 views

Mapping of message onto elliptic curve and reverse it

I would like to perform a variant of Elliptic Curve ElGamal in java using the BouncyCastle libraries. I currently face the difficulty of mapping a message $m$ onto the elliptic curve $E_p$. I have so ...
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285 views

why inverse in diffie-hellman protocol will not give same value?

Security of diffie hellman protocol is $K=g^{ab}$.if sender want to calculate value of $b$(given $a$) he can do $g^{{{ab}^b}^{-1}}$(where K=$g^{ab}$) which will give $g^{a}$ as we are cancelling value ...
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Private Set Intersection Polynomial Computation [duplicate]

I am trying to implement the protocol mentioned in Section 3.4 of “Efficient Robust Private Set Intersection” in Java. In the Second Step, the Client computes a polynomial of degree $n$ over the ...
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60 views

Plaintext patterns leaked based on single bit

Assuming that Elgamal is used as an encryption cipher, where lets say $p$ is 2048bit prime. Is it possible for an attacker to figure out $x$, a secret key, if any part of 2048 bits ciphertext and ...
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1answer
143 views

ElGamal with elliptic curves I

It is very interesting to see @tylo's answer on ElGamal with elliptic curves. Instead of mapping the message to the elliptic curve point it just reduces an elliptic curve point to its $x$ coodrinate. ...
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ElGamal Homomorphic Encryption Formula Question [duplicate]

With Pubic Key $(G, q, g, h)$ where $G$ is a group, $q$ prime, $g$ a generator of $G$, Am I right in thinking that: $$\mathrm{Enc}(m;r) := (g^r, h^r \cdot g^m)$$
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Efficient Robust Private Set Intersection Questions

I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: $p = 17$ (prime) $g ...
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1answer
334 views

Z*p Generator (Cyclic Group) in java

I am trying to implement ElGamal in java without using the in-built libraries. The problem occurs when I am trying to find the generators of the number(in this case 11). Everything works perfectly ...
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94 views

ElGamal encryption with private key [closed]

Does the encryption with a private key and decryption with a public key works in ElGamal likewise what is done when we use RSA for sender authentication?
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Efficient Robust Private Set Intersection Additive ElGamal [duplicate]

I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: $p = 17$ (prime) $g ...
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1answer
51 views

when to do elgamal exponentiation computation

Recetly while studying about cryptographic primtives, I have come across below line in wiki : http://en.wikipedia.org/wiki/ElGamal_encryption Encryption under ElGamal requires two exponentiations; ...
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ElGamal in private set intersection: how to handle negative numbers?

I am trying to implement the Efficient Robust Private Set Intersection using Additive ElGamal. For this, from the client side, my inputs are $C = \{1, 2\}$. So, the polynomial is $(x-1)(x-2)$ which ...
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Advantages using Diffie-Hellman or Elgamal

For what kind of usage should we prefer using Diffie-Hellman in order to exchange keys instead of Elgamal, and most important why should we use one or the other? I do not see a clear difference ...
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EC ElGamal versus static+ephemeral ECDH

A client application needs to encrypt a UDP datagram for a server with known EC public key $P$. Performing a full ECDH key exchange would defeat the benefit of using UDP as a connectionless protocol. ...
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Attacks against El Gamal private key

El Gamal encryption involves picking $(p,g,b)$ which is our public key. We compute $b=a^x$ $mod$ $p$. Here, $x$ is the private key which we don't know. What are some efficient and strong algorithms ...
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252 views

Difference between Pedersen commitment and commitment based on ElGamal

Does any of you know what is the difference between the Pedersen commitment and the commitment that uses the ElGamal encryption scheme? For the sake of completeness, I recall what both of them look ...
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1answer
135 views

Recovering the random number r

For a padded message, M, using the El Gamal encryption schema, how can we determine the random number $r$, when we are given $p$, the prime number, $g$ which is the primitive root of $p$, $b$ and $x$ ...
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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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In Elgamal, the generator g is always quadratic non-residue modulo p where p is a safe prime and inverse of g can be also generator?

In Elgamal, the generator $g$ is always quadratic non-residue modulo $p$, where $p$ is a safe prime and the inverse of $g$ can also be generator? Can I prove it? I can't come up with it at all.
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Does ElGamal Encryption create a different key for each block sent?

I ask about ElGamal algorithm. Is ElGamal algorithm used new key for each encryption process. in other word it should we use new key for each chunk? For example, if we have message that has four block ...
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1answer
321 views

Proof of correct construction of a private key in distributed cryptography

In an exponential ElGamal encryption scheme where the key generation is done in a distributed way among $n$ trustees we have that each trustee $i$ (where $1 \leq i \leq n$): Selects a private key ...
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1answer
191 views

Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
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ElGamal with elliptic curves

I've searched some information on ECC, but so far I have only found Diffie-Hellman key-exchange implementations using ECC, but I don't want to exchange keys, I want to encrypt & decrypt data like ...
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How does an oblivious test of plaintext equality work?

Assume an ElGamal Cryptosystem. Assume a set of three players, $P_1$, $P_2$ and $P_3$. The private key $x$ is shared among the players. The player $P_1$ has a piece of the private key $x_1$, $P_2$ has ...