Questions tagged [elgamal-signature]
A digital signature scheme based on the discrete logarithm problem, published by Taher ElGamal in 1984. Not to be confused with the ElGamal encryption system.
87
questions
0
votes
0
answers
47
views
ElGamal signature scheme problem and unsure whether my calculations are wrong or that's the answer
Trying to solve problem with verifying a message through the ElGamal signature scheme and I end up getting two different values.
I'm given a prime number p=881
, e1=3,
d=60
, and a random value r=11
. ...
- 1
0
votes
0
answers
43
views
What is the purpose of $k \in \{2, \dots, p-2\}$ in ElGamal signatures on ${\mathbb{Z_{p}^{*}}}$?
The question is mainly stated in the title. I had to do a refreshment on public key cryptography. The algorithms are pretty straightforward however, I always stumbled upon this question. Is it in ...
- 878
3
votes
1
answer
81
views
Occasional failure of an attack on ElGamal signature
I am following the procedure described on p. 319 of the fourth edition of Douglas Stinson and (since that edition) Maura Paterson's Cryptography − Theory and Practice (IBSN 978-1-03-247604-9).
The ...
- 33
5
votes
1
answer
965
views
Is it insecure to sign the value 0 with ElGamal?
Is it insecure to sign the plaintext 0 with ElGamal signature algorithm? Can this leak the private key, give the possibility to forge other signatures or does provide any other attack vector?
- 63
0
votes
0
answers
135
views
Difference between ElGamal and Schnorr signature
A question about Schnorr group.
Am I right that this is basically a protection against discrete-log solvers?
So Schnorr signature is better than ElGamal in that sense?
3
votes
2
answers
172
views
How is sum of two share of (2,n) shamir scheme equal to the secret?
I am refering to Privacy Aware Incentive Mechanism to Collect
Mobile Data While Preventing Duplication https://ieeexplore.ieee.org/document/7357616.
They claim to split secret $X$ into $X_s=\{x_0,\...
- 33
1
vote
2
answers
234
views
Using ElGamal instead of RSA in FDH
In RSA-FDH to sign a message $m$, we apply a hash function $H$ and then "decrypt" it using the private key $d$, so $Sign(m) = H(m)^d \mod N =: \sigma$ and then to verify, we use the public ...
- 13
0
votes
1
answer
450
views
ElGamal same private and random key attack
I'm having difficulty understanding this.
Consider two messages are encrypted using the same cyclic group order $q$, generator $g$, private key $x$, and random parameter $y$.
The attacker knows a ...
- 21
0
votes
1
answer
451
views
Malleability of El Gamal encryption
Suppose Alice encrypts a number 𝑥 which indicates her bid on a contract, using textbook ElGamal encryption (malleable). This encryption of 𝑥 produces a ciphertext pair 𝑐1 and 𝑐2.
How can Eve ...
1
vote
1
answer
203
views
Why $s=0$ is not allowed in Elgamal signature?
In Elgamal signature scheme $\text{sig}_{k_{pr}}(x,k_E)=(r,s)$, $s=0$ is not allowed. How does this lead to finding the private key $d$?
0
votes
1
answer
81
views
Security of ElGamal signature scheme with generator of small order
For $p$ a 1024-bit prime, we have a 1021-bit element $g \in \mathbb{Z}_p^*$, where the order of $g$ is much smaller than the order of $\mathbb{Z}_p^*$. How does this small-order $g$ affect the ...
- 41
0
votes
0
answers
255
views
Using GP/PARI how would you solve this randomised Elgamal question?
I know how to solve this question manually, but I don't know how to solve it using the program gp/pari. It is based on randomised Elgamal
Let p = 739. Given the following ciphertext of some message m1 ...
- 1
0
votes
1
answer
229
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 ...
- 11
0
votes
1
answer
274
views
How many valid signatures can the same message have using ElGamal?
I know that messages in ElGamal are not deterministic, so a message can have more than one valid signature. But is the number of valid subscriptions infinite?
- 103
2
votes
0
answers
59
views
Does having CDH oracle breaks El-Gamal signature scheme?
Having a oracle that solves Computational Diffie-Hellman problem which for given values $(g, g^a, g^b)$ outputs $g^{ab}$, is it possible to forge a signature in El-Gamal (wiki) signature scheme?
0
votes
2
answers
221
views
Break El Gamal for Elliptic Curves
There is an elliptic curve El Gamal digital signature scheme. Alice fixes an elliptic curve $E$, a prime $p$, a point $A$ on $E$, a secret integer $a$, and computes $B = aA$. She makes $(E, ...
1
vote
1
answer
322
views
How to compute certificates using Diffie-Hellman key exchange with certificates and Elgamal signature scheme
We consider the Diffie–Hellman key exchange scheme with certificates. We have a system with the three users Alice, Bob and Charley. The Diffie–Hellman algorithm uses p = 61 and α = 18. The three ...
- 31
2
votes
0
answers
382
views
Elgamal security if same key used twice
Assume that user A sends to user B a message, unencrypted, and signs it with an Elgamal signature.
Can some adversary, call it C, who eavesdrops, learn the private key if user A signed both messages ...
0
votes
0
answers
122
views
In ElGamal, how does knowing the secret number used for a signature reveal the signer's private key?
In ElGamal, how does knowing the secret number used for a signature reveal the signer's private key? How do two signatures using the same secret number reveal the signer's private key?
[Hint: p-1 is ...
1
vote
2
answers
471
views
How to properly sign and verify using DSA? Can anyone spot my mistake?
The question that I am trying to answer is as follows:
10.14. The parameters of DSA are given by p = 59,q = 29,α = 3, and Bob’s private key is d = 23. Show the process of signing (Bob) and ...
- 31
9
votes
2
answers
2k
views
What is largest prime factor in Diffie-Hellman?
I was reading the paper of A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms by TAHER ELGAMAL to better understand ElGamal public-key scheme, and he stated that for any ...
- 445
2
votes
1
answer
522
views
Why ElGamal signature is insecure with nonrandom k?
In ElGamal signature scheme like:
Keygen:
$\beta:=\alpha^a\bmod p$ where $\alpha$ and $p$ are large prime numbers. Public key is $(p,\alpha,\beta)$ and secret key is $a$.
Sign:
Choosing random $k$ ...
0
votes
0
answers
141
views
In DSA digital signature, why does k have to be random and unique each for each signing? [duplicate]
If we repeat k, I think there is little chance for s to repeat since user's private key x is ...
- 1
0
votes
1
answer
529
views
How to compute ElGamal decryption by hand
Lets say that $u=3, x=5, v=2$, how do we work out $u^{-x}*v$, so $3^{-5} * 2$. I know how to work out the answer if it was $3^5 * 2$ but how do we do it with negative exponents?
2
votes
2
answers
493
views
Whats wrong with my El Gamal signature example
I'm trying to digitally sign a message m using El Gamal. So far I've been unable to verify the digital signature ive made using El Gamal.
I am using prime number, p = 8369. prime root g = 3031. ...
- 31
2
votes
1
answer
1k
views
find $a$ and $k$ for a given el gamal cryptosystem
I am given this question:
Suppose Alice is using the ElGamal Signature scheme with parameters
$p = 31847$, $\alpha = 5$, and $\beta = 25703$
Assuming that we have received signed messages
$(x_1,(\...
- 131
5
votes
1
answer
215
views
Security analysis for a extended ElGamal Signature against selective unforgeability
Let $H$ is a cryptography hash function and $\Pi=(\mathsf{G}, \mathsf{S}, \mathsf{V})$ is a digital signature, as follows:
$(h_1=g^x,h_2=g^y) \leftarrow \mathsf{G}(1^n)$, where $x,y$ uniformly ...
- 71
1
vote
1
answer
404
views
Is K=1 a valid random integer in ElGamal signature?
In the ElGamal signature scheme, in addition to the public/private keypair, a random integer $K$ such that $\operatorname{gcd}(K,p-1)=1$ is chosen in the range $[1,p-1]$.
This clearly excludes $K=p-1$...
- 466
1
vote
1
answer
2k
views
How to recover secret $x$ from Elgamal signatures with repeated $k$?
Set generator $g \equiv 5 \pmod p$ where $p=647$ and $p$ is prime.
With the same $g$, $p$ and secret signing key $x$, Alice sends two messages, $428$ and $129$, with signatures $(433, 239)$ and $(433,...
- 13
0
votes
1
answer
247
views
Find private key from knowing random exponents are an arithmetic series
Let $p$ be a large prime and $g$ a primitive root modulo $p$, and $h$ a collision-resistant hash function.
Person A chooses a random integer $1 < u< p$ and $y \equiv g^u \pmod p$ is publicly ...
- 101
4
votes
2
answers
7k
views
Recovering private key from Secp256k1 signatures
I've seen many answers here and many articles that says we can recover the private key from reused R signatures.
But, what if the r,s signatures are different in transaction of bitcoin then is there a ...
- 41
1
vote
1
answer
3k
views
primitive root of a very big prime number (Elgamal DS)
For encryption methods there is a need for (very large) prime numbers. So for Elgamal digital signature there is the problem of finding a primitive root of $(p)$ where $p$ must be very large prime ...
- 21
5
votes
1
answer
320
views
Signature Scheme with proof of data possession
Most signature schemes first hash the data and than sign the hash. Correct me if I am wrong: The signature does not prove that the signatory was in possession of the document itself? In cases where ...
- 153
2
votes
1
answer
362
views
Any scenario for using ElGamal-SIGNATURE over RSA?
On a homework assignment, we're asked to give an example in which scenario one would use an ElGamal-Signature over an RSA-Signature.
I found this question, but the answer also only describes why RSA ...
- 123
1
vote
1
answer
270
views
Does ElGamal authentication exist?
Are there any natural ways to transform ElGamal encryption system or ElGamal signature scheme into an authentication protocol?
- 558
1
vote
1
answer
87
views
Given 2 Digital Signature generated by $S=D\times k^r$ how do you solve for $k$?
Given 2 signature $(D_1, r_1, S_1)$ and $(D_2, r_2, S_2)$ and the Signature is generated as $S=D\times k^r \mod N$ where $N$ is a product of 2 primes and $r_1$, $r_2$ is co-prime. How do you solve for ...
- 137
0
votes
1
answer
1k
views
El Gamal Signature: Attack to recover private key if $k$ is generated as $k_{i+1}=k_{i}+a$ where $a$ is a large unknown constant
$k_0$ is randomly generated and subsequently $k_{i+1} = k_{i}+a$, where $a$ is a large unknown constant
I've tried formulating an attack as such:
Given 3 Messages $M_0$, $M_1$ $M_2$and with $(r_0,...
- 137
3
votes
1
answer
2k
views
ElGamal encryption and signature using same keys
In ElGamal scheme we have message $M$; $p$, $g$ and $y=g^x \bmod p$ as public key where $x$ is unknown private key.
Encrypted message $(c,d)$, where $c=g^k \bmod p$ and $d=M \cdot y^k \bmod p$.
...
2
votes
1
answer
4k
views
Base Point on elliptic curve
How can i define the base point of the elliptic curve group element used as the elliptic curve domain parameter over Fp (prime)
4
votes
1
answer
755
views
Why is the El Gamal commitment scheme information theoretically binding?
I am a bit stuck on the following claim:
The ElGamal commitment scheme is information theoretically binding
As far as I understand, an adversary $A$ would win the binding game if it is able to ...
- 257
4
votes
1
answer
697
views
Length of ElGamal signature compared to RSA signature
In his original work (1) on the ElGamal encryption and signature scheme Taher ElGamal states in chapter V. section B.:
For the signature scheme using the above arguments for the
sizes ...
- 41
2
votes
1
answer
309
views
ElGamal signature - show that $(\gamma, \delta)$ signs $m$
We have as a given: $gcd(j, p − 1) = 1$.
$$γ = \alpha^i \beta^j \bmod p $$
$$ \delta = −\gamma j^{-1} \bmod (p−1) $$
$$m = i \delta \bmod (p − 1)$$
I want to show that $(\gamma; \delta)$ is an ...
- 115
3
votes
1
answer
788
views
Is it possible to combine digital signature to provide message addition?
Let's assume we are using the textbook RSA where $Sig(x)=x^d$. Alice has public key $(e,N)$, and private key $(d,p,q)$.
Now, if Alice sends $Sig(5)$ and $Sig(10)$ to Bob, where $5$ and $10$ is just ...
- 452
0
votes
1
answer
1k
views
What is wrong with my Elgamal signature example?
I want to construct an Elgamal signature scheme with the group $\mathbb{Z}_{23}^{\star}$ and then to compute the signature for the message $m$ with $h(m)=4$, where $h$ is the hash function that we are ...
- 133
2
votes
0
answers
131
views
Could be El-Gamal signature scheme constructed via Fiat-Shamir heuristic?
For example, Schnorr signature is pretty similar to El-Gamal.
And everywhere where Schnorr signature is explained (for example - on Wikipedia),
there's said that there's Schnorr scheme which is ...
- 742
2
votes
2
answers
2k
views
How to apply Pollard's Rho Method on elliptic curves to solve discrete logarithm problem in finite field?
I have ElGamal signature scheme implemented in finite field $\mathbb{F}_p$. The thing is that I need to apply Pollard's Rho Method on elliptic curve $E(\mathbb{F}_p)$ to this scheme, solve discrete ...
- 23
0
votes
1
answer
201
views
Elgamal Protocol Failure
I'm having a difficult time trying to solve this problem.
Suppose Alice uses the Elgamal signature scheme with $(\alpha,
\beta, p) = (2, 33384, 65539)$. She publishes the two signed
messages:...
2
votes
2
answers
675
views
How to find $r$ for El-Gamal signature with known private key
For public key $(g,b,P)$ and private key $x$ I have that...
...
- 131
2
votes
3
answers
2k
views
What can I do if I get private key of signing algorithm in Digital signiture
I am confused in digital signature. what is use of encryption with private key and decryption with public key. Using public key we can decrypt the signature then what is use of private key privacy. ...
3
votes
1
answer
901
views
El Gamal signature scheme variant
Suppose we have the following El Gamal digital signature scheme variant: We fix a prime number $p$ and a generator $g$ of the group $Z_p^*$. We choose $x \in Z_{p-1}^*$, which is going to be our ...
- 33