Questions tagged [discrete-logarithms]

For questions related to the discrete logarithm problem; modulo $p$, in finite fields, over elliptic curves, or in an abstract group.

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prove that (A/p) =1 <=> index of A relative to G is even [closed]

I'm studying about number theory but I cannot do it... please help me.. p is a odd prime, G is primitive root modulo p, A is interger, gcd(A,p) = 1 is given. Question is Prove that (A/p) =1 <=> ...
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Solving for $x$ in discrete logarithm [closed]

$$9 = 2^x \text{ mod } 11$$ How do you use a calculator to obtain this value? The $x$ is an integer. Used in Diffie–Hellman key exchange algorithm.
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What does "underlying field" mean in the context of groups?

I read a statement in this answer which said "In conics, the discrete logarithm problem of this group (conics) is no more difficult than the discrete logarithm over the underlying field". ...
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Discrete logarithm problem in base 10. When is it of a very special form?

Doing some personal research I just stumbled upon this problem: Given an integer $m\in \mathbb{Z}$ that is coprime to 10, I am interested in whether or not there exists an integer $n\in\mathbb{Z}$ ...
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Hardness to solve DL-Problem

I was wondering why some groups provide more security to cryptosystems relying on DL-Problem. It is not clear to me wether it is just due to the known attacks or if there are some other reasons. So ...
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Can I find the exponent of a matrix given only a vector and its image?

here is my problem : Given a $GL(m,2)$ matrix $A$, and $x,y$ two non-zero $F_2$ vectors of length $m$ with the premise that $y = x(A^n)$ for some positive integer $n$. The goal is to find n. Is it ...
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Finding discrete logarithm of composite numbers

I started to learn discete logarithm the definition says that:suppose that "p" is a prime number , "r" is a primitive root (modulo p) and "a" is an integer between "1 and p-1" inclusive.If r^e (...
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Extending "the ring of exponents" from $\Bbb{Z}$ to that which contains a solution to $4^x - 3 = 0 \pmod 5$?

Let $R = \Bbb{Z}/5\Bbb{Z}$ be the ring of integers modulo $5$. Then $4^x = 1, 4, 1, 4, 1, 4, \dots$ as $x$ ranges over $\Bbb{Z}$. Thus $4^x = 3$ and $4^x = 2$ have no solution $x \in \Bbb{Z}$. ...
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Elliptic Curve - Prime Generator

This question is in regards to the prime generator for an elliptic curve. I have taken the prime curve $\mathbb Z_p$ and have the $5$ prime number factors for the prime curve using Euler's Totient. Is ...
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Is there an upper bound for $2^x \bmod P$ in range again?

Is there an upper bound for $x \in \mathbb{N}_+$ in $$v \cdot 2^x \equiv m \mod P$$ to get a remainder $m$ with $$N\le m <2N$$ given a random initial value $v$ with: $$N\le v <2N$$ $P$ is a ...
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What is the significance of using the term "discrete" in discrete logarithm?

I'm trying to clear up my confusion in using the term "discrete" in discrete logarithm. I'm focusing on why the word "discrete" is used to differentiate it from a logarithm. Wikipedia defines a ...
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