# 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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### Help me out with this algorithm I came across [closed]

I saw this question on my email sent by my colleague to check out. I am still confused with this question; $\begin{cases}20^6 \mod 12 = 4\\ 33^2 \mod 10 = 9\end{cases}$. The question can be seen like ...
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### The Discrete Logarithm

Can someone help me out with explaining the discrete logarithm in lay man's term. here's the Wikipedia article: https://en.wikipedia.org/wiki/Discrete_logarithm
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### DLP - formulae for length of $G_{list}$ in terms of prime $p$ for $g=2,3,…$

The DLP is defined as: $$g^x \cong h \pmod{p}$$ Using $g=2$ and $g=3$ I've found that the size of list of unique $h$ values (I call the $G_{list}$) for primes from $p=3$ upto $p=19$ are of the form ...
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### How do I solve this logarithmic equation, which has an answer of 7? [closed]

$$10 - \log_5{20} - \log_5{25\over4}$$ The $5$'s are the bases and the answer to this equation is $7$, but I don't know how to solve it.
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### primitive root of a number

Here in the definition of primitive root, it states: "a to be a primitive root modulo n, φ(n) has to be the smallest power of a which is congruent to 1 modulo n" (taking the set of integers) What my ...
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### Finding all solutions of 'Discrete Root'

Ques: $x^k \equiv a \pmod n$, where n is prime. What are the possible values of x? I know how to find a discrete root using both primitive root and discrete logarithm concepts. But I am wondering ...
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### Solving DLP using the method of Pohlig-Hellman

I want to solve the DLP for $p=29$, $a=2$ and $b=5$ using the method of Pohlig-Hellman.  I have done the following: We have that $p-1=28=2^2\cdot 7$. We get \begin{align*}&x_2= x\pmod {...
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### Distribution of elements of a particular order in $(\mathbb{Z}/m\mathbb{Z})^*$

Consider the group $G = (\mathbb{Z}/m\mathbb{Z})^*$, where $m$ is such that $G$ is cyclic. Let $g\in G$ be some fixed generator, and let $a_1,\dots,a_{\varphi(m)}$ be an enumeration of the elements of ...
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### Geometric interpretation of the Logarithm (in $\mathbb{R}$)

(Note: limited to $\mathbb{R}$) (Note: Geometric here means with straightedge and compass) Standard approaches to introducing the concept of Logarithm rely on a previous exposition of the ...
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### Solve for $b$ in the equation $2^b \equiv 893 \pmod{1373}$

The question asks to solve for $b$ in the following equation: $2^b \equiv 893 \pmod{1373}$ However I am not sure how to solve this, as I only know how to solve for integers on the left hand side. The ...
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### Is it possible to find such a $n\in \mathbb {Z^{+}}$, for given value of $\lambda;$ $\frac {2^{10+\lambda+n}-2^{10+\lambda}-144759}{3^{10}}<349525$
I'm trying to solve a mathematical problem. I expressed the point where I was stuck with the modular arithmetic. Here is my problem; Is it possible to find such a $n\in \mathbb {Z^{+}}$, for given ...