# Questions tagged [discrete-logarithm]

In cryptography, a discrete logarithm is the number of times a generator of a group must be multiplied by itself to produce a known number. By choosing certain groups, the task of finding a discrete logarithm can be made intractable.

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### Is $H:\mathbb{Z} \rightarrow \mathbb{Z}_{p}^{*}$ and $a \mapsto g^a\bmod p$ with $p$ prime (strongly) collision-free?

Let $H:\mathbb{Z} \rightarrow \mathbb{Z}_{p}^{*}$ and $a \mapsto g^a\bmod p$ for $g \in \mathbb{Z}_{p}^{*}$ where $p$ is prime. Is this function (strongly) collision-free meaning we cannot find ...
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### Group Signature by Camenisch and Stadler

Page 8, Paper: "Efficient Group Signature Schemes for Large Groups" by Camenisch and Stadler (1) I was trying to understand membership certificate part. I am have only basic knowledge of ...
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### How to factorize the group order in Pohlig-Hellman algorithm

The Pohlig-Hellman algorithm is for computing discrete logarithms in a group whose order is a smooth integer. This algorithm requires the factorization of the group order. However we know that ...
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### Independent parameters basis for torsion-groups in SIDH: Is the Weil-pairing necessary?

In the original SIDH paper by De Feo, Jao and Plût, the basis points $P_A$ and $Q_A$ are supposed to be independent points in $E(\mathbb{F}_{p^2})$ of order $\ell_A^{e_A}$ for some small prime $\ell_A$...
### Use the Index Calculus to solve for $19^x \equiv 205\pmod{337}$, using the factor base $B=\{2,3,5,7\}$
I'm supposed to use the following information to solve the question, but I don't know how. \begin{align} 19^2 &\equiv 2^3 \times 3^1 \times 5^0 \times 7^0&\pmod{337}\\ 19^5 &\equiv 2^5 \...
Is the solution to a discrete logarithm a reasonable commitment scheme? By my analysis, the following scheme is a reasonable commitment scheme: Let $p$ and $q$ be large primes such that $q∣(p−1)$, let ...