All Questions

Let $n \in \mathbb{N}$ be a predefined integer. Consider the following bijection (between the ring of integers modulo $2^n$ and finite field with $2^n$ elements: $$ \phi: \mathbb{Z}_{2^n} \to \mathbb{...

The recent papers: R. Granger, T. Kleinjung, J. Zumbragel, "On the Discrete Logarithm Problem in Finite Fields of Fixed Characteristic," Trans. Amer. Math. Soc., 370(5) (2018), 3129–3145. T....

In the Schoof's algorithm we are particularly interested in $char(K)>3$, where $K$ is the field. I know Schoof's algorithm is mostly used over large prime fields. Also, when we are transforming ...

I'm trying to solve efficiently a quadratic equation in the finite field $\text{GF}(2^{128})$ represented as $(\mathbb{Z}/2\mathbb{Z})[x] / (x^{128} + x^7 + x^2 + x + 1)$. Until now, I came across ...

As far I understand, when it comes to finite fields, Pollard rho and Pollard’s lambda are still the best algorithm for solving discrete logarithms in a multiplicative subgroup/suborder… Index calculus ...