5 problems

Let $N\geqslant 2$ and let $\delta$ be the order-finding parameter in an algorithm that returns either an element of $\mathbb{Z}_N^*$ of order greater than $\delta$, a nontrivial f…

Let $\mathrm{IF}$ denote the integer factorization problem, and let $\mathrm{P}$ and $\mathrm{NP}$ denote the standard classical complexity classes. A problem is NP-intermediate if…

Let $x$ be a positive integer, let $B=L(\alpha,x):=\exp(\alpha\sqrt{\log x\log\log x})$ with $\alpha>0$, and let $s_B(m)$ denote the largest $B$-smooth divisor of $m$. Define … and…

Hyperbola-based factoring conjecture. The set $\Gamma$ has exactly three elements and satisfies

A quadratic polynomial modulo a prime induces an iteration on the residue classes modulo that prime; its rho length is the length statistic arising from the resulting orbit structu…