Assume factorization of $N$ is unknown. What is the best complexity we know to find roots of the irreducible equation $$ax^2+bx+c\equiv0\bmod N?$$


Is this problem equivalent to any hardness results?



On roots of irreducible quadratics modulo composites
Ability to find all roots leads to finding factorization of $N$. For example, if $N=pq$ is a product of two odd primes, and we find a root $x'$ of $x^2-1\equiv 0\pmod N$ such that $x'\equiv 1\pmod p$ and $x'\equiv -1\pmod q$, then we can compute $p$ as $\gcd(N,x'-1)$.


