Optimized Discrete Logarithm Computation for Faster Square Roots in Finite Fields

ePrint Report: Optimized Discrete Logarithm Computation for Faster Square Roots in Finite Fields

Thomas Pornin

For computing square roots in a finite field $GF(q)$ where $q - 1 = 2^n m$ for an odd integer $m$ and some integer $n$, the classic Tonelli-Shanks algorithm starts with an exponentiation (the exponent has size about $\log_2 q - n$ bits), followed by a discrete logarithm computation in the subgroup of $2^n$-th roots of unity in $GF(q)$; the latter operation has cost $O(n^2)$ …

algorithm computation computing eprint report integer report square thomas