Index calculus

In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ${\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}}$ where ${\displaystyle q}$ is a prime, index calculus lead to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete logarithms of small primes, computes them by a linear algebra procedure and finally expresses the desired discrete logarithm with respect to the discrete logarithms of small primes.

Roughly speaking, the discrete log problem asks us to find an x such that ${\displaystyle g^{x}\equiv h{\pmod {n}}}$, where g, h, and the modulus n are given.

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