Discrete Logarithms

Log(b, x): QuadBinElt, QuadBinElt -> RngIntElt

The discrete logarithm of binary quadratic form \(x\) with respect to base \(b\), or -1 if Magma can that determine no solution exists. This function exists only for negative discriminant forms. Computation is done via the Pohlig-Hellman algorithm along with a collision search subroutine (a variant of Pollard’s rho method). If the user is unsure whether a solution exists, it is safest to use Log with a time limit (see below) to prevent an infinite loop in the collision search.

Log(b, x, t): QuadBinElt, QuadBinElt, RngIntElt -> RngIntElt

Searches for up to \(t\) seconds for the discrete logarithm of binary quadratic form \(x\) with respect to base \(b\). This function exists only for negative discriminant forms. If Magma is able to determine no solution exists, then -1 will be returned. If no solution is found within the given time frame, then -2 will be returned. Computation is done via the Pohlig-Hellman algorithm along with a collision search subroutine (a variant of Pollard’s rho method).