discretelog

To solve the discrete logarithm problem using Shor's algorithm, this Skill constructs a two-register QPE circuit with an IQFT to find the period, then applies classical post-processing via continued fractions to recover the exponent x from measured indices.

A two-register QPE circuit estimates the phase of a modular exponentation unitary. It works by applying an Inverse Quantum Fourier Transform (IQFT) to extract phase indices, which classical post-processing then maps to the discrete logarithm solution.

You can calculate discrete logarithms for a prime modulus P in polynomial time by running a quantum period-finding simulation. The Skill automates the circuit construction and result visualization for problems formatted as g^x ≡ y (mod P).

No, you cannot use this quantum algorithm simulation if your base g and target y are not coprime to P. The quantum period-finding approach strictly requires both g and y to be coprime to the prime modulus P to function correctly.

Yes, the discrete logarithm quantum simulation handles classical post-processing automatically. It executes a built-in routine to recover the order r and extract the discrete logarithm x from the measured indices using continued fractions.

A key limitation of using quantum period finding for cryptography research here is simulation scale; while the algorithm runs in polynomial time relative to the bit-length of P, circuit simulation requires valid coprime inputs and proper two-register QPE setup.