The 2001 paper Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes (Boneh & Venkatesan, 2001) attempts to answer the question: is it easier to calculate just a few bits of a secret key than the entire secret?

Along the way, this paper introduces the hidden number problem: the challenge of recovering a secret hidden number given partial knowledge of its linear relations (Surin & Cohney, 2023)

As it turns out, this problem is difficult even for quantum computers. So hidden number problems are at the heart of post-quantum cryptography.