On Mon, Jan 31, 2022 at 8:13 AM, Stefan Claas
   <stefan@ctemplar.com> wrote:
   --------- Original Message ----------
   On Sun, January 30, 2022 at 8:15 PM,  [1]grarpamp@gmail.com wrote:
   On 1/30/22, jim bell  wrote:
   > Quantum Computing Threatens Everything — Could it be Worse Than the
   > Apocalypse?
   >
   >> [2]https://www.entrepreneur.com/article/404091
   >
   >> Jim Bell's comment:
   >>  Headline sounds overblown, but...
   >What are peoples current estimated years for when QC will...
   a) Break some of today's modern yet non-PQC cryptosystems?
   I seem to recall that cryptosystems based on multi-dimensional lattices
   are thought to be quantum-resistant.
   https://en.wikipedia.org/wiki/Lattice-based_cryptography?wprov=sfla1
   From that:
   "Lattice-based cryptography is the generic term for constructions
   of [3]cryptographic primitives that involve [4]lattices, either in the
   construction itself or in the security proof. Lattice-based
   constructions are currently important candidates for [5]post-quantum
   cryptography. Unlike more widely used and known public-key schemes such
   as the [6]RSA, [7]Diffie-Hellman or [8]elliptic-curve cryptosystems,
   which could, theoretically, be [9]easily attacked by a [10]quantum
   computer, some lattice-based constructions appear to be resistant to
   attack by both classical and quantum computers. Furthermore, many
   lattice-based constructions are considered to be secure under
   the [11]assumption that certain well-studied [12]computational lattice
   problems cannot be solved efficiently."
   (End of quote)
   An RSA-type system depends on the difficulty of factoring a huge
   composite number, but I think that involves only one 'degree of
   freedom'.   That is, as your guess for one factor goes up, the other
   goes down.
   However, finding distances in a large-dimensional lattice might involve
   as many degrees of freedom as dimensions, or maybe (dimensions minus
   1).  Perhaps this is what would defeat quantum calculations.

References

   1. mailto:grarpamp@gmail.com
   2. https://www.entrepreneur.com/article/404091
   3. https://en.wikipedia.org/wiki/Cryptographic_primitive
   4. https://en.wikipedia.org/wiki/Lattice_(group)
   5. https://en.wikipedia.org/wiki/Post-quantum_cryptography
   6. https://en.wikipedia.org/wiki/RSA_(cryptosystem)
   7. https://en.wikipedia.org/wiki/Diffie-Hellman
   8. https://en.wikipedia.org/wiki/Elliptic-curve_cryptography
   9. https://en.wikipedia.org/wiki/Shor's_algorithm
  10. https://en.wikipedia.org/wiki/Quantum_computing
  11. https://en.wikipedia.org/wiki/Computational_hardness_assumption
  12. https://en.wikipedia.org/wiki/Lattice_problem