Abstract
In this paper we analyze computational properties of the Diophantine problem (and its search variant) for spherical equations (Formula presented (and their variants) over the class of finite metabelian groups (Formula presented), where n ∈ N and p is prime. We prove that the problem of finding solutions for certain constrained spherical equations is computationally hard on average (assuming that some lattice approximation problem is hard in the worst case).
| Original language | English |
|---|---|
| Pages (from-to) | 3:1-3:18 |
| Journal | Groups, Complexity, Cryptology |
| Volume | 16 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2024 |
Keywords
- Spherical equations
- average case complexity
- finite groups
- group-based cryptography
- hash function family
- metabelian groups
- semidirect products
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