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A Terr algorithm for computations in the infrastructure of real-quadratic number fields

Johannes BuchmannUlrich Volmer — 2006

Journal de Théorie des Nombres de Bordeaux

We show how to adapt Terr’s variant of the baby-step giant-step algorithm of Shanks to the computation of the regulator and of generators of principal ideals in real-quadratic number fields. The worst case complexity of the resulting algorithm depends only on the square root of the regulator, and is smaller than that of all other previously specified unconditional deterministic algorithm for this task.

Cryptography based on number fields with large regulator

Johannes BuchmannMarkus MaurerBodo Möller — 2000

Journal de théorie des nombres de Bordeaux

We explain a variant of the Fiat-Shamir identification and signature protocol that is based on the intractability of computing generators of principal ideals in algebraic number fields. We also show how to use the Cohen-Lenstra-Martinet heuristics for class groups to construct number fields in which computing generators of principal ideals is intractable.

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