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The special case of cyclotomic fields in quantum algorithms for unit groups. (arXiv:2303.03978v1 [cs.CR])
cs.CR updates on arXiv.org arxiv.org
Unit group computations are a cryptographic primitive for which one has a
fast quantum algorithm, but the required number of qubits is $\tilde O(m^5)$.
In this work we propose a modification of the algorithm for which the number of
qubits is $\tilde O(m^2)$ in the case of cyclotomic fields. Moreover, under a
recent conjecture on the size of the class group of $\mathbb{Q}(\zeta_m +
\zeta_m^{-1})$, the quantum algorithms is much simpler because it is a hidden
subgroup problem (HSP) algorithm …
algorithm algorithms case class fast modification quantum quantum algorithms qubits size special under work