Power Residue Symbol Order Detecting Algorithm for Subset Product over Algebraic Integers

Trey Li

Paper 2022/1310

Power Residue Symbol Order Detecting Algorithm for Subset Product over Algebraic Integers

Trey Li

Abstract

We give a probabilistic polynomial time algorithm for high F_ell-rank subset product problem over the order O_K of any algebraic field K with O_K a principal ideal domain and the ell-th power residue symbol in O_K polynomial time computable, for some rational prime ell.

Note: This is the 3rd paper of the series.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Subset product Unique factorization domain Power residue symbol Order detect Algorithm Characteristic matrix Rank
Contact author(s): treyquantum @ gmail com
History: 2022-10-03: approved; 2022-10-03: received; See all versions
Short URL: https://ia.cr/2022/1310
License: CC BY

BibTeX

@misc{cryptoeprint:2022/1310,
      author = {Trey Li},
      title = {Power Residue Symbol Order Detecting Algorithm for Subset Product over Algebraic Integers},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1310},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/1310}},
      url = {https://eprint.iacr.org/2022/1310}
}