### Code Equivalence in the Sum-Rank Metric: Hardness and Completeness

##### Abstract

In this work, we define and study equivalence problems for sum-rank codes, giving their formulation in terms of tensors. Moreover, we introduce the concept of generating tensors of a sum-rank code, a direct generalization of the generating matrix for a linear code endowed with the Hamming metric. In this way, we embrace well-known definitions and problems for Hamming and rank metric codes. Finally, we prove the TI-completeness of code equivalence for rank and sum-rank codes, and hence, in the future, these problems could be used in the design of post-quantum schemes.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint.
Keywords
Code Equivalence Sum-Rank Metric Rank Metric Tensor Isomorphism
Contact author(s)
giuseppe dalconzo @ polito it
History
2022-07-28: approved
See all versions
Short URL
https://ia.cr/2022/968

CC BY

BibTeX

@misc{cryptoeprint:2022/968,
author = {Giuseppe D'Alconzo},
title = {Code Equivalence in the Sum-Rank Metric: Hardness and Completeness},
howpublished = {Cryptology ePrint Archive, Paper 2022/968},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/968}},
url = {https://eprint.iacr.org/2022/968}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.