Practical post-quantum signature schemes from isomorphism problems of trilinear forms
In this paper, we propose a practical signature scheme based on the alternating trilinear
form equivalence problem. Our scheme is inspired by the Goldreich-Micali-Wigderson's zero …
form equivalence problem. Our scheme is inspired by the Goldreich-Micali-Wigderson's zero …
On the complexity of isomorphism problems for tensors, groups, and polynomials I: tensor isomorphism-completeness
We study the complexity of isomorphism problems for tensors, groups, and polynomials.
These problems have been studied in multivariate cryptography, machine learning, quantum …
These problems have been studied in multivariate cryptography, machine learning, quantum …
General linear group action on tensors: A candidate for post-quantum cryptography
Starting from the one-way group action framework of Brassard and Yung (Crypto'90), we
revisit building cryptography based on group actions. Several previous candidates for one …
revisit building cryptography based on group actions. Several previous candidates for one …
Faster Isomorphism for 𝑝-Groups of Class 2 and Exponent 𝑝
X Sun - Proceedings of the 55th Annual ACM Symposium on …, 2023 - dl.acm.org
The group isomorphism problem determines whether two groups, given by their Cayley
tables, are isomorphic. For groups with order n, an algorithm with n (log n+ O (1)) running …
tables, are isomorphic. For groups with order n, an algorithm with n (log n+ O (1)) running …
Code equivalence and group isomorphism
The isomorphism problem for groups given by their multiplication tables has long been
known to be solvable in time n log n+ O (1). The decades-old quest for a polynomial-time …
known to be solvable in time n log n+ O (1). The decades-old quest for a polynomial-time …
On p-Group Isomorphism: Search-to-Decision, Counting-to-Decision, and Nilpotency Class Reductions via Tensors
JA Grochow, Y Qiao - ACM Transactions on Computation Theory, 2024 - dl.acm.org
In this article, we study some classical complexity-theoretic questions regarding Group
Isomorphism (GpI). We focus on p-groups (groups of prime power order) with odd p, which …
Isomorphism (GpI). We focus on p-groups (groups of prime power order) with odd p, which …
[HTML][HTML] A fast isomorphism test for groups whose Lie algebra has genus 2
Motivated by the desire for better isomorphism tests for finite groups, we present a
polynomial-time algorithm for deciding isomorphism within a class of p-groups that is well …
polynomial-time algorithm for deciding isomorphism within a class of p-groups that is well …
Algorithms based on*-algebras, and their applications to isomorphism of polynomials with one secret, group isomorphism, and polynomial identity testing
We consider two basic algorithmic problems concerning tuples of (skew-) symmetric
matrices. The first problem asks us to decide, given two tuples of (skew-) symmetric matrices …
matrices. The first problem asks us to decide, given two tuples of (skew-) symmetric matrices …
Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions
JA Grochow, Y Qiao - arXiv preprint arXiv:1907.00309, 2019 - arxiv.org
In this paper we consider the problems of testing isomorphism of tensors, $ p $-groups,
cubic forms, algebras, and more, which arise from a variety of areas, including machine …
cubic forms, algebras, and more, which arise from a variety of areas, including machine …