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Chapter and Conference Paper
Algorithms for Matrix Code and Alternating Trilinear Form Equivalences via New Isomorphism Invariants
We devise algorithms for finding equivalences of trilinear forms over finite fields modulo linear group actions. Our focus is on two problems under this umbrella, Matrix Code Equivalence (MCE) and Alternating Tri...
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Chapter and Conference Paper
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-knowledge protocol for graph ...
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Chapter and Conference Paper
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-way group actions no longer stand...
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Chapter and Conference Paper
On the Complexity of Trial and Error for Constraint Satisfaction Problems
In a recent work of Bei, Chen and Zhang (STOC 2013), a trial and error model of computing was introduced, and applied to some constraint satisfaction problems. In this model the input is hidden by an oracle wh...
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Chapter and Conference Paper
Polynomial-Time Isomorphism Test for Groups with No Abelian Normal Subgroups
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial n logn bound on the time complexity for the general case has not been impro...
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Chapter and Conference Paper
Counting Method for Multi-party Computation over Non-abelian Groups
In the Crypto’07 paper [5], Desmedt et al. studied the problem of achieving secure n-party computation over non-Abelian groups. The function to be computed is f G ...