How to Achieve a McEliece-Based Digital Signature Scheme
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Semantic security for the McEliece cryptosystem without random oracles
Designs, Codes and Cryptography
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
McEliece and niederreiter cryptosystems that resist quantum fourier sampling attacks
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Code equivalence and group isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Further results on the semilinear equivalence of linear codes
Information Sciences: an International Journal
| Hi-index | 754.84 |
We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem code equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not collapse, code equivalence is not NP-complete. On the other hand, we present a polynomial-time reduction from the graph isomorphism problem to code equivalence. Thus if one could find an efficient (i.e., polynomial-time) algorithm for code equivalence, then one could settle the long-standing problem of determining whether there is an efficient algorithm for solving graph isomorphism