Decoding Generalized ReedSolomon Codes and Its Application to RLCE Encryption Schemes
Abstract
This paper compares the efficiency of various algorithms for implementing quantum resistant public key encryption scheme RLCE on 64bit CPUs. By optimizing various algorithms for polynomial and matrix operations over finite fields, we obtained several interesting (or even surprising) results. For example, it is well known (e.g., Moenck 1976 \cite{moenck1976practical}) that Karatsuba's algorithm outperforms classical polynomial multiplication algorithm from the degree 15 and above (practically, Karatsuba's algorithm only outperforms classical polynomial multiplication algorithm from the degree 35 and above ). Our experiments show that 64bit optimized Karatsuba's algorithm will only outperform 64bit optimized classical polynomial multiplication algorithm for polynomials of degree 115 and above over finite field $GF(2^{10})$. The second interesting (surprising) result shows that 64bit optimized Chien's search algorithm ourperforms all other 64bit optimized polynomial root finding algorithms such as BTA and FFT for polynomials of all degrees over finite field $GF(2^{10})$. The third interesting (surprising) result shows that 64bit optimized Strassen matrix multiplication algorithm only outperforms 64bit optimized classical matrix multiplication algorithm for matrices of dimension 750 and above over finite field $GF(2^{10})$. It should be noted that existing literatures and practices recommend Strassen matrix multiplication algorithm for matrices of dimension 40 and above. All our experiments are done on a 64bit MacBook Pro with i7 CPU and single thread C codes. It should be noted that the reported results should be appliable to 64 or larger bits CPU architectures. For 32 or smaller bits CPUs, these results may not be applicable. The source code and library for the algorithms covered in this paper are available at http://quantumca.org/.
 Publication:

arXiv eprints
 Pub Date:
 February 2017
 arXiv:
 arXiv:1702.07737
 Bibcode:
 2017arXiv170207737W
 Keywords:

 Computer Science  Information Theory