• Corpus ID: 16050720

Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes

@article{Wang2017DecodingGR,
  title={Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes},
  author={Yongge Wang},
  journal={ArXiv},
  year={2017},
  volume={abs/1702.07737}
}
  • Yongge Wang
  • Published 1 February 2017
  • Computer Science
  • ArXiv
This paper compares the efficiency of various algorithms for implementing quantum resistant public key encryption scheme RLCE on 64-bit 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… 

Tables from this paper

Revised Quantum Resistant Public Key Encryption Scheme RLCE and IND-CCA2 Security for McEliece Schemes
  • Yongge Wang
  • Computer Science, Mathematics
    IACR Cryptol. ePrint Arch.
  • 2017
TLDR
It is shown that RLCE schemes have smaller public key sizes compared to binary Goppa code based McEliece encryption schemes for corresponding security levels, and message padding schemes for RLCE to achieve IND-CCA2 security.
Computer Algebra Tales on Goppa Codes and McEliece Cryptography
The 40-year old McEliece public-key crypto-system is revisited with the help of recently developed resources: an improved Peterson–Gorenstein–Zierler decoder for alternant error-correcting codes;

References

SHOWING 1-10 OF 23 REFERENCES
Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes
  • M. Alekhnovich
  • Computer Science
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
This work presents a new fast algorithm for soft-decoding of Reed-Solomon codes different from the procedure proposed by Feng (1999), which works in time (w/r)/sup O(1)/ n log/sup 2/ n loglogn, where r is the rate of the code, and w is the maximal weight assigned to a vertical line.
An Interpolation Procedure for List Decoding Reed–Solomon Codes Based on Generalized Key Equations
TLDR
A link is provided between syndrome-based decoding approaches based on Key Equations and the interpolation-based list decoding algorithms of Guruswami and Sudan for Reed-Solomon codes, capable of decoding beyond half the minimum distance.
Quantum resistant random linear code based public key encryption scheme RLCE
  • Yongge Wang
  • Computer Science, Mathematics
    2016 IEEE International Symposium on Information Theory (ISIT)
  • 2016
TLDR
The analysis shows that the scheme RLCE is secure against existing attacks and it is hoped that the security of the RLCE scheme is equivalent to the hardness of decoding random linear codes.
Revised Quantum Resistant Public Key Encryption Scheme RLCE and IND-CCA2 Security for McEliece Schemes
  • Yongge Wang
  • Computer Science, Mathematics
    IACR Cryptol. ePrint Arch.
  • 2017
TLDR
It is shown that RLCE schemes have smaller public key sizes compared to binary Goppa code based McEliece encryption schemes for corresponding security levels, and message padding schemes for RLCE to achieve IND-CCA2 security.
Improved decoding of Reed-Solomon and algebraic-geometric codes
  • V. Guruswami, M. Sudan
  • Computer Science
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
TLDR
An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometric codes is presented, including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed- Solomon codes.
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
A list decoding algorithm is presented for the family of generalized Reed-Solomon (GRS) codes, capable of correcting a number of errors greater than half the minimum distance d of the code. Based on
Fast generalized minimum-distance decoding of algebraic-geometry and Reed-Solomon codes
TLDR
An efficient general GMD decoding scheme for linear block codes in the framework of error-correcting pairs is derived and it is shown that it can find all relevant error-erasure-locating functions with complexity O(o/ sub 1/nd), where o/sub 1/ is the size of the first nongap in the function space associated with the code.
Decoding of Reed Solomon Codes beyond the Error-Correction Bound
TLDR
To the best of the knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides error recovery capability beyond the error-correction bound of a code for any efficient code.
Accelerating Cryptanalysis with the Method of Four Russians
  • G. Bard
  • Computer Science, Mathematics
    IACR Cryptol. ePrint Arch.
  • 2006
TLDR
This paper specifies an algorithm that is much faster than both Gaussian Elimination and Strassen's Algorithm in practice, and performance is formally modeled, and experimental running times are provided, including for the optimal setting of the algorithm’s parameter.
Improved decoding of Reed-Solomon and algebraic-geometry codes
TLDR
An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometry codes is presented and a solution to a weighted curve-fitting problem is presented, which may be of use in soft-decision decoding algorithms for Reed- Solomon codes.
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