# Mathematical Models of Modified Crypto-Code Means of Information Protection Based on Coding Theory Schemes

Published on Jul 1, 2019in Automation and Remote Control 0.59
· DOI :10.1134/S0005117919070087
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Abstract
We develop mathematical models of modified crypto-code means of information protection based on the McEliece coding theory scheme using algebro-geometric block codes with shortening and extending of the information package, analyze the security and power costs of their software implementation.
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Published on Nov 13, 2017in Cluster Computing 1.85
Guangzhi Zhang2
Estimated H-index: 2
(HEU: Harbin Engineering University),
Shaobin Cai1
Estimated H-index: 1
(HEU: Harbin Engineering University)
+ 1 AuthorsDongqiu Zhang1
Estimated H-index: 1
The McEliece cryptosystem based on quasi-cyclic low-density parity check (QC-LDPC) codes is presented to offer both security and error-correction simultaneously in network coding system. The characteristics of the cryptosystem make it does not need to reduce information rate additionally to offer security. The messages $$\mu$$ is coded into x with QC-LDPC. x is transmitted through a network where a MDS network coding error-correcting scheme is performed. $$\rho$$ links are observed by adversar...
Published on Nov 6, 2017in Cluster Computing 1.85
Guangzhi Zhang2
Estimated H-index: 2
(HEU: Harbin Engineering University),
Shaobin Cai1
Estimated H-index: 1
(HEU: Harbin Engineering University)
The McEliece cryptosystem based on rank-metric codes is presented to offer both security and error-correction simultaneously in random network coding system. In the multicast network, the original messages are encoded with McEliece cryptosystem based on Gabidulin codes. Key distribution will be done one time. The rank codes decoding is performed in the sink. As long as $$t < {d_R}\left( C \right) /2$$, the decoding is guaranteed, where t is the number of corrupted packets and \({d_R}\left( C \ri...
Published on Apr 30, 2017
Joo Yeon Cho8
Estimated H-index: 8
(ADVA Optical Networking),
Helmut Griesser13
Estimated H-index: 13
(ADVA Optical Networking),
Danish Rafique5
Estimated H-index: 5
(ADVA Optical Networking)
The McEliece cryptosystem is one of the public-key cryptosystems that do not have known vulnerabilities to attacks using quantum computers. However, the McEliece cryptosystem has not been widely used for practical applications due to the large key size. We present an authenticated key exchange protocol based on the McEliece cryptosystem. We show that the proposed protocol is well suited for the G.709 Optical Transport Network (OTN) framework and satisfies a typical key refreshing rate used in in...
Published on Jan 5, 2017
Kirill Morozov9
Estimated H-index: 9
,
Partha Sarathi Roy2
Estimated H-index: 2
(Kyushu University),
Kouichi Sakurai26
Estimated H-index: 26
(Kyushu University)
In this work, we construct a dual version of statistically binding commitment scheme by Jain et al. (Asiacrypt 2012) with shorter commitment size under hardness of syndrome decoding. Then, we point out that perfectly binding variants of the above schemes follow directly from the Randomized McEliece and Niederreiter public key encryption schemes, assuming indistinguishability of permuted Goppa codes, as well as hardness of the exact learning parity with noise (xLPN) problem (for the McEliece sche...
Published on Apr 1, 2016
Lidong Chen7
Estimated H-index: 7
,
Stephen P. Jordan1
Estimated H-index: 1
+ 4 AuthorsDaniel C. Smith-Tone6
Estimated H-index: 6
Published on Jan 1, 2016
S.H.S. de Vries1
Estimated H-index: 1
Niederreiter is a candidate post-quantum cryptosystem. Its large public key size currently discourages its use in practice. We demonstrate and evaluate how Niederreiter can be used for quantum-secure key exchanges by implementing it in OpenVPN. We contribute an analysis of how much Grover’s algorithm can speed up existing attacks on Niederreiter and McEliece and what code parameters can protect against these attacks. We provide parameters for 128-bit quantum security that result in almost 35% sm...
Published on Aug 14, 2011 in CRYPTO (International Cryptology Conference)
Hang Dinh5
Estimated H-index: 5
(Indiana University South Bend),
Cristopher Moore41
Estimated H-index: 41
(UNM: University of New Mexico),
Alexander Russell26
Estimated H-index: 26
(UConn: University of Connecticut)
Quantum computers can break the RSA, El Gamal, and elliptic curve public-key cryptosystems, as they can efficiently factor integers and extract discrete logarithms. This motivates the development of post-quantum cryptosystems: classical cryptosystems that can be implemented with today's computers, that will remain secure even in the presence of quantum attacks. In this article we show that the McEliece cryptosystem over rational Goppa codes and the Niederreiter cryptosystem over classical Goppa ...
Published on Jan 1, 1983
Richard E. Blahut1
Estimated H-index: 1
Published on Jun 30, 1981
George C. Clark1
Estimated H-index: 1
,
J. Bibb Cain5
Estimated H-index: 5
1. Fundamental Concepts of Coding.- 2. Group Codes.- 3. Simple Nonalgebraic Decoding Techniques for Group Codes.- 4. Soft Decision Decoding of Block Codes.- 5. Algebraic Techniques for Multiple Error Correction.- 6. Convolutional Code Structure and Viterbi Decoding.- 7. Other Convolutional Decoding Techniques.- 8. System Applications.- Appendix A. Code Generators for BCH Codes.- Appendix B. Code Generators for Convolutional Codes.- B.1. Viterbi Decoding.- B.2. Table Look-up Decoding.- B.3. Thres...
Published on Jan 1, 1977
Florence Jessie MacWilliams1
Estimated H-index: 1
,
N. J. A. Sloane59
Estimated H-index: 59
Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, Designs and Perfect Codes. Cyclic Codes. Cyclic Codes: Idempotents and Mattson-Solomon Polynomials. BCH Codes. Reed-Solomon and Justesen Codes. MDS Codes. Alternant, Goppa and Other Generalized BCH Codes. Reed-Muller Codes. First-Order Reed-Muller Codes. Second-Order Reed-Muller, Kerdock and Preparata Codes. ...
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