• Honam Mathematical Journal
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• v.35 no.4
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• pp.793-808
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• 2013

An interpolation-based unique decoding algorithm of Algebraic Geometry codes was recently introduced. The algorithm iteratively computes the sent message through a majority voting procedure using the Gr$\ddot{o}$bner bases of interpolation modules. We now combine the main idea of the Guruswami-Sudan list decoding with the algorithm, and thus obtain a hybrid unique decoding algorithm of plane AG codes, significantly improving the decoding speed.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.43-54
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• 2002

McEliece introduced a public-key cryptosystem based on Algebraic codes, specially binary classical Goppa which have a good decoding algorithm and vast number of inequivalent codes with given parameters. And the advantage of this system low cost of their encryption and decryption procedures compared with other public-key systems specially RSA, ECC based on DLP(discrete logarithm problem). But in [1], they resent new attack based on probabilistic algorithm to find minimum weight codeword, so for a sufficient security level, much larger parameter size [2048, 1608,81]is required. Then the big size of public key make McEliece PKC more inefficient. So in this paper, we will propose New Type PKC using q-ary Hyperelliptic code so that with smaller parameter(1 over 3) but still work factor as hi인 as McEliece PKC and faster encryption, decryption can be maintained.

• Journal of Communications and Networks
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• v.15 no.2
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.119-125
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• 2005

We propose a new code-based publick key encryption scheme. It is obtained by modifying the Augot and Finiasz scheme proposed at Eurocrypt 2003. We replace the Reed-Solomon codes with general algebraic-geometry codes and employ Guruswami-Sudan decoding algorithm for decryption. The scheme is secure against Colon's attack or Kiayias and Yung's attack to which the Augot and Finiasz scheme is vulnerable. Considering basic attacks aprlied to the Augot and Finiasz scheme, we claim that the proposed scheme provides similar security levels as the Augot and Finiasz scheme was claimed to provide for given key lengths.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.83-98
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• 2014

We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gr$\ddot{o}$bner bases of modules on the coordinate ring of the base curve. The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding. Moreover the smaller Gr$\ddot{o}$bner bases imply smaller space and time complexity of the algorithm.