• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.4
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• pp.910-922
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• 2013

In 2008, Chin et al. proposed an efficient and provable secure identity-based identification scheme in the standard model. However, we discovered a subtle flaw in the security proof which renders the proof of security useless. While no weakness has been found in the scheme itself, a scheme that is desired would be one with an accompanying proof of security. In this paper, we provide a fix to the scheme to overcome the problem without affecting the efficiency as well as a new proof of security. In particular, we show that only one extra pre-computable pairing operation should be added into the commitment phase of the identification protocol to fix the proof of security under the same hard problems.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.101-116
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• 2005

The purpose of this study is to survey mathematics teacher's cognition of proof along with their proof forms of expression and proof ability, and to explore the relationship between their proof scheme and teaching practice. This study shows that mathematics teachers tend to regard proof as a deduction from assumption to conclusion and that they prefer formal proof with mathematical symbols. Mathematics teachers also recognize that prof is an important area in school mathematics but they reveal poor understanding of teaching methods of proof. Teachers tend to depend on the proof style employed in mathematics textbooks. This study demonstrates that a proof scheme is a major factor of determining the teaching method of proof.

• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.191-205
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• 2017

The purpose of this study is to investigate the types and characteristics of the Seventh Graders' proofs. Harel, & Sowder's proof schemes were used to analyze the subjects' responses. As a result of the study, there was a difference in the type of proof schemes used by the students depending on the academic achievement level. While the proportion of students using a transformative proof scheme decreased from the top to the bottom, the proportion of students using inductive (measure) proof scheme increased. In addition, features of each type of proof schemes were shown, such as using informal codes in the proof process, and dividing a given picture into a specific ratio in the problem. Based on this, we extracted four meaningful conclusions and discussed implications for proof teaching and learning.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.7
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• pp.2532-2553
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• 2014

In Asiacrypt 2003, Al-Riyami and Paterson proposed the notion of certificateless cryptography, a technique to remove key escrow from traditional identity-based cryptography as well as circumvent the certificate management problem of traditional public key cryptography. Subsequently much research has been done in the realm of certificateless encryption and signature schemes, but little to no work has been done for the identification primitive until 2013 when Chin et al. rigorously defined certificateless identification and proposed a concrete scheme. However Chin et al.'s scheme was proven in the random oracle model and Canetti et al. has shown that certain schemes provable secure in the random oracle model can be insecure when random oracles are replaced with actual hash functions. Therefore while having a proof in the random oracle model is better than having no proof at all, a scheme to be proven in the standard model would provide stronger security guarantees. In this paper, we propose the first certificateless identification scheme that is both efficient and show our proof of security in the standard model, that is without having to assume random oracles exist.

• The Journal of the Korea Contents Association
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• v.19 no.9
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• pp.637-645
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• 2019

The RFID group proof is an extension of the yoking proof proving that multiple tags are scanned by a reader simultaneously. Existing group proof schemes provide only delayed tag loss detection which detects loss of tag response in a verification phase. However, delayed tag loss detection is not suitable for real-time applications where tag loss must be detected immediately. In this study, I propose a tag response loss detection scheme which detects loss of tag response in the proof generation process quickly. In the proposed scheme, the tag responds with the sequence number assigned to the tag group, and the reader detects the loss of the tag response through the sequence number. Through an experiment for indistinguishability, I show that the sequence number is secure against an analyzing message attack to distinguish between specific tags and tag groups. In terms of efficiency, the proposed scheme requires fewer transmissions and database operations than existing techniques to determine which tags response is lost.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.553-562
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• 2005

It is well-known that the smoothness of 4-point interpolatory Deslauriers-Dubuc(DD) subdivision scheme is $C^{1}$. N. Dyn[3] proved that 4-point interpolatory subdivision scheme is $C^{1}$ by means of eigenanalysis. In this paper we take advantage of Laurent polynomial method to get the same result, and give new way of strict proof on Laurent polynomial method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.8
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• pp.4093-4107
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• 2019

Proof of Work (PoW) based blockchains have limitations in throughput, time consumption, and energy efficiency. In these systems, a miner will consume significant time and resources to obtain a reward for contributing to the blockchain. To overcome these limitations, recent research on blockchains are focused on accelerating the speed, scalability, and enhancing the security level. By enhancing specific procedures of blockchain system, the level of data integrity supported by the blockchain can become more robust, and efficient. In this paper, a new blockchain consensus model based on the Bryllite Consensus Protocol (BCP) is proposed to support a hyper-connected massively multiplayer online game (MMOG) ecosystem. The BCP scheme enables users to participate directly in new consensus processes through a Proof of Participation (PoP) algorithm. In this model, the consensus algorithm has a simpler form while maintaining high security level. In addition, because the BCP scheme gives users an equal chance to make a contribution to the blockchain, rewards are distributed in an equal fashion, which motivates user participation. The analysis of the proposed scheme is applied to the Bryllite consortium blockchain system (homed in Hong Kong), which is a new blockchain network developed for international game industries, gamers, and game events.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.5
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• pp.83-94
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• 2011

Yoking proof is a concept proposed by A. Juels in 2004. It proves that a pair of tags are scanned simultaneously by one reader. After the first yoking proof protocol is proposed by A. Juels, replay attack vulnerabilities of yoking proof are considered and many other yoking proof schemes are proposed to improve it. However, compared with the first yoking proof scheme which emphasizes protocol efficiency due to the limited performance of tags, other yoking proof protocols need more computing power and storage of the tags. We propose two security protocols that consider both the general condition and limited performance of tags. The proposed scheme can protect the tags from replay attack and Brute-force attack as well. Moreover, many pairs of tags or several tag groups can be proved at the same time by executing the protocol only once.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.917-931
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• 2013

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1483-1486
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• 2002

In this paper, a new scheme of iterative loaming control of a robot manipulator is presented. The proposed method uses a fuzzy sliding mode controller(FSMC), which is designed based on the similarity between the fuzzy logic control(FLC) and the sliding mode control(SMC), for the feedback. With this, the proposed method makes possible fDr fast iteration and has advantages that no linear approximation is used for the derivation of the learning law or in the stability proof Full proof of the convergence of the fuzzy sliding base learning scheme Is given.