• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.7
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• pp.693-700
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• 2016

It is important that we can calculate the order of non-supersingular elliptic curves with large prime factors over the finite field GF(q) to guarantee the security of public key cryptosystems based on discrete logarithm problem(DLP). Schoof algorithm, however, which is used to calculate the order of the non-supersingular elliptic curves currently is so complicated that many papers are appeared recently to update the algorithm. To avoid Schoof algorithm, in this paper, we propose an algorithm to calculate orders of elliptic curves over finite composite fields of the forms $GF(2^m)=GF(2^{rs})=GF((2^r)^s)$ using Weil's theorem. Implementing the program based on the proposed algorithm, we find a efficient non-supersingular elliptic curve over the finite composite field $GF(2^5)^{31})$ of the order larger than $10^{40}$ with prime factor larger than $10^{40}$ using the elliptic curve $E(GF(2^5))$ of the order 36.

• KIPS Transactions on Software and Data Engineering
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• v.9 no.2
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• pp.39-44
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• 2020

In this paper, we show a modified Diffie-Hellman key exchange protocol that can exchange keys by exposing only minimal information using pre-computable session key pairs. The discrete logarithm problem, which provides the safety of existing Diffie-Hellman and Diffie-Hellman based techniques, is modified to prevent exposure of primitive root. We prove the algorithm's operation by applying the actual value to the proposed scheme and compare the execution time and safety with the existing algorithm, shown that the security of the algorithm is improved more than the product of the time complexity of the two base algorithms while maintaining the computation amount at the time of key exchange. Based on the proposed algorithm, it is expected to provide a key exchange environment with improved security.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.27 no.3
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• pp.477-487
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• 2017

Multiparty computation (MPC) is a computation technique where many participants provide their data and jointly compute operations to get a computation result. Earlier MPC protocols were mostly depended on communication between the users. Several schemes have been presented that mainly work by delegating operations to two non-colluding servers. Peter et al. propose a protocol that perfectly eliminates the need of users' participation during the whole computation process. However, the drawback of their scheme is the excessive dependence on the server communication. To cater this issue, we propose a protocol that reduce server communication overhead using the proxy re-encryption (PRE). Recently, some authors have put forward their efforts based on the PRE. However, these schemes do not achieve the desired goals and suffer from attacks that are based on the collusion between users and server. This paper, first presents a comprehensive analysis of the existing schemes and then proposes a secure and efficient MPC protocol. The proposed protocol completely eliminates the need of users' participation, incurs less communication overhead and does not need to solve the discrete logarithm problem (DLP) in order to get the computation results.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.3
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• pp.1439-1444
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• 2013

Recently, as the use of the applications like online banking and stock trading is increasing by the rapid development of the network, security of data content is becoming more and more important. Accordingly, public key or symmetric key encryption algorithm is widely used in open networks such as the internet for the protection of data. Generally, public key cryptographic systems is based on two famous number theoretic problems namely factoring or discrete logarithm problem. So, public key cryptographic systems is relatively slow compared to symmetric key cryptography systems. Among public key cryptographic systems, the advantage of ECC compared to RSA is that it offers equal security for a far smaller key. For this reason, ECC is faster than RSA. In this paper, we propose a efficient key generation method for elliptic curve cryptography system based on the real number field.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.353-359
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• 2004

The illegal copying and redistribution of digitally-stored information is a crucial problem to distributors who electronically sell digital data. Fingerprinting scheme is a techniques which supports copyright protection to track redistributors of electronic information using cryptographic techniques. Anonymous fingerprinting schemes, differ from symmetric fingerprinting, prevent the merchant from framing a buyer by making the fingerprinted version known to the buyer only. And the scheme, differ from asymmetric fingerprinting, allows the buyer to purchase goods without revealing her identity to the merchant. In this paper, a new anonymous fingerprinting scheme based on secret sharing is introduced. The merchant finds a sold version that has been distributed, and then he is able to retrieve a buyer's identity and take her to court. And Schnorr's digital signature prevents the buyer from denying the fact he redistributed. The buyer's anonymity relies on the security of discrete logarithm and secure two-party computations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.5 no.1
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• pp.37-50
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• 1995

The smart card with the cryptography and VLSI technologies makes it possible to implement the electronic cash easily. A number of electronic each schemes have been proposed by many cryptographic researchers. In this paper, we propose a practical electronic cash system, using blind digital signature scheme. Schnorr's authentication scheme based on the discrete logarithm problem, and the hierarchical cash tree based on two one-way hash functions for dividable payment. Thisf electronic cash scheme has such properties as privacy of the payment, off-line payment, non-reuseability of cash, transferability of cash to another customer, and dividable payment of cash. This electronic cash protocol is well suited for implementing in smart card.

• Journal of KIISE:Information Networking
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• v.30 no.1
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• pp.75-81
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• 2003

User authentication, including confidentiality, integrity over untrusted networks, is an important part of security for systems that allow remote access. Using human-memorable Password for remote user authentication is not easy due to the low entropy of the password, which constrained by the memory of the user. This paper presents a new password authentication and key agreement protocol suitable for authenticating users and exchanging keys over an insecure channel. The new protocol resists the dictionary attack and offers perfect forward secrecy, which means that revealing the password to an attacher does not help him obtain the session keys of past sessions against future compromises. Additionally user passwords are stored in a form that is not plaintext-equivalent to the password itself, so an attacker who captures the password database cannot use it directly to compromise security and gain immediate access to the server. It does not have to resort to a PKI or trusted third party such as a key server or arbitrator So no keys and certificates stored on the users computer. Further desirable properties are to minimize setup time by keeping the number of flows and the computation time. This is very useful in application which secure password authentication is required such as home banking through web, SSL, SET, IPSEC, telnet, ftp, and user mobile situation.