• Journal of the Korean School Mathematics Society
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• v.3 no.2
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• pp.165-176
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• 2000

This note introduces elliptic curve cryptosystems and related algorithms and gives an elliptic curve cryptosystems practice program made with Javascript. We can find the practice program at author′s homepage "http://my.dreamwiz.com/math88". It is useful for students to study about elliptic curve cryptosystems.

• Journal of Communications and Networks
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• v.15 no.5
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• pp.464-468
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• 2013

The widespread use of cryptographic technologies is complicated by inconsistencies and duplication in the key management systems supporting their applications. The proliferation of key management systems or protocols also results in higher operational and infrastructure costs, and fails in interoperability. Thus, it is essential to realize key management interoperability between different and heterogeneous cryptosystems. This paper presents a practical and separable key management system for heterogeneous public-key cryptosystems. We achieve the interoperability between different cryptosystems via cryptography approaches rather than communication protocols. With our scheme, each client can freely use any kind of cryptosystemthat it likes. The proposed scheme has two advantages over the key management interoperability protocol introduced by the organization for the advancement of structured information standards. One is that all the related operations do not involve the communication protocol and thus no special restrictions are taken on the client devices. The other is that the proposed scheme does not suffer from single-point fault and bottleneck problems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.12C
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• pp.977-983
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• 2010

The output values of chaotic functions look highly unpredictable and random-like. These features are in accord with the requirements for secure cryptosystems. For this reason, many kinds of cryptosystems using chaotic functions have been proposed so far. However, most of those algorithms are not applicable for light cryptosystems because they need a high level of computing ability. In this paper, we propose a new light chaotic cryptosystems which are suitable for the systems with a low level of computing ability. From the simulations, we show the performance of proposed cryptosystems on computational complexity and security level.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.2
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• pp.127-132
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• 2003

Cryptosystems have received very much attention in recent years as importance of information security is increased. Most of Cryptosystems are defined over finite or Galois fields GF($2^m$) . In particular, the finite field GF($2^m$) is mainly used in public-key cryptosystems. These cryptosystems are constructed over finite field arithmetics, such as addition, subtraction, multiplication, and multiplicative inversion defined over GF($2^m$) . Hence, to implement these cryptosystems efficiently, it is important to carry out these operations defined over GF($2^m$) fast. Among these operations, since multiplicative inversion is much more time-consuming than other operations, it has become the object of lots of investigation. Recently, many methods for computing multiplicative inverses at hi호 speed has been proposed. These methods are based on format's theorem, and reduce the number of required multiplication using normal bases over GF($2^m$) . The method proposed by Itoh and Tsujii[2] among these methods reduced the required number of times of multiplication to O( log m) Also, some methods which improved the Itoh and Tsujii's method were proposed, but these methods have some problems such as complicated decomposition processes. In practical applications, m is frequently selected as a power of 2. In this parer, we propose a fast method for computing multiplicative inverses in GF($2^m$) , where m = ($2^n$) . Our method requires fewer ultiplications than the Itoh and Tsujii's method, and the decomposition process is simpler than other proposed methods.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2006.06a
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• pp.356-360
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• 2006

Recently, many power analysis attacks have been proposed. Since the attacks are powerful, it is very important to implement cryptosystems securely against the attacks. We propose countermeasures against power analysis attacks for elliptic curve cryptosystems based on Koblitz curves (KCs), which are a special class of elliptic curves. That is, we make our countermeasures be secure against SPA, DPA, and new DPA attacks, specially RPA, ZPA, using a random point at each execution of elliptic curve scalar multiplication. And since our countermeasures are designed to use the Frobenius map of KC, those are very fast.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2576-2578
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• 2001

Elliptic curve cryptosystems based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm in an elliptic curve group appears to be more difficult than discrete logarithm problem in other groups while using the relatively small key size. An implementation of elliptic curve cryptosystems needs finite field arithmetic computation. Hence finite field arithmetic modules must require less hardware resources to archive high performance computation. In this paper, a new architecture of finite field multiplier using conversion scheme of normal basis representation into polynomial basis representation is discussed. Proposed architecture provides less resources and lower complexity than conventional bit serial multiplier using normal basis representation. This architecture has synthesized using synopsys FPGA express successfully.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.81-88
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• 2002

For efficient implementation of scalar multiplication in Elliptic Curve Cryptosystems over Small Fields of Odd Characterist, robenius endomorphism is useful. We discuss new algorithm for multiplying points on Elliptic Curve Cryptosystems over Small ields. Our algorithm can reduce more the length of the Frobenius expansion than that of Smart.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2003.12a
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• pp.412-416
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• 2003

This paper introduces a new joint signed expansion method for computing simultaneous scalar multiplication on an elliptic curve and a modified binary algorithm for efficient use of the new expansion method. The proposed expansion method can be also be used in cryptosystems such as RSA and EIGamal cryptosystems.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.6
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• pp.3-12
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• 2011

A hashing function that maps arbitrary messages directly onto curve points (MapToPoint) has non-negligible complexity in pairing-based cryptosystems. Unlike elliptic curve cryptosystems, pairing-based cryptosystems require the hashing function in ternary fields. Barreto et al. observed that it is more advantageous to hash the message to an ordinate instead of an abscissa. So, they significantly improved the hashing function by using a matrix with coefficients of the abscissa. In this paper, we improve the method of Barreto et al. by reducing the matrix. Our method requires only 44% memory of the previous result. Moreover we can hash a message onto a curve point 2~3 times faster than Barreto's Method.

• ETRI Journal
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• v.32 no.1
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• pp.102-111
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• 2010

Recently power attacks on RSA cryptosystems have been widely investigated, and various countermeasures have been proposed. One of the most efficient and secure countermeasures is the message blinding method, which includes the RSA derivative of the binary-with-random-initial-point algorithm on elliptical curve cryptosystems. It is known to be secure against first-order differential power analysis (DPA); however, it is susceptible to second-order DPA. Although second-order DPA gives some solutions for defeating message blinding methods, this kind of attack still has the practical difficulty of how to find the points of interest, that is, the exact moments when intermediate values are being manipulated. In this paper, we propose a practical second-order correlation power analysis (SOCPA). Our attack can easily find points of interest in a power trace and find the private key with a small number of power traces. We also propose an efficient countermeasure which is secure against the proposed SOCPA as well as existing power attacks.