• Journal of Korea Society of Industrial Information Systems
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• v.12 no.1
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• pp.28-38
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• 2007

In this paper, we implement Microsoft COM software modules for elliptic curve cryptographic applications and analyze its performance. The implemented COM software modules support all elliptic curve key exchange protocols and elliptic curve digital signature algorithm in IEEE 1363 finite fields GF(p) and GF(2m). Since the implemented software modules intend to focus on a component-based software development method, and thus it have a higher productivity and take systematic characteristics to be open outward and to be standardized. Accordingly, it enable a software to be developed easier and faster rather than a method using C library. In addition it support the Microsoft COM interface, we can easily implement secure software applications based on elliptic curve cryptographic algorithms.

• The KIPS Transactions:PartC
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• v.13C no.2 s.105
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• pp.137-146
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• 2006

Because the traditional public key-based cryptosystems are unsuitable for the sensor node with limited computational and communication capability, a secure communication between two neighbor sensor nodes becomes an important challenging research in sensor network security. Therefore several session key establishment protocols have been proposed for that purpose. In this paper, we analyzed and compared the existing session key establishment protocols based on the criterions of generation strategy and uniqueness of the session key, connectivity, overhead of communication and computation, and vulnerability to attacks. Based on the analysis results, we specify the requirements for the secure and efficient protocols for establishing session keys. Then, we propose an advanced protocol to satisfy the specified requirements and verify the superiority of our protocol over the existing protocols through the detailed analysis.

• Journal of Information Processing Systems
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• v.6 no.3
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• pp.335-346
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• 2010

The present study investigates the difficulty of solving the mathematical problem, namely the DLP (Discrete Logarithm Problem) for ephemeral keys. The DLP is the basis for many public key cryptosystems. The ephemeral keys are used in such systems to ensure security. The DLP defined on a prime field $Z^*_p of random prime is considered in the present study. The most effective method to solve the DLP is the ICM (Index Calculus Method). In the present study, an efficient way of computing the DLP for ephemeral keys by using a new variant of the ICM when the factors of p-1 are known and small is proposed. The ICM has two steps, a pre-computation and an individual logarithm computation. The pre-computation step is to compute the logarithms of a subset of a group and the individual logarithm step is to find the DLP using the precomputed logarithms. Since the ephemeral keys are dynamic and change for every session, once the logarithms of a subset of a group are known, the DLP for the ephemeral key can be obtained using the individual logarithm step. Therefore, an efficient way of solving the individual logarithm step based on the newly proposed precomputation method is presented and the performance is analyzed using a comprehensive set of experiments. The ephemeral keys are also solved by using other methods, which are efficient on random primes, such as the Pohlig-Hellman method, the Van Oorschot method and the traditional individual logarithm step. The results are compared with the newly proposed individual logarithm step of the ICM. Also, the DLP of ephemeral keys used in a popular password key exchange protocol known as Chang and Chang are computed and reported to launch key recovery attack.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.43 no.3 s.345
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• pp.40-47
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• 2006

The finite-field multiplication can be applied to the elliptic curve cryptosystems. However, an efficient algorithm and the hardware design are required since the finite-field multiplication takes much time to compute. In this paper, we propose a radix-4 systolic multiplier on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed standard-basis multiplier is mathematically developed to map on low-cost systolic cells, so that the proposed systolic architecture is suitable for VLSI design. Compared to the bit-parallel, bit-serial and systolic multipliers, the proposed multiplier has relatively effective high performance and low cost. We design and synthesis $GF(2^{193})$ finite-field multiplier using Hynix $0.35{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.3 s.357
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• pp.35-42
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• 2007

The finite-field division can be applied to the elliptic curve cryptosystems. However, an efficient algorithm and the hardware design are required since the finite-field division takes much time to compute. In this paper, we propose a radix-4 systolic divider on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed divide, is mathematically developed and new counter structure is proposed to map on low-cost systolic cells, so that the proposed systolic architecture is suitable for YLSI design. Compared to the bit-parallel, bit-serial and digit-serial dividers, the proposed divider has relatively effective high performance and low cost. We design and synthesis $GF(2^{193})$ finite-field divider using Dongbuanam $0.18{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.9
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• pp.1565-1572
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• 2006

Recently with the ever increasing growth of data communication, the need for security and privacy has become a necessity. The advent of wireless communication and other handheld devices like Personal Digital Assistants and smart cards have made the implementation of cryptosystems a major issue. The Cellular Automata(CA) can be programmed to implement hardware sharing between the encryption and decryption. In this paper, we give conditions for a linear hybrid cellular automata with 60, 102 or 204 to be a linear hybrid group cellular automata C. And we present the conditions which the complemented hybrid group cellular automata C' with complement vectors derived from C has maximum equal lengths in the state transition diagram of C' Also we analyze the relationship among cycles of C' These results generalize Mukhopadhyay's results.

• The Transactions of the Korea Information Processing Society
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• v.7 no.8
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• pp.2421-2429
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• 2000

With the advance of wireless communications technology, mobile communications have become more convenient than ever. Nowadays, people can communicate with each other on any place at any time. However, because of the openness of wireless communications, the way to protect the privacy between communicating parties is becoming a very important issue. In this paper, we present a study on the authentication and message encryption algorithm to support roaming service to the GSM network. To propose an authentication and message encryption algorithm applicable to the GSM system, the security architecture of the GSM outlined in the GSM standard is briefly introduced. In the proposed cryptosystems we use a new hash function for user authentication and a stream cipher based on Linear Feedback Shift Register(LFSR) for message encryption and decryption. Moreover, each algorithm is programmed with C language and simulated on IBM-PC system and we analyze the randomness properties of the proposed algorithms by using statistical tests.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1297-1308
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• 2006

Multiplications in finite fields are one of the most important arithmetic operations for implementations of elliptic curve cryptographic systems. In this paper, we propose a new multiplication algorithm and VLSI architecture over $GF(2^m)$ using Gaussian normal basis. The proposed algorithm is designed by using a symmetric property of normal elements multiplication and transforming coefficients of normal elements. The proposed multiplication algorithm is applicable to all the five recommended fields $GF(2^m)$ for elliptic curve cryptosystems by NIST and IEEE 1363, where $m\in${163, 233, 283, 409, 571}. A new VLSI architecture based on the proposed multiplication algorithm is faster or requires less hardware resources compared with previously proposed normal basis multipliers over $GF(2^m)$. In addition, we gives an easy method finding a basic multiplication matrix of normal elements.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.1C
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• pp.14-21
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• 2011

Cryptographic protocols based on bilinear pairings provide excellent alternatives to conventional elliptic curve cryptosystems based on discrete logarithm problems. Through active research has been done toward fast computation of the bilinear pairings, it is still believed that the computational cost of one pairing computation is heavier than the cost of one ECC scalar multiplication. However, there have been many progresses in pairing computations over binary fields. In this paper, we compare the cost of BLS signature scheme with ECDSA with equvalent level of security parameters. Analysis shows that the cost of the pairing computation is quite comparable to the cost of ECC scalar multiplication for the case of binary fields.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.9
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• pp.702-713
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• 2003

The importance of protection for data and information is increasing by the rapid development of information communication and network. And the concern for protecting private information is also growing due to the increasing demand for lots of services by users. Asymmetric cryptosystem is the mainstream in encryption system rather than symmetric cryptosystem by above reasons. But asymmetric cryptosystem is restricted in applying fields by the reason it takes more times to process than symmetric cryptosystem. In this paper, encryption system which executes authentication works of asymmetric cryptosystem by means of symmetric cryptosystem. The proposed cryptosystem uses an algorithms combines that combines block cipherment with stream cipherment and has a high stability in aspect of secret rate by means of transition of key sequence according to the information of plaintext while symmetric/asymmetric cryptosystem conducts encipherment/deciphermeent using a fixed key. Consequently, it is very difficult to crack although unauthenticator acquires the key information. So, the proposed encryption system which has a certification function of asymmetric cryptosystem and a processing time equivalent to symmetric cryptosystems will be highly useful to authorize data or exchange important information.