• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.3
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• pp.41-48
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• 2004

Finite field multiplication and division are important arithmetic operation in error-correcting codes and cryptosystems. The elements of the finite field GF($2^m$) are represented by bases with a primitive polynomial of degree m over GF(2). We can be easily realized for multiplication or computing multiplicative inverse in GF($2^m$) based on a normal basis representation. The number of product terms of logic function determines a complexity of the Messay-Omura multiplier. A normal basis exists for every finite field. It is not easy to find the optimal normal element for a given primitive polynomial. In this paper, the generating method of normal basis is investigated. The normal bases whose product terms are less than other bases for multiplication in GF($2^m$) are found. For each primitive polynomial, a list of normal elements and number of product terms are presented.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.3
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• pp.77-89
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• 2005

As the ID-based public key cryptosystems become a very active research area, a number of ID-based key agreement protocols have been proposed, but unfortunately many of them were analyzed that there were some security flaws in the protocols. In addition to key agreement protocols, in recent, Liu et al. and Kim et al. proposed the key agreement protocols that multiple session keys are established at once among participated entities. In this paper, we propose an ID-based tripartite key agreement protocol that establishes 8 keys by improving the efficiency of the Liu et al's. Moreover, the proposed protocol can be used in the situation where multiple different private key generators(PKG) are involved. Therefore, because the private key issued by different PKGs belonging to each entity's domain can be used, our proposed scheme is more efficiently applicable to the practical applications.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.6A
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• pp.17-25
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• 2008

The differential power attack (DPA)[8] is a very powerful side-channel attack tool against various cryptosystems and the masking method[10] is known to be one of its algorithmic countermeasures. But it is non-trivial to apply the masking method to non-linear functions, especially, to arithmetic adders. This paper proposes simple and efficient masking methods applicable to arithmetic adders. For this purpose, we use the fact that every combinational logic circuit (including the adders) can be decomposed into basic logic gates (AND, OR, NAND, NOR, XOR, XNOR, NOT) and try to devise efficient masking circuits for these basic gates. The resulting circuits are then applied to the arithmetic adders to get their masking algorithm. As applications, we applied the proposed masking methods to SEED and SHA-1 in hardware.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.103-114
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• 1999

Recently, various prototypes for electronic commerce are realized and its related researches are active under the present condition which it is increasing for the reality of its extended applications. First of all, actual demands are increasing for more secure and efficient electronic payment systems. Electronic cash, one of the Electronic payment systems, must have several properties like real money. Blind signature scheme by D. Chaum stands for the methods of obtaining privacy. In this paper, we propose a method for obtaining the blind signature based on the Elliptic Curve Cryptosystems, where the crytosystems are known as solving some problems of conventional crytosystems in views of computation time and key space. Also, we present a method for the divisibility of the electronic cash using our proposal by re-signing spare cash. Thus applying the proposed method, we can develop an efficient electronic payment systems.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.6
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• pp.71-80
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• 2002

To provide the confidentiality of messages transmitted over the network, the use of cryptographic system is increasing gradually and the hybrid cryptosystem, which combines the advantages of the symmetric cryptosystem and the public key cryptosystem is widely used. In this paper, we proposes a new hybrid cryptosystem capable of providing implicit authentication for the sender of the ciphertext by means of the 1-pass key distribution protocol that offers implicit key authentication, hash function and symmetric cryptosystem. Also, we describe some examples such as the Diffie-Hellman based system and the Nyberg-Ruppel based system. The proposed hybrid cryptosystem is an efficient more than general public key cryptosystems in the aspect of computation work and provides implicit authentication for the sender without additional increase of the communication overhead.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.6
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• pp.95-109
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• 2006

Elliptic Curve Cryptosystem (ECC) is suitable for resource-constrained devices such as smartcards, and sensor motes because of its short key size. This paper presents an efficient multi-scalar multiplication algorithm which is the main component of the verification procedure in Elliptic Curve Digital Signature Algorithm (ECDSA). The proposed algorithm can make use of a precomputed table of variable size and provides an optimal efficiency for that precomputed table. Furthermore, the given scalar is receded on-the-fly so that it can be merged with the main multiplication procedure. This can achieve more savings on memory than other receding algorithms. Through experiments, we have found that the optimal sizes of precomputed tables are 7 and 15 when uP+vQ is computed for u, v of 163 bits and 233 bits integers. This is shown by comparing the computation time taken by the proposed algorithm and other existing algorithms.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.2
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• pp.115-123
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• 2007

In cryptographic devices like a smart-card whose computing ability and memory are limited, cryptographic algorithms should be performed efficiently. Scalar multiplication is very important operation in Elliptic Curve Cryptosystems, and so must be constructed in safety against side channel attack(SCA). But several countermeasures proposed against SCA are exposed weaknesses by new un-dreamed analysis. 'Double-and-add always scalar multiplication' algorithm adding dummy operation being known to secure against SPA is exposed weakness by Doubling Attack. But Doubling Attack cannot apply to sABS receding proposed by Hedabou, that is another countermeasure against SPA. Our paper proposes new strengthened Doubling Attacks that can break sABS receding SPA-countermeasure and a detailed method of our attacks through experimental result.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.4
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• pp.3-19
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• 2009

This paper proposes efficient scalar multiplication algorithms based on Montgomery ladder method. The proposed algorithm represents the scalar as ternary or quaternary and applies new composite formulas utilizing only x coordinate on affine coordinate system in order to improve performance. Furthermore, side-channel atomicity mechanism is applied on the proposed composite formulas to prevent simple power analysis. The proposed methods saves at least 26% of running time with the reduced number of storage compared with existing algorithms such as window-based methods and comb-based methods.

• Smart Media Journal
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• v.12 no.2
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• pp.76-82
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• 2023

In the 4th industrial revolution, the blockchain that distributes and manages data through a P2P network is used as a new decentralized networking paradigm in various fields such as manufacturing, culture, and public service. However, with the advent of quantum computers, quantum algorithms that are able to break existing cryptosystems such as hash function, symmetric key, and public key cryptography have been introduced. Currently, because most major blockchain systems use an elliptic curve cryptography to generate signatures for transactions, they are insecure against the quantum adversary. For this reason, the research on the quantum-resistant blockchain that utilizes lattice-based cryptography for transaction signatures is needed. Therefore, in this paper, we propose a blind signature scheme for the blockchain in which the contents of the signature can be verified later, as well as signing by hiding the contents to be signed using lattice-based cryptography with the property of quantum resistance. In addition, we prove the security of the proposed scheme using a random oracle model.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.9 s.339
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• pp.51-60
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• 2005

The design of efficient cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. Especially, among the basic arithmetic over finite field, the rnultiplicative inversion is the most time consuming operation. In this paper, a fast inversion algerian in finite field $GF(2^m)$ with the standard basis representation is proposed. It is based on the Extended binary gcd algorithm (EBGA). The proposed algorithm executes about $18.8\%\;or\;45.9\%$ less iterations than EBGA or Montgomery inverse algorithm (MIA), respectively. In practical applications where the dimension of the field is large or may vary, systolic array sDucture becomes area-complexity and time-complexity costly or even impractical in previous algorithms. It is not suitable for low-weight and low-power systems, i.e., smartcard, the mobile phone. In this paper, we propose a new hardware architecture to apply an area-efficient and a synchronized inverter on low-complexity systems. It requires the number of addition and reduction operation less than previous architectures for computing the inverses in $GF(2^m)$ furthermore, the proposed inversion is applied over either prime or binary extension fields, more specially $GF(2^m)$ and GF(P) .