• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.3
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• pp.93-100
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• 2007

Since Koblitz and Miller suggested the use of elliptic curves in cryptography, there has been an extensive literature on elliptic curve cryptosystem (ECC). The use of ECC is based on the observation that the points on an elliptic curve form an additive group under point addition operation. To realize secure cryptosystems using these groups, it is very important to find an elliptic curve whose group order is divisible by a large prime, and also to find a base point whose order equals this prime. While there have been many dramatic improvements on finding an elliptic curve and computing its group order efficiently, there are not many results on finding an adequate base point for a given curve. In this paper, we propose an efficient method to find a random base point on an elliptic curve defined over $GF(p^m)$. We first show that the critical operation in finding a base point is exponentiation. Then we present efficient algorithms to accelerate exponentiation in $GF(p^m)$. Finally, we implement our algorithms and give experimental results on various practical elliptic curves, which show that the new algorithms make the process of searching for a base point 1.62-6.55 times faster, compared to the searching algorithm based on the binary exponentiation.

• Journal of Internet of Things and Convergence
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• v.6 no.2
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• pp.25-29
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• 2020

The elliptic curve crypto-algorithm is widely used in authentication for IoT environment, since it has small key size and low communication overhead compare to the RSA public key algorithm. If the scalar multiplication, a core operation of the elliptic curve crypto-algorithm, is not implemented securely, attackers can find the secret key to use simple power analysis or differential power analysis. In this paper, an elliptic curve scalar multiplication algorithm using a randomized scalar and an elliptic curve point blinding is suggested. It is resistant to power analysis but does not significantly reduce efficiency. Given a random r and an elliptic curve random point R, the elliptic scalar multiplication kP = u(P+R)-vR is calculated by using the regular variant Shamir's double ladder algorithm, where l+20-bit u≡rn+k(modn) and v≡rn-k(modn) using 2^lP=∓cP for the case of the order n=2^l±c.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.4
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• pp.548-555
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• 2022

This paper describes the hardware implementation of elliptic curve cryptography (ECC) used as a core operation in elliptic curve digital signature algorithm (ECDSA). The ECC processor supports eight operation modes (four point operations, four modular operations) on the NIST P-521 curve. In order to minimize computation complexity required for point scalar multiplication (PSM), the radix-4 Booth encoding scheme and modified Jacobian coordinate system were adopted, which was based on the complexity analysis for five PSM algorithms and four different coordinate systems. Modular multiplication was implemented using a modified 3-Way Toom-Cook multiplication and a modified fast reduction algorithm. The ECC processor was implemented on xczu7ev FPGA device to verify hardware operation. Hardware resources of 101,921 LUTs, 18,357 flip-flops and 101 DSP blocks were used, and it was evaluated that about 370 PSM operations per second were achieved at a maximum operation clock frequency of 45 MHz.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

• International Journal of Computer Science & Network Security
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• v.23 no.3
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• pp.169-176
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• 2023

The vehicular ad hoc network (VANET) is currently an important approach to improve personal safety and driving comfort. ANEL is a MAC-based authentication scheme that offers all the advantages of MAC-based authentication schemes and overcomes all their limitations at the same time. In addition, the given scheme, ANEL, can achieve the security objectives such as authentication, privacy preservation, non-repudiation, etc. In addition, our scheme provides effective bio-password login, system key update, bio-password update, and other security services. Additionally, in the proposed scheme, the Trusted Authority (TA) can disclose the source driver and vehicle of each malicious message. The heavy traffic congestion increases the number of messages transmitted, some of which need to be secretly transmitted between vehicles. Therefore, ANEL requires lightweight mechanisms to overcome security challenges. To ensure security in our ANEL scheme we can use cryptographic techniques such as elliptic curve technique, session key technique, shared key technique and message authentication code technique. This article proposes a new efficient and light authentication scheme (ANEL) which consists in the protection of texts transmitted between vehicles in order not to allow a third party to know the context of the information. A detail of the mapping from text passing to elliptic curve cryptography (ECC) to the inverse mapping operation is covered in detail. Finally, an example of application of the proposed steps with an illustration

• Convergence Security Journal
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• v.19 no.5
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• pp.37-45
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• 2019

Video security systems change from analog based systems to network based CCTVs. Therefore, such network based systems are always exposed not only to threats of eavesdropping and hacking, but to personal damage or public organizations' damage due to image information leakage. Therefore, in order to solve the problem, this study conducts a comparative analysis on proposes the optimal ECC(Elliptic Curve Cryptography) scalar multiplication algorithms for image information protection in data communication process and thereby proposes the optimal operation algorithm of video security system.

• JSTS:Journal of Semiconductor Technology and Science
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• v.16 no.1
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• pp.118-125
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• 2016

This paper presents a new high-efficient algorithm and architecture for an elliptic curve cryptographic processor. To reduce the computational complexity, novel modified Lopez-Dahab scalar point multiplication and left-to-right algorithms are proposed for point multiplication operation. Moreover, bit-serial Galois-field multiplication is used in order to decrease hardware complexity. The field multiplication operations are performed in parallel to improve system latency. As a result, our approach can reduce hardware costs, while the total time required for point multiplication is kept to a reasonable amount. The results on a Xilinx Virtex-5, Virtex-7 FPGAs and VLSI implementation show that the proposed architecture has less hardware complexity, number of clock cycles and higher efficiency than the previous works.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.3
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• pp.1546-1565
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• 2019

Signcryption schemes offer the possibility to simultaneously sign and encrypt a message. In order to guarantee the authentication of both signer and receiver in the most efficient way during the signcryption, certificate based solutions have been proposed in literature. We first compare into detail three recently proposed certificate based signcryption systems relying on the elliptic curve discrete logarithm problem and without the usage of compute intensive pairing operations. Next, we demonstrate how the performance of these certificate based systems can be improved by using the Elliptic Curve Qu Vanstone (ECQV) implicit certificates. What is more, generalized signcryption schemes are easily derived from these schemes and the anonymity feature of sender and receiver is already inherently included or can be very efficiently obtained without a significant additional cost.

• Proceedings of the IEEK Conference
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• 2003.07b
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• pp.935-938
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• 2003

The performance of elliptic curve based on public key cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. This work describes a finite field multiplier and divider which is implemented using SystemC. Also this present an efficient hardware for performing the elliptic curve point multiplication using the polynomial basis representation. In order to improve the speed of the multiplier with as a little extra hardware as possible, adopted hybrid finite field multiplication and finite field divider.