• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.469-472
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• 2003

The computational cost of encryption is a barrier to wider application of a variety of data security protocols. Virtually all research on Elliptic Curve Cryptography(ECC) provides evidence to suggest that ECC can provide a family of encryption algorithms that implementation than do current widely used methods. This efficiency is obtained since ECC allows much shorter key lengths for equivalent levels of security. This paper suggests how improvements in execution of ECC algorithms can be obtained by changing the representation of the elements of the finite field of the ECC algorithm. Specifically, this research compares the time complexity of ECC computation eve. a variety of finite fields with elements expressed in the polynomial basis(PB) and normal basis(NB).

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.05a
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• pp.63-65
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• 2021

This paper describes an integrated H/W-S/W implementation of elliptic curve digital signature algorithm (EC-DSA) using a security system-on-chip (SoC). The security SoC uses the Cortex-A53 APU as CPU, and the hardware IPs of high-performance elliptic curve cryptography (HP-ECC) core and SHA3 (secure hash algorithm 3) hash function core are interfaced via AXI4-Lite bus protocol. The signature generation and verification processes of EC-DSA were verified by the implementation of the security SoC on a Zynq UltraScale+ MPSoC device.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.7
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• pp.1267-1275
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• 2017

This paper describes a design of cryptographic processor supporting 233-bit elliptic curves over binary field defined by NIST. Scalar point multiplication that is core arithmetic in elliptic curve cryptography(ECC) was implemented by adopting modified Montgomery ladder algorithm, making it robust against simple power analysis attack. Point addition and point doubling operations on elliptic curve were implemented by finite field multiplication, squaring, and division operations over $GF(2^{233})$, which is based on affine coordinates. Finite field multiplier and divider were implemented by applying shift-and-add algorithm and extended Euclidean algorithm, respectively, resulting in reduced gate counts. The ECC processor was verified by FPGA implementation using Virtex5 device. The ECC processor synthesized using a 0.18 um CMOS cell library occupies 49,271 gate equivalents (GEs), and the estimated maximum clock frequency is 345 MHz. One scalar point multiplication takes 490,699 clock cycles, and the computation time is 1.4 msec at the maximum clock frequency.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2018.10a
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• pp.190-192
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• 2018

This paper describes a design of an elliptic curve cryptography (ECC) processor that supports five pseudo-random curves and five Koblitz curves over binary field defined by the NIST standard. The ECC processor adopts the Lopez-Dahab projective coordinate system so that scalar multiplication is computed with modular multiplier and XORs. A word-based Montgomery multiplier of $32-b{\times}32-b$ was designed to implement ECCs of various key lengths using fixed-size hardware. The hardware operation of the ECC processor was verified by FPGA implementation. The ECC processor synthesized using a 0.18-um CMOS cell library occupies 10,674 gate equivalents (GEs) and 9 Kbits RAM at 100 MHz, and the estimated maximum clock frequency is 154 MHz.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.8
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• pp.2930-2947
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• 2014

With the rapid growth of the communication technology, intelligent terminals (i.e. PDAs and smartphones) are widely used in many mobile applications. To provide secure communication in mobile environment, in recent years, many user authentication schemes have been proposed. However, most of these authentication schemes suffer from various attacks and cannot provide provable security. In this paper, we propose a novel remote user mutual authentication scheme for multi-server environments using elliptic curve cryptography (ECC). Unlike other ECC-based schemes, the proposed scheme uses ECC in combination with a secure hash function to protect the secure communication among the users, the servers and the registration center (RC). Through this method, the proposed scheme requires less ECC-based operations than the related schemes, and makes it possible to significantly reduce the computational cost. Security and performance analyses demonstrate that the proposed scheme can solve various types of security problems and can meet the requirements of computational complexity for low-power mobile devices.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.9
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• pp.5790-5795
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• 2014

Elliptic curve cryptography (ECC) is an extremely important part of information protection systems because it has outstanding safety among public key encryption algorithms. On the other hand, as ECC cannot obtain accurate values using a real number field because of the slow calculation and errors from rounding off, studies of ECC have focused on a finite field. If ECC can be extended to the real number field, more diverse keys can be selected compared to ECC only based on a finite field. Accordingly, in this paper, a method for constructing a cryptographic system with a high degree of safety is proposed through the diversification of keys selected by the user based on the operant extension method instead of extracting keys only using integer values.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.11
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• pp.1470-1476
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• 2020

This paper describes a design of a lightweight security system-on-chip (SoC) suitable for the implementation of security protocols for IoT and mobile devices. The security SoC using Cortex-M0 as a CPU integrates hardware crypto engines including an elliptic curve cryptography (ECC) core, a SHA3 hash core, an ARIA-AES block cipher core and a true random number generator (TRNG) core. The ECC core was designed to support twenty elliptic curves over both prime field and binary field defined in the SEC2, and was based on a word-based Montgomery multiplier in which the partial product generations/additions and modular reductions are processed in a sub-pipelining manner. The H/W-S/W co-operation for elliptic curve digital signature algorithm (EC-DSA) protocol was demonstrated by implementing the security SoC on a Cyclone-5 FPGA device. The security SoC, synthesized with a 65-nm CMOS cell library, occupies 193,312 gate equivalents (GEs) and 84 kbytes of RAM.

• Journal of IKEEE
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• v.23 no.1
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• pp.58-67
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• 2019

A design of an elliptic curve cryptography (ECC) processor that supports both pseudo-random curves and Koblitz curves over $GF(2^m)$ defined by the NIST standard is described in this paper. A finite field arithmetic circuit based on a word-based Montgomery multiplier was designed to support five key lengths using a datapath of fixed size, as well as to achieve a lightweight hardware implementation. In addition, Lopez-Dahab's coordinate system was adopted to remove the finite field division operation. The ECC processor was implemented in the FPGA verification platform and the hardware operation was verified by Elliptic Curve Diffie-Hellman (ECDH) key exchange protocol operation. The ECC processor that was synthesized with a 180-nm CMOS cell library occupied 10,674 gate equivalents (GEs) and a dual-port RAM of 9 kbits, and the maximum clock frequency was estimated at 154 MHz. The scalar multiplication operation over the 223-bit pseudo-random elliptic curve takes 1,112,221 clock cycles and has a throughput of 32.3 kbps.

• Journal of Communications and Networks
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• v.11 no.6
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• pp.599-606
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• 2009

For many mission-critical related wireless sensor network applications such as military and homeland security, user's access restriction is necessary to be enforced by access control mechanisms for different access rights. Public key-based access control schemes are more attractive than symmetric-key based approaches due to high scalability, low memory requirement, easy key-addition/revocation for a new node, and no key predistribution requirement. Although Wang et al. recently introduced a promising access control scheme based on elliptic curve cryptography (ECC), it is still burdensome for sensors and has several security limitations (it does not provide mutual authentication and is strictly vulnerable to denial-of-service (DoS) attacks). This paper presents an energy-efficient access control scheme based on ECC to overcome these problems and more importantly to provide dominant energy-efficiency. Through analysis and simulation based evaluations, we show that the proposed scheme overcomes the security problems and has far better energy-efficiency compared to current scheme proposed byWang et al.

• 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.