• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.8
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• pp.1095-1102
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• 2021

A scalable ECC architecture with high scalability and flexibility between performance and hardware complexity is proposed. For architectural scalability, a modular arithmetic unit based on a one-dimensional array of processing element (PE) that performs finite field operations on 32-bit words in parallel was implemented, and the number of PEs used can be determined in the range of 1 to 8 for circuit synthesis. A scalable algorithms for word-based Montgomery multiplication and Montgomery inversion were adopted. As a result of implementing scalable ECC processor (sECCP) using 180-nm CMOS technology, it was implemented with 100 kGEs and 8.8 kbits of RAM when N_PE=1, and with 203 kGEs and 12.8 kbits of RAM when N_PE=8. The performance of sECCP with N_PE=1 and N_PE=8 was analyzed to be 110 PSMs/sec and 610 PSMs/sec, respectively, on P256R elliptic curve when operating at 100 MHz clock.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2680-2700
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• 2017

Finite field arithmetic over GF($2^m$) is used in a variety of applications such as cryptography, coding theory, computer algebra. It is mainly used in various cryptographic algorithms such as the Elliptic Curve Cryptography (ECC), Advanced Encryption Standard (AES), Twofish etc. The multiplication in a finite field is considered as highly complex and resource consuming operation in such applications. Many algorithms and architectures are proposed in the literature to obtain efficient multiplication operation in both hardware and software. In this paper, a modified serial multiplication algorithm with interleaved modular reduction is proposed, which allows for an efficient realization of a sequential polynomial basis multiplier. The proposed sequential multiplier supports multiplication of any two arbitrary finite field elements over GF($2^m$) for generic irreducible polynomials, therefore made versatile. Estimation of area and time complexities of the proposed sequential multiplier is performed and comparison with existing sequential multipliers is presented. The proposed sequential multiplier achieves 50% reduction in area-delay product over the best of existing sequential multipliers for m = 163, indicating an efficient design in terms of both area and delay. The Application Specific Integrated Circuit (ASIC) and the Field Programmable Gate Array (FPGA) implementation results indicate a significantly less power-delay and area-delay products of the proposed sequential multiplier over existing multipliers.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.1
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• pp.19-30
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• 2021

In this paper, when SIDH is instantiated using only 3- and 5-isogeny, we demonstrate which curve is more efficient among the Montgomery, Edwards, and Huff curves. To this end, we present the computational cost of the building blocks of SIDH on Montgomery, Edwards, and Huff curves. We also present the prime we used and parameter settings for implementation. The result of our work shows that the performance of SIDH on Montgomery and Huff curves is almost the same and they are 0.8% faster than Edwards curves. With the possibility of using isogeny of degree other than 3 and 4, the performance of 5-isogeny became even more essential. In this regard, this paper can provide guidelines on the selection of the form of elliptic curves for implementation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.533-544
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• 2021

Using Shor algorithm, factoring and discrete logarithm problem can be solved effectively. The public key cryptography, such as RSA and ECC, based on factoring and discrete logarithm problem can be broken in polynomial time using Shor algorithm. NIST has been conducting a PQC(Post Quantum Cryptography) standardization process to select quantum-resistant public key cryptography. The multivariate quadratic based signature scheme, which is one of the PQC candidates, is suitable for IoT devices with limited resources due to its short signature and fast sign and verify process. We analyzes classic attacks and quantum attacks for Rainbow which is the only multivatiate quadratic based signature scheme to be finalized up to the round 3. Also we compute the attack complexity for the round 3 Rainbow parameters, and analyzes the security level of Rainbow, one of the PQC standardization candidates.

• 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.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.414-426
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• 2022

Elliptic Curve Cryptography (ECC) is one of the finest cryptographic technique of recent time due to its lower key length and satisfactory performance with different hardware structures. In this paper, a High Throughput Multiplier architecture is introduced for Elliptic Cryptographic applications based on concurrent computations. With the aid of the concurrent computing approach, the High Throughput Concurrent Computation (HTCC) technology that was just presented improves the processing speed as well as the overall efficiency of the point-multiplier architecture. Here, first and second distinct group operation of point multiplier are combined together and synthesised concurrently. The synthesis of proposed HTCC technique is performed in Xilinx Virtex - 5 and Xilinx Virtex - 7 of Field-programmable gate array (FPGA) family. In terms of slices, flip flops, time delay, maximum frequency, and efficiency, the advantages of the proposed HTCC point multiplier architecture are outlined, and a comparison of these advantages with those of existing state-of-the-art point multiplier approaches is provided over GF(2¹⁶³), GF(2²³³) and GF(2²⁸³). The efficiency using proposed HTCC technique is enhanced by 30.22% and 75.31% for Xilinx Virtex-5 and by 25.13% and 47.75% for Xilinx Virtex-7 in comparison according to the LC design as well as the LL design, in their respective fashions. The experimental results for Virtex - 5 and Virtex - 7 over GF(2²³³) and GF(2²⁸³)are also very satisfactory.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.497-508
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• 2021

In this paper, we focus on optimizing the performance of CSURF, which uses the tweaked Montgomery curves. The projective version of elliptic curve arithmetic is slower on tweaked Montgomery curves than on Montgomery curves, so that CSURF is slower than the hybrid version of CSIDH. However, as the square-root Velu formula uses less number of ellitpic curve arithmetic than the standard Velu formula, there is room for optimization We optimize the square-root Velu formula and 2-isogeny formula on tweaked Montgomery curves. Our CSURFis 14% faster than the standard CSURF, and 10.8% slower than the CSIDH using the square-root Velu formula. The constant-time CSURF is 6.8% slower than constant-time CSIDH. Compared to the previous implementations, this is a remarkable result.

• ETRI Journal
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• v.30 no.3
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• pp.365-376
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• 2008

This paper presents the design and implementation of a hyperelliptic curve cryptography (HECC) coprocessor over affine and projective coordinates, along with measurements of its performance, hardware complexity, and power consumption. We applied several design techniques, including parallelism, pipelining, and loop unrolling, in designing field arithmetic units, group operation units, and scalar multiplication units to improve the performance and power consumption. Our affine and projective coordinate-based HECC processors execute in 0.436 ms and 0.531 ms, respectively, based on the underlying field GF($2^{89}$). These results are about five times faster than those for previous hardware implementations and at least 13 times better in terms of area-time products. Further results suggest that neither case is superior to the other when considering the hardware complexity and performance. The characteristics of our proposed HECC coprocessor show that it is applicable to high-speed network applications as well as resource-constrained environments, such as PDAs, smart cards, and so on.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.6
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• pp.1137-1148
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• 2021

The main obstacle for implementing CSIDH-based cryptography is that it requires generating a kernel of a small prime order to compute the group action using Velu's formula. As this is a quite painstaking process for small torsion points, a new approach called radical isogeny is recently proposed to compute chains of isogenies from a coefficient of an elliptic curve. This paper presents an optimized implementation of radical isogenies and analyzes its ideal use in CSIDH-based cryptography. We tailor the formula for transforming Montgomery curves and Tate normal form and further optimized the radical 2- and 3- isogeny formula and a projective version of radical 5- and 7- isogeny. For CSIDH-512, using radical isogeny of degree up to 7 is 15.3% faster than standard constant-time CSIDH. For CSIDH-4096, using only radical 2-isogeny is the optimal choice.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.8
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• pp.1443-1448
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• 2006

As computers and networks become popular, distributing information on the Internet is common in our daily life. In the past, e-mail has been the primary choice of exchanging information but messengers are gaining popularity abroad and domestically because of their nature of getting immediate responses. Information leakage by invasion that is enemy of evil in communication of communications division Server and Agent between each agents that become burden of communication for effective administration of data for most of existing messenger is becoming an issue. In this paper, we design a secure messenger system that could be obtained maximum security. It use ECC based on ElGamal methodology using PKI for secure communication. For the message encryption and decryption between the same group non, each group is kept distinct by drawing an elliptic curve and an arbitrary point is chosen on the curve.