The Experts below are selected from a list of 5778 Experts worldwide ranked by ideXlab platform
Peng Dai-yuan - One of the best experts on this subject based on the ideXlab platform.
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Fast Scalar Multiplication Based on Sliding Window Technology
Computer Science, 2012Co-Authors: Peng Dai-yuanAbstract:Scalar Multiplication is the heart of elliptic curve cryptosystems.In recent years,how to realize efficient Scalar Multiplication is a research focus of information security field.By means of the wMOF representations of Scalar and the direct computation 2kQ+P strategy,we modified the Scalar Multiplication algorithm based on sliding window technology.The analysis results indicate that the efficiency of the algorithms is improved obviously and the storage requirements are reduced,and it can enhance the ECC's efficiency.
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Efficient Scalar Multiplication without Precomputation
Journal of the China Railway Society, 2012Co-Authors: Peng Dai-yuanAbstract:Scalar Multiplication is the fundamental and time-consuming operation in elliptic curve cryptosystems,the performance of the elliptic curve cryptosysytem deeply depends on the efficiency of Scalar Multiplication.In this paper,the new signed binary Scalar representation method of the digit set {-1,0,1},with the minimal Hamming weight,shortest significant length and longer average zero-run length,was presented,and the efficient Scalar Multiplication algorithm was obtained by using direct computation of the 2kQ+P strategy.The analysis results show that the average calculation time is shortened by 26.1% in comparison to the traditional NAF method.
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Fast Scalar Multiplication Algorithm with Low Memory Requirement
Computer Engineering, 2012Co-Authors: Li Zhong, Peng Dai-yuanAbstract:(Abstract )The Scalar Multiplication of Elliptic Curve Cryptosysytem(ECC) has big computational costs and memory consumption. Aiming at this problem, by means of the 2MOF representation of Scalar, this paper uses the direct computation 2Q+P strategy, proposes a lower memory cost and some efficient left0to0right Scalar Multiplication algorithm. The analysis result indicates that this algorithm has lower computational cost and memory consumption, and can enhance the ECC's efficiency in resource constrained environment.
Toru Akishita - One of the best experts on this subject based on the ideXlab platform.
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fast simultaneous Scalar Multiplication on elliptic curve with montgomery form
Selected Areas in Cryptography, 2001Co-Authors: Toru AkishitaAbstract:We propose a new methodto compute x-coordinate of kP + lQ simultaneously on the elliptic curve with Montgomery form over Fp without precomputedp oints. To compute x-coordinate of kP +lQ is requiredin ECDSA signature verification. The proposedmetho dis about 25% faster than the methodusing Scalar Multiplication andthe recovery of Y -coordinate of kP and lQ on the elliptic curve with Montgomery form over Fp, and also slightly faster than the simultaneous Scalar Multiplication on the elliptic curve with Weierstrass form over Fp using NAF and mixedco ordinates. Furthermore, our methodis applicable to Montgomery methodon elliptic curves over F2n.
Sylvain Duquesne - One of the best experts on this subject based on the ideXlab platform.
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Efficient Scalar Multiplication for Ate Based Pairing over KSS Curve of Embedding Degree 18
Information Security Applications, 2017Co-Authors: Md. Al-amin Khandaker, Hwajeong Seo, Yasuyuki Nogami, Sylvain DuquesneAbstract:Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient Scalar Multiplication on higher degree rational points. In this paper we proposed a Scalar Multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree $$k = 18$$k=18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation $$\#E({\mathbb {F}}_{p}) = p+1-t$$#E(Fp)=p+1-t mod r by applying Frobenius mapping with rational point to enhance the Scalar Multiplication. In addition we proposed z-adic representation of Scalar s. In combination of Frobenious mapping with multi-Scalar Multiplication technique we efficiently calculate Scalar Multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster Scalar Multiplication compared to binary Scalar Multiplication, sliding-window and non-adjacent form method.
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Montgomery Scalar Multiplication for genus 2 curves
2016Co-Authors: Sylvain DuquesneAbstract:Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for Scalar Multiplication to the jacobian of these curves. Previously this method was only known for elliptic curves. We obtain an algorithm that is competitive compared to the usual methods of Scalar Multiplication and that has additional properties such as resistance to timings attacks. This algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on smart cards.
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ANTS - Montgomery Scalar Multiplication for Genus 2 Curves
Lecture Notes in Computer Science, 2004Co-Authors: Sylvain DuquesneAbstract:Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for Scalar Multiplication to the jacobian of these curves. Previously this method was only known for elliptic curves. We obtain an algorithm that is competitive compared to the usual methods of Scalar Multiplication and that has additional properties such as resistance to timings attacks. This algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on smart cards.
Ding Yong - One of the best experts on this subject based on the ideXlab platform.
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Extended Algorithm for Scalar Multiplication Based on Point Halving and MBNS
Computer Engineering, 2011Co-Authors: Ding YongAbstract:This paper proposes a representation of a Scalar k in the form of,where d belongs to a given digit set.This representation is a combination of the point halving and MBNS representation using the method of Extended DBNS.A Scalar Multiplication relying on the representation is given.Experimental results show that the approach leads to a shorter MBNS expansion and a lower complexity in elliptic curve Scalar Multiplication at the cost of a few pre-computations and storages.
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φ -NAF_w Decomposition of Scalar Multiplication of ECC
Computer Engineering, 2009Co-Authors: Ding YongAbstract:For fast computation of Scalar Multiplication of the elliptic curve over GF(p), with the utilization of the endomorphismφ whose characteristic polynomial is φ 2 + 2 = 0, φ -NAF expansion of the integer k is proposed by Ciet in order to speed up the computation of Scalar Multiplication kP. In this paper, a window technic is applied to the φ -NAF representation, which gets the φ -NAF w decomposition of k and can obtain better result than φ -NAF representation with the cost of some quantities of storages. The length and the density of the expansion is accurately estimated.
Camille Vuillaume - One of the best experts on this subject based on the ideXlab platform.
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Short-Memory Scalar Multiplication for Koblitz Curves
IEEE Transactions on Computers, 2008Co-Authors: Camille Vuillaume, K. Okeya, Tsuyoshi TakagiAbstract:This paper presents a Scalar Multiplication method for Koblitz curves. Koblitz curves are elliptic curves where the Scalar Multiplication can be computed in a much faster way than with other curves, allowing designs and implementations without arithmetic coprocessor. The new method is as fast as the fastest known techniques on Koblitz curves but requires much less memory; therefore, it is of particular interest for environments with low resources. Our technique is well suited for both hardware and software implementations. In hardware, we show that a normal basis implementation reduces memory consumption by 85 percent compared to conventional methods, but this still has exactly the same computational cost. In software, thanks to a mixed normal-polynomial bases approach, our technique allows memory savings up to 70 percent and, depending on the instruction set of the CPU, can be as fast as the fastest known Scalar Multiplication methods or can even beat them by a large margin. Therefore, in software and in hardware, our Scalar Multiplication technique offers high performance without sacrifice in view of memory.
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Short memory Scalar Multiplication on Koblitz curves
Lecture Notes in Computer Science, 2005Co-Authors: K. Okeya, Tsuyoshi Takagi, Camille VuillaumeAbstract:We present a new method for computing the Scalar Multiplication on Koblitz curves. Our method is as fast as the fastest known technique but requires much less memory. We propose two settings for our method. In the first setting, well-suited for hardware implementations, memory requirements are reduced by 85%. In the second setting, well-suited for software implementations, our technique reduces the memory consumption by 70%. Thus, with much smaller memory usage, the proposed method yields the same efficiency as the fastest Scalar Multiplication schemes on Koblitz curves.
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CHES - Short memory Scalar Multiplication on koblitz curves
Cryptographic Hardware and Embedded Systems – CHES 2005, 2005Co-Authors: K. Okeya, Tsuyoshi Takagi, Camille VuillaumeAbstract:We present a new method for computing the Scalar Multiplication on Koblitz curves. Our method is as fast as the fastest known technique but requires much less memory. We propose two settings for our method. In the first setting, well-suited for hardware implementations, memory requirements are reduced by 85%. In the second setting, well-suited for software implementations, our technique reduces the memory consumption by 70%. Thus, with much smaller memory usage, the proposed method yields the same efficiency as the fastest Scalar Multiplication schemes on Koblitz curves.
