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Efficient Scalar Multiplication for Ate Based Pairing over KSS Curve of Embedding Degree 18 査読

Khandaker, Md. Al-Amin, Nogami, Yasuyuki, Seo, Hwajeong, Duquesne, Sylvain

INFORMATION SECURITY APPLICATIONS, WISA 2016 10144 221 - 232 2017年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：SPRINGER INTERNATIONAL PUBLISHING AG

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 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(F-p) = 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.

DOI： 10.1007/978-3-319-56549-1_19

その他リンク： https://dblp.uni-trier.de/db/conf/wisa/wisa2016.html#KhandakerNSD16

Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18 査読

Md Al Amin Khandaker, Yasuyuki Nogami, Hwajeong Seo, Sylvain Duquesne

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10144 LNCS 221 - 232 2017年

掲載種別：研究論文（国際会議プロシーディングス）

© Springer International Publishing AG 2017. 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 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(F p) = 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.

DOI： 10.1007/978-3-319-56549-1_19

Efficient Optimal Ate Pairing at 128-Bit Security Level. 査読

Md. Al-Amin Khandaker, Yuki Nanjo, Loubna Ghammam, Sylvain Duquesne, Yasuyuki Nogami, Yuta Kodera

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10698 LNCS 186 - 205 2017年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：SPRINGER INTERNATIONAL PUBLISHING AG

Following the emergence of Kim and Barbulescu’s new number field sieve (exTNFS) algorithm at CRYPTO’16 [21] for solving discrete logarithm problem (DLP) over the finite field; pairing-based cryptography researchers are intrigued to find new parameters that confirm standard security levels against exTNFS. Recently, Barbulescu and Duquesne have suggested new parameters [3] for well-studied pairing-friendly curves i.e., Barreto-Naehrig (BN) [5], Barreto-Lynn-Scott (BLS-12) [4] and Kachisa-Schaefer-Scott (KSS-16) [19] curves at 128-bit security level (twist and sub-group attack secure). They have also concluded that in the context of Optimal-Ate pairing with their suggested parameters, BLS-12 and KSS-16 curves are more efficient choices than BN curves. Therefore, this paper selects the atypical and less studied pairing-friendly curve in literature, i.e., KSS-16 which offers quartic twist, while BN and BLS-12 curves have sextic twist. In this paper, the authors optimize Miller’s algorithm of Optimal-Ate pairing for the KSS-16 curve by deriving efficient sparse multiplication and implement them. Furthermore, this paper concentrates on the Miller’s algorithm to experimentally verify Barbulescu et al.’s estimation. The result shows that Miller’s algorithm time with the derived pseudo 8-sparse multiplication is most efficient for KSS-16 than other two curves. Therefore, this paper defends Barbulescu and Duquesne’s conclusion for 128-bit security.

DOI： 10.1007/978-3-319-71667-1_10

An ECC Implementation with a Twisted Montgomery Curve over Fq32 on an 8-Bit Microcontroller. 査読

Yuta Hashimoto, Md. Al-Amin Khandaker, Yuta Kodera, Taehwan Park, Takuya Kusaka, Howon Kim, Yasuyuki Nogami

Proceedings - 2017 5th International Symposium on Computing and Networking, CANDAR 2017 2018-January 445 - 450 2017年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

The security of Internet of Things (IoT) devices is one of the most important problems. The processing ability of IoT devices is limited, therefore a more light-weight and secure cryptography is necessary. This paper shows the implementation of 256-bit Elliptic Curve Cryptography (ECC) on an 8-bit microcontroller by applying towering for extension field of degree 32. The authors use a twisted Montgomery curve with a Montgomery ladder which enables fast calculations without inverse elements. In addition to that, this implementation is considered resistant to the Side Channel Attack (SCA) since it applies the Montgomery ladder for the scalar multiplication (SCM). This ECC implementation on Arduino UNO, an 8-bit microcontroller board, takes 3 seconds for an SCM which can be made faster by careful assembly implementation.

DOI： 10.1109/CANDAR.2017.90

Interleaved sequences of geometric sequences binarized with Legendre symbol of two types.

Kazuyoshi Tsuchiya, Yasuyuki Nogami, Satoshi Uehara

CoRR abs/1709.05163 2017年

Efficient operation over F<inf>(24)2</inf> for security technologies

Norito Jitsui, Yasuyuki Nogami, Hwajeong Seo, Nasima Begum

2016 IEEE International Conference on Consumer Electronics-Taiwan, ICCE-TW 2016 17 - 18 2016年7月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Binary extension field F28 is recently used for AES encryption and IoT (Internet of Things) security with PUF (Physical Unclonable Function). The calculations over tower field such as F(24)2 or F((22)2)2 become more efficient than that of over F28. This paper focuses on the efficient calculations over F(24)2.

DOI： 10.1109/ICCE-TW.2016.7520896

A dynamic job scheduling method for reliable and high-performance volunteer computing

Shinya Yasuda, Yasuyuki Nogami, Masaru Fukushi

2015 IEEE 2nd International Conference on InformationScience and Security, ICISS 2015 100 - 103 2016年1月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

This paper proposes a dynamic job scheduling method for reliable and high-performance volunteer computing. In volunteer computing, each job is replicated and allocated to multiple participants (workers) to remove incorrect results by a voting mechanism. Hence, the number of workers necessary to complete a job is an important factor for the system performance; however, this is not well-considered in the existing methods. The proposed method defines the expected probability of completion for each job based on the worker's secession probability. By allocating each job so that the expected probability is always greater than a specified value, the proposed method avoids excess job allocation, which leads to the higher performance. The performance of the proposed method is evaluated by computer simulation, under the two scenarios of workers having uniform and different processing speeds. It is found that the performance of the proposed method is higher than the existing method especially under the practical latter scenario.

DOI： 10.1109/ICISSEC.2015.7370964

An Improvement of Scalar Multiplication on Elliptic Curve Defined over Extension Field F-q(2) 査読

Khandaker Md. Al-Amin, Yasuyuki Nogami

2016 IEEE INTERNATIONAL CONFERENCE ON CONSUMER ELECTRONICS-TAIWAN (ICCE-TW) 13 - 14 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

In elliptic curve cryptography (ECC), a scalar multiplication for rational point is the most time consuming operation. This paper proposes an efficient calculation for a scalar multiplication by applying Frobenious Mapping. Particularly, this paper deals with Barreto-Naehrig curve defined over extension field F-q(2), where q - p(6) and p is a large prime.

DOI： 10.1109/ICCE-TW.2016.7520894

A Consideration of Towering Scheme for Efficient Arithmetic Operation over Extension Field of Degree 18 査読

Khandaker, Md. Al-Amin, Nogami, Yasuyuki

PROCEEDINGS OF THE 2016 19TH INTERNATIONAL CONFERENCE ON COMPUTER AND INFORMATION TECHNOLOGY (ICCIT) 276 - 281 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Barreto-Naehrig (BN) curve is a well studied pairing friendly curve of embedding degree 12, that uses arithmetic in F-p12. Therefore the arithmetic of F-p12 extension field is well studied. In this paper, we have proposed an efficient approach of arithmetic operation over the extension field of degree 18 by towering. F-p18 extension field arithmetic is considered to be the basis of implementing the next generation pairing based security protocols. We have proposed to use F-p element to construct irreducible binomial for building tower of extension field up to F-p6, where conventional approach uses the root of previous irreducible polynomial to create next irreducible polynomials. Therefore using F-p elements in irreducible binomial construction, reduces the number of multiplications in F-p to calculate inversion and multiplication over F-p18, which effects acceleration in total arithmetic operation over F-p18.

DOI： 10.1109/ICCITECHN.2016.7860209

Isomorphic Mapping for Ate-based Pairing over KSS Curve of Embedding Degree 18 査読

Khandaker, Md. Al-Amin, Nogami, Yasuyuki

2016 FOURTH INTERNATIONAL SYMPOSIUM ON COMPUTING AND NETWORKING (CANDAR) 629 - 634 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Pairing based cryptography is considered as the next generation of security for which it attracts many researcher to work on faster and efficient pairing to make it practical. Among the several challenges of efficient pairing; efficient scalar multiplication of rational point defined over extension field of degree k >= 12 is important. However, there exists isomorphic rational point group defined over relatively lower degree extension field. Exploiting such property, this paper has showed a mapping technique between isomorphic rational point groups in the context of Ate-based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree k = 18. In the case of KSS curve, there exists sub-field sextic twisted curve that includes sextic twisted isomorphic rational point group defined over F(p)3. This paper has showed the mapping procedure from certain F(p)18 rational point group to its sub-field isomorphic rational point group in F(p)3 and vice versa. This paper has also showed that scalar multiplication is about 20 times faster after applying the proposed mapping which in-turns resembles that the impact of this mapping will greatly enhance the pairing operation in KSS curve.

DOI： 10.1109/CANDAR.2016.38

その他リンク： https://dblp.uni-trier.de/db/conf/ic-nc/candar2016.html#KhandakerN16

A new approach for generating well balanced Pseudo-random signed binary sequence over odd characteristic field. 査読

Ali Md. Arshad, Yasuyuki Nogami, Chiaki Ogawa, Hiroto Ino, Satoshi Uehara, Robert Morelos-Zaragoza,Kazuyoshi Tsuchiya

2016 International Symposium on Information Theory and Its Applications, ISITA 2016, Monterey, CA, USA, October 30 - November 2, 2016 777 - 780 2016年

Auto and Cross Correlation of Well Balanced Sequence over Odd Characteristic Field. 査読

Ali Md. Arshad, Yasuyuki Nogami, Hiroto Ino, Satoshi Uehara

Fourth International Symposium on Computing and Networking, CANDAR 2016, Hiroshima, Japan, November 22-25, 2016 604 - 609 2016年

Pseudo Random Sequence over Finite Field using Mobius Function 査読

Fatema Akhter, Yasuyuki Nogami

2016 INTERNATIONAL WORKSHOP ON COMPUTATIONAL INTELLIGENCE (IWCI) 68 - 72 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Pseudo random sequences play an important role in cryptography and network security system. This paper proposes a new approach for generation of pseudo random sequence over odd characteristic field. The sequence is generated by applying a primitive polynomial over odd characteristic field, trace function and mobius function. Then, some important properties of the newly generated sequence such as period, autocorrelation and cross-correlation have been studied in this work. The properties of the generated sequence are evaluated on various bit length of odd characteristics. Finally, the experimental results are compared with existing works which show the superiority of the proposed sequence over existing ones.

Linear Complexity of Signed Binary Sequence Over Odd Characteristic Field 査読

Ali Md. Arshad, Hiroto Ino, Chiaki Ogawa, Yasuyuki Nogami

PROCEEDINGS OF THE 2016 19TH INTERNATIONAL CONFERENCE ON COMPUTER AND INFORMATION TECHNOLOGY (ICCIT) 266 - 269 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

In our previous work, well balanced pseudo random signed binary sequence generated by using trace function and Legendre symbol has been researched. Our previous sequence generated by applying primitive polynomial over odd characteristic field F-p, trace function and Legendre symbol. The important features such as period, periodic autocorrelation, and cross-correlation have already been well discussed in our previous work. In this paper, the signed binary sequence is generated by utilizing one additional parameter A. Let p be an odd prime and F-p is an odd characteristic prime field and m be the degree of the primitive polynomial f(x). The procedure for generating sequence is as follows: primitive polynomial f (x) generates maximum length vector sequence, then trace function Tr (.) maps an element of extension field F(p)m to an element of prime field F-p, next a non-zero scalar A is an element of F-p is added to the trace value and finally Legendre symbol is used to map the scalars into signed binary sequence. In this paper, the authors have restricted the discussion on linear complexity and linear complexity profile properties of signed binary sequence based on some experimental results.

DOI： 10.1109/ICCITECHN.2016.7860207

Parallel Implementations of LEA, Revisited.

Hwajeong Seo, Taehwan Park, Shinwook Heo, Gyuwon Seo, Bongjin Bae, Zhi Hu, Lu Zhou, Yasuyuki Nogami, Youwen Zhu, Howon Kim

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10144 LNCS 318 - 330 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：SPRINGER INTERNATIONAL PUBLISHING AG

In this paper we revisited the parallel implementations of LEA. By taking the advantages of both the light-weight features of LEA and the parallel computation abilities of ARM-NEON platforms, performance is significantly improved. We firstly optimized the implementations on ARM and NEON architectures. For ARM processor, barrel shifter instruction is used to hide the latencies for rotation operations. For NEON engine, the minimum number of NEON registers are assigned to the round key variables by performing the on-time round key loading from ARM registers. This approach reduces the required NEON registers for round key variables by three registers and the registers and temporal registers are used to retain four more plaintext for encryption operation. Furthermore, we finely transform the data into SIMD format by using transpose and swap instructions. The compact ARM and NEON implementations are combined together and computed in mixed processing way. This approach hides the latency of ARM computations into NEON overheads. Finally, multiple cores are fully exploited to perform the maximum throughputs on the target devices. The proposed implementations achieved the fastest LEA encryption within 3.2 cycle/byte for Cortex-A9 processors.

DOI： 10.1007/978-3-319-56549-1_27

その他リンク： https://dblp.uni-trier.de/db/conf/wisa/wisa2016.html#SeoPHSBHZNZK16

Pseudo random sequence over finite field using Möbius Function.

Fatema Akhter, Yasuyuki Nogami

IWCI 2016 - 2016 International Workshop on Computational Intelligence 69 - 73 2016年

掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Pseudo random sequences play an important role in cryptography and network security system. This paper proposes a new approach for generation of pseudo random sequence over odd characteristic field. The sequence is generated by applying a primitive polynomial over odd characteristic field, trace function and möbius function. Then, some important properties of the newly generated sequence such as period, autocorrelation and cross-correlation have been studied in this work. The properties of the generated sequence are evaluated on various bit length of odd characteristics. Finally, the experimental results are compared with existing works which show the superiority of the proposed sequence over existing ones.

DOI： 10.1109/IWCI.2016.7860341

その他リンク： https://dblp.uni-trier.de/db/conf/iwci/iwci2016.html#AkhterN16

A Pseudo-random Binary Sequence Generated by Using Primitive Polynomial of Degree 2 over Odd Characteristic Field F-p 査読

Ali Md. Arshad, Yasuyuki Nogami

2016 IEEE INTERNATIONAL CONFERENCE ON CONSUMER ELECTRONICS-TAIWAN (ICCE-TW) 15 - 16 2016年

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

Let p be an odd prime number as the characteristic of finite field, this paper introduces a pseudo random binary sequence generated by a primitive polynomial of degree 2 over F-p, trace function, and Legendre symbol. Then, its period and autocorrelation are introduced with a small example.

DOI： 10.1109/ICCE-TW.2016.7520895

Highly Efficient GF(2^8) Inversion Circuit Based on Redundant GF Arithmetic and Its Application to AES Design 査読

Rei Ueno, Naofumi Homma, Yukihiro Sugawara, Yasuyuki Nogami, Takafumi Aoki

International Conference on Cryptographic Hardware and Embedded Systems 9293 ( 9293 ) 63 - 80 2015年9月

Efficient implimentation of NTRU over all one polynomial ring with CVMA

Koki Misumi, Yasuyuki Nogami

2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015 384 - 385 2015年8月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

It is shown that public key cryptosystems based on discrete logarithm probrem can be solved if the quantum computer and Shor's algorithm are realized. Thus a new cryptosystem called post-quantum cryptosystem so as not to be broken by quantum computer is needed. NTRU is proposed by Hoffstein et al. in 1998. It is one of post-quantum cryptosystem. It is based on problems on lattice for which there are no efficient algorithms to solve. In NTRU, using convolution polynomial ring as Zq[X]/(Xn-1). However, (X-1), that is a trivial factor of Xn-1 sometimes make problems. Thus we consider a variant using a quotient polynomial ring such as Zq[X]/(Xn + Xx-1 +...+X + 1) and CVMA: Cyclic Vector Multiplication Algorithm.

DOI： 10.1109/ICCE-TW.2015.7216956

A performance evaluation of Web-based volunteer computing using applications with GMP

Shoma Kajitani, Yasuyuki Nogami, Masaru Fukushi, Noriki Amano

2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015 41 - 42 2015年8月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）出版者・発行元：IEEE

This paper presents the performance evaluations of GMP-based applications on Web-based Volunteer Computing (VC) systems. Web-based VC is expected to gather many volunteer participants (workers) by allowing workers to execute a computation program (job) on Web browsers. On the other hand, the job execution performance on workers degraded because jobs are executed on Web browsers. To reveal the actual performance of Web-based VC, we convert practical applications which use GMP, that is a multi-precision library for scientific computations, and evaluate its performance. The experimental results show that the performance degradation is negligibly small in some cases, e.g. a short bit-length of arguments. This paper also shows a potential for the performance improvement of Web-based VC by substituting GMP functions.

DOI： 10.1109/ICCE-TW.2015.7216970

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