Implementing the Tate Pairing

Galbraith, Steven D.; Harrison, K. J.; Soldera, David

doi:10.1007/3-540-45455-1_26

Cited by 380 publications

(221 citation statements)

References 13 publications

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“…To our knowledge, [29] is the first work that describes GF (3 m ) architectures for applications of cryptographic significance, thus we describe it in some detail. The authors describe a representation similar to the one used by [10] to represent their polynomials. They combine all the least significant bits of the coefficients of an element, say A, into one value and all the most significant bits of the coefficients of A into a second value (notice the coefficients of A are elements of GF (3) and thus 2 bits are needed to represent each of them).…”

Section: Related Workmentioning

confidence: 99%

“…Three implementation were developed which support the fields GF (3 97 ), GF (2 151 ), and GF (2 241 ). The fields GF (3 97 ) and GF (2 241 ) are used in Weil and Tate pairing schemes for systems with comparable degrees of security (see [10,5,29]). The field GF (2 151 ) offers security comparable to that of GF (3 97 ) for cryptosystems based on the EC discrete logarithm problem.…”

Section: Irreducible Polynomials Over Gf (3)mentioning

confidence: 99%

“…Because characteristic 2 field arithmetic has been extensively studied in the literature, authors have concentrated the efforts to improve the performance of systems based on characteristic 3 arithmetic 4 . For example, [5,10] describe algorithms to improve the efficiency of the pairing computations. [10] also introduces some clever tricks to improve the efficiency of the underlying arithmetic in software based solutions.…”

Section: Introductionmentioning

confidence: 99%

“…For example, [5,10] describe algorithms to improve the efficiency of the pairing computations. [10] also introduces some clever tricks to improve the efficiency of the underlying arithmetic in software based solutions. [29] treats the hardware implementation of fields of characteristic 3.…”

Section: Introductionmentioning

confidence: 99%

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Efficient GF(p m ) Arithmetic Architectures for Cryptographic Applications

Bertoni

Guajardo

Kumar

et al. 2003

Lecture Notes in Computer Science

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Abstract.Recently, there has been a lot of interest on cryptographic applications based on fields GF (p m ), for p > 2. This contribution presents GF (p m ) multipliers architectures, where p is odd. We present designs which trade area for performance based on the number of coefficients that the multiplier processes at one time. Families of irreducible polynomials are introduced to reduce the complexity of the modulo reduction operation and, thus, improved the efficiency of the multiplier. We, then, specialize to fields GF (3 m ) and provide the first cubing architecture presented in the literature. We synthesize our architectures for the special case of GF (3 97 ) on the XCV1000-8-FG1156 and XC2VP20-7-FF1156 FPGAs and provide area/performance numbers and comparisons to previous GF (3 m ) and GF (2 m ) implementations. Finally, we provide tables of irreducible polynomials over GF (3) of degree m with 2 ≤ m ≤ 255.

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Section: Related Workmentioning

confidence: 99%

Section: Irreducible Polynomials Over Gf (3)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient GF(p m ) Arithmetic Architectures for Cryptographic Applications

Bertoni

Guajardo

Kumar

et al. 2003

Lecture Notes in Computer Science

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“…In this case, the verifying process remains just two pairing computations. Although pairing computation is expensive, there are many improvements in implementation of the pairings as in [4,12]. Utilizing those good implementations, our scheme can be efficient in performance.…”

Section: Discussionmentioning

confidence: 99%

Yet Another Forward Secure Signature from Bilinear Pairings

Kim

2006

Information Security and Cryptology - ICISC 2005

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Abstract. In this work, we have proposed yet another forward secure signature based on bilinear pairings. Our forward secure signature requires the general security parameters only independent to the total number of time periods. The scheme can perform key evolving for unlimited time periods while maintaining sizes of keys and signature fixed. In addition, the signing algorithm is very efficient with the simple verification algorithm. We also provide a formal definition along with a detailed security proof of our signature scheme under the assumption of Computational Diffie-Hellman problem.

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A home security system for seniors based on the beacon technology

Tsai

2018

Concurrency and Computation

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Summary Many elderly people have a hard time adapting to information technology (IT); for instance, many wearable devices have such rich functions that render them highly power‐consuming, creating operational difficulties for the elderly. The wearable devices must constantly be recharged, which is also an issue for disabled elderly people. Hence, this study utilizes transmitter and receiver of the beacon to learn about the habits of elderly people in their residence while monitoring their heart rate to track their physical condition; when and if they press the medical alarm, help can be sent on their way. This study uses the beacon device to position the location of elderly people in their residence. We have developed a wearable wristband that transmits data through the beacon. The only button on the wristband is a medical alarm; other functions include home positioning and heart rate monitoring, which operate automatically to relieve the elderly people from information technology adaptation issues. This paper will also develop an integrative monitoring platform that aims at detecting whether an elderly person has pressed the medical alarm as well as analyzing whether their heart rate is regular. Given that elderly people stay mostly within the range of their residence, the platform will conduct statistical analysis on schedule of the elderly person of being in and out of the house; if they have left their house for too long or have displayed irregular behavior in leaving or entering the house, then their family will be notified. The proposed method has added privacy and access authority control to prevent malicious parties from tracking the schedule or the residence of elderly people from being invaded. This study has also completed application development and conducted privacy efficacy analysis.

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Implementing the Tate Pairing

Cited by 380 publications

References 13 publications

Efficient GF(p m ) Arithmetic Architectures for Cryptographic Applications

Efficient GF(p m ) Arithmetic Architectures for Cryptographic Applications

Yet Another Forward Secure Signature from Bilinear Pairings

A home security system for seniors based on the beacon technology

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