A Comparison between Hardware Accelerators for the Modified Tate Pairing over $\mathbb{F}_{2^m}$ and $\mathbb{F}_{3^m}$

Beuchat, Jean-Luc; Brisebarre, Nicolas; Detrey, Jérémie; Okamoto, Eiji; Rodríguez-Henríquez, Francisco

doi:10.1007/978-3-540-85538-5_20

Cited by 29 publications

(39 citation statements)

References 31 publications

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“…To our knowledge, the place-and-route results on several Xilinx FPGA devices of our designs improved both the computation time and the area-time tradeoff of all the hardware pairing coprocessors previously published in the open literature [28,29,1,30,19,32,41,40,39,7,43,10,25]. We are also currently applying the same methodology used in this work to design a coprocessor for the Tate pairing over F 2 m , with promising preliminary results.…”

Section: Resultsmentioning

confidence: 65%

“…Table 2 provides the reader with a comparison between our work and accelerators for the Tate and the η T pairing over supersingular (hyper)elliptic curves published in the open literature (our comparison remains fair since the Tate pairing can be computed from the η T pairing at no extra cost [7]). The third column measures the security of the curve as the key length required by a symmetric-key algorithm of equivalent security.…”

Section: Results and Comparisonsmentioning

confidence: 99%

“…Beuchat et al [7] introduced a unified arithmetic operator in order to reduce the silicon footprint of the circuit to ensure scalability, while trying to minimize the impact on the overall performances. In this work, we focused on the other end of the hardware design spectrum and significantly reduced the computation time reported by Beuchat et al in [7]. A much more unexpected result is that we also improved the AT product.…”

Section: Results and Comparisonsmentioning

confidence: 99%

“…In 2004, Barreto et al [3] introduced the η T approach, which further shortens the loop of Miller's algorithm. Recall that the modified Tate pairing can be computed from the reduced η T pairing at almost no extra cost [7]. More recently, Hess, Smart, and Vercauteren generalized these results to ordinary curves [24,45,23].…”

Section: Introductionmentioning

confidence: 95%

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Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

Beuchat

Detrey

Estibals

et al. 2009

Lecture Notes in Computer Science

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Abstract. This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier. Thanks to a careful selection of algorithms for computing the tower field arithmetic associated to the Tate pairing, we manage to keep the pipeline busy. We also describe the strategies we considered to design our parallel multiplier. They are included in a VHDL code generator allowing for the exploration of a wide range of operators. Then, we outline the architecture of a coprocessor for the Tate pairing over F3m . However, a final exponentiation is still needed to obtain a unique value, which is desirable in most of the cryptographic protocols. We supplement our pairing accelerator with a coprocessor responsible for this task. An improved exponentiation algorithm allows us to save hardware resources.According to our place-and-route results on Xilinx FPGAs, our design improves both the computation time and the area-time trade-off compared to previoulsy published coprocessors.

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Section: Resultsmentioning

confidence: 65%

Section: Results and Comparisonsmentioning

confidence: 99%

Section: Results and Comparisonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

Beuchat

Detrey

Estibals

et al. 2009

Lecture Notes in Computer Science

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“…Several architectures for the computation of cryptographic pairings have been proposed in the literature [14,15,16,17,18,19,20,21,22,23,24,25,26]. All these implementations use supersingular curves over fields of characteristic 2 or 3, achieving only very low security levels, sometimes even below 80 bit.…”

Section: Related Workmentioning

confidence: 99%

Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves

Kammler

Zhang

Schwabe

et al. 2009

Lecture Notes in Computer Science

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Abstract. This paper presents a design-space exploration of an application-specific instruction-set processor (ASIP) for the computation of various cryptographic pairings over Barreto-Naehrig curves (BN curves). Cryptographic pairings are based on elliptic curves over finite fields-in the case of BN curves a field Fp of large prime order p. Efficient arithmetic in these fields is crucial for fast computation of pairings. Moreover, computation of cryptographic pairings is much more complex than elliptic-curve cryptography (ECC) in general. Therefore, we facilitate programming of the proposed ASIP by providing a C compiler.In order to speed up Fp arithmetic, a RISC core is extended with additional scalable functional units. Because the resulting speedup can be limited by the memory throughput, utilization of multiple data-memory banks is proposed.The presented design needs 15.8 ms for the computation of the Optimal-Ate pairing over a 256-bit BN curve at 338 MHz implemented with a 130 nm standard cell library. The processor core consumes 97 kGates making it suitable for the use in embedded systems.

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Fast Symmetric Pairing Revisited

Zhang

Wang

2014

Pairing-Based Cryptography – Pairing 2013

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A Comparison between Hardware Accelerators for the Modified Tate Pairing over $\mathbb{F}_{2^m}$ and $\mathbb{F}_{3^m}$

Cited by 29 publications

References 31 publications

Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves

Fast Symmetric Pairing Revisited

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