Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves

Aranha, Diego F.; Beuchat, Jean-Luc; Detrey, Jérémie; Estibals, Nicolas

doi:10.1007/978-3-642-27954-6_7

Cited by 14 publications

(26 citation statements)

References 46 publications

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“…by two sets of 2-input XORs as defined by x (1) 4 in Table 2. Similarly, we perform m 4 and x (2) 4 in parallel and also do m 6 and x 2 .…”

Section: −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−mentioning

confidence: 99%

“…All the existing designs except [1] are based on elliptic curves. The design of [1] computes optimal-eta pairing on 128-bit secure supersingular Genus-2 binary hyperelliptic curves.…”

Section: Comparison With Existing Designsmentioning

confidence: 99%

“…The design of [1] computes optimal-eta pairing on 128-bit secure supersingular Genus-2 binary hyperelliptic curves. The compact design proposed in [10] computes η T pairing on supersingular elliptic curves over F 3 m fields.…”

Section: Comparison With Existing Designsmentioning

confidence: 99%

“…These CMOS based designs take 15.8ms and 2.9ms for computing an optimal-ate pairing, respectively. Thereafter, designs in [10,14,1,9] are appeared in literature, which computes 128-bit secure pairings in 2.3ms, 16.4ms, 3.5ms, and 1.07ms respectively. However, to the best of our knowledge there is no hardware implementation results available in the literature which computes 128-bit secure pairings below one ms time limit.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High Speed Cryptoprocessor for η T Pairing on 128-bit Secure Supersingular Elliptic Curves over Characteristic Two Fields

Ghosh

Roychowdhury

Das

2011

Cryptographic Hardware and Embedded Systems – CHES 2011

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Abstract. This paper presents an efficient architecture for computing cryptographic ηT pairing for providing 128-bit security. A cryptoprocessor is proposed for Miller's Algorithm with a new 1223-bit Karatsuba multiplier that exploits parallelism. To the best of our knowledge this is the first hardware implementation of 128-bit secure ηT pairing on supersingular elliptic curves over characteristic two fields. The design has been implemented on Xilinx FPGAs. The place-and-route results show that the proposed design takes only 190μs to complete an 128-bit secure ηT pairing on a Virtex-6 FPGA. The proposed cryptoprocessor achieves eight times speedup compared to the best known existing design. It also outperforms the previous designs with respect to area × time product.

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“…by two sets of 2-input XORs as defined by x (1) 4 in Table 2. Similarly, we perform m 4 and x (2) 4 in parallel and also do m 6 and x 2 .…”

Section: −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−mentioning

confidence: 99%

“…All the existing designs except [1] are based on elliptic curves. The design of [1] computes optimal-eta pairing on 128-bit secure supersingular Genus-2 binary hyperelliptic curves.…”

Section: Comparison With Existing Designsmentioning

confidence: 99%

Section: Comparison With Existing Designsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High Speed Cryptoprocessor for η T Pairing on 128-bit Secure Supersingular Elliptic Curves over Characteristic Two Fields

Ghosh

Roychowdhury

Das

2011

Cryptographic Hardware and Embedded Systems – CHES 2011

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show abstract

“…Other types of pairing functions (like Weil, Tate, ate, and R-ate pairings) are also widely studied from implementation perspectives. The hardware and software implementations reported in [2,7,11] (to name a recent few) use other types of pairing.…”

Section: Introductionmentioning

confidence: 99%

GPU-Based Implementation of 128-Bit Secure Eta Pairing over a Binary Field

Bose

Bhattacharya

Das

2013

Progress in Cryptology – AFRICACRYPT 2013

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Abstract. Eta pairing on a supersingular elliptic curve over the binary field F 2 1223 used to offer 128-bit security, and has been studied extensively for efficient implementations. In this paper, we report our GPUbased implementations of this algorithm on an NVIDIA Tesla C2050 platform. We propose efficient parallel implementation strategies for multiplication, square, square root and inverse in the underlying field. Our implementations achieve the best performance when López-Dahab multiplication with four-bit precomputations is used in conjunction with one-level Karatsuba multiplication. We have been able to compute up to 566 eta pairings per second. To the best of our knowledge, ours is the fastest GPU-based implementation of eta pairing. It is about twice as fast as the only reported GPU implementation, and about five times as fast as the fastest reported single-core SIMD implementation. We estimate that the NVIDIA GTX 480 platform is capable of producing the fastest known software implementation of eta pairing.

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Hybrid Digit-Serial Multiplier for Shifted Polynomial Basis of GF(2 m )

Lee

Chiou

et al. 2014

Advances in Intelligent Systems and Computing

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Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves

Cited by 14 publications

References 46 publications

High Speed Cryptoprocessor for η T Pairing on 128-bit Secure Supersingular Elliptic Curves over Characteristic Two Fields

High Speed Cryptoprocessor for η T Pairing on 128-bit Secure Supersingular Elliptic Curves over Characteristic Two Fields

GPU-Based Implementation of 128-Bit Secure Eta Pairing over a Binary Field

Hybrid Digit-Serial Multiplier for Shifted Polynomial Basis of GF(2 m )

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