Fast, Uniform Scalar Multiplication for Genus 2 Jacobians with Fast Kummers

Chung, Ping Ngai; Costello, Craig; Smith, Benjamin

doi:10.1007/978-3-319-69453-5_25

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…Each point ±P is represented by a 4-tuple where each element is 127-bit wide which sums up to 508 bit in total. As described in [CCS16,RSSB16], we assume that the public key (respectively public generator) is represented by a 3-tuple in its wrapped 381-bit representation denoted by ±P . Renes et al [RSSB16] showed that keeping the input points in their wrapped representation offers two advantages: first, it reduces the required amount of data that needs to be transmitted and second, it results in a speed-up for the ladder computation.…”

Section: Diffie-hellman Key Exchange Using Kummer Surfacesmentioning

confidence: 99%

“…Similar to previous works, we use the fast Kummer surface K C ∈ P 3 of [CC86, CCS16,Gau07], which is defined as:…”

Section: Kummer Surfacementioning

confidence: 99%

“…We present the first FPGA implementations of Diffie-Hellman using the Kummer surface of a genus-2 hyperelliptic curve and show its competitiveness compared to elliptic curve based implementations. Following previous high-speed genus-2 implementations in software [BCHL13, BCLS14, RSSB16], we use the Kummer surface [CC86,CCS16,Gau07] of Gaudry and Schost's genus-2 curve [GS12]. Synthesized on a Zynq-7020, our single-core architecture is about 1.91-times faster than the FourQ implementation [JMAL16], which has been the fastest prime-field curve scalar multiplication on the same FPGA so far.…”

Section: Introductionmentioning

confidence: 99%

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Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve

Koppermann

Santis

Heyszl

et al. 2018

TCHES

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We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost’s genus-2 curve targeting a 128-bit security level. We describe a single-core architecture for lowlatency applications and a multi-core architecture for high-throughput applications. Synthesized on a Xilinx Zynq-7020 FPGA, our architectures perform a key exchange with lower latency and higher throughput than any other reported implementation using prime-field elliptic curves at the same security level. Our single-core architecture performs a scalar multiplication with a latency of 82 microseconds while our multicore architecture achieves a throughput of 91,226 scalar multiplications per second. When compared to similar implementations of Microsoft’s Fourℚ on the same FPGA, this translates to an improvement of 48% in latency and 40% in throughput for the single-core and multi-core architecture, respectively. Both our designs exhibit constant-time execution to thwart timing attacks, use the Montgomery ladder for improved resistance against SPA, and support a countermeasure against fault attacks.

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Section: Diffie-hellman Key Exchange Using Kummer Surfacesmentioning

confidence: 99%

“…Similar to previous works, we use the fast Kummer surface K C ∈ P 3 of [CC86, CCS16,Gau07], which is defined as:…”

Section: Kummer Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve

Koppermann

Santis

Heyszl

et al. 2018

TCHES

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“…An analogue of y-coordinate recovery (see §4.3) exists in genus 2: Chung and the authors give an explicit algorithm in [16], recovering Jacobian elements from the output of the Montgomery ladder on the Kummer. This enables the implementation of full signature schemes using Kummer surfaces [44].…”

Section: The Montgomery Ladder On Hyperelliptic Curvesmentioning

confidence: 99%

Montgomery curves and their arithmetic

Costello

Smith

2017

J Cryptogr Eng

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Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryptosystems. This article surveys the theory and cryptographic applications of Montgomery curves over non-binary finite fields, including Montgomery's x-only arithmetic and Ladder algorithm, xonly Diffie-Hellman, y-coordinate recovery, and 2-dimensional and Euclidean differential addition chains such as Montgomery's PRAC algorithm.

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