Fast Cryptography in Genus 2 |
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Authors: | Joppe W Bos Craig Costello Huseyin Hisil Kristin Lauter |
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Affiliation: | 1.Microsoft Research,Redmond,USA;2.Yasar University,Izmir,Turkey;3.Microsoft Research,Redmond,USA |
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Abstract: | In this paper, we highlight the benefits of using genus 2 curves in public-key cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically more involved but allows us to work with moduli of half the size. We give a taxonomy of the best known techniques to realize genus 2-based cryptography, which includes fast formulas on the Kummer surface and efficient four-dimensional GLV decompositions. By studying different modular arithmetic approaches on these curves, we present a range of genus 2 implementations. On a single core of an Intel Core i7-3520M (Ivy Bridge), our implementation on the Kummer surface breaks the 125 thousand cycle barrier which sets a new software speed record at the 128-bit security level for constant-time scalar multiplications compared to all previous genus 1 and genus 2 implementations. |
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