Browsing by Author "Lauter, Kristin"

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    Citation - WoS: 9
    Citation - Scopus: 10
    Fast Cryptography in Genus 2
    (SPRINGER, 2016) Joppe W. Bos; Craig Costello; Huseyin Hisil; Kristin Lauter; Bos, Joppe W.; Lauter, Kristin; Costello, Craig; Hisil, Huseyin
    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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    Conference Object
    Citation - WoS: 51
    Citation - Scopus: 57
    Fast cryptography in genus 2
    (Springer-Verlag Berlin, 2013) Joppe W. Bos; Craig Costello; Hüseyin Hişil; Kristin Estella Lauter; Bos, Joppe W.; Lauter, Kristin; Costello, Craig; Hisil, Huseyin
    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 4-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 120 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. © 2013 International Association for Cryptologic Research. © 2013 Elsevier B.V. All rights reserved.
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    Conference Object
    Citation - WoS: 22
    Citation - Scopus: 29
    High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition
    (SPRINGER-VERLAG BERLIN, 2013) Joppe W. Bos; Craig Costello; Huseyin Hisil; Kristin Lauter; Bos, Joppe W.; Lauter, Kristin; Costello, Craig; Hisil, Huseyin; G Bertoni; JS Coron
    This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography motivated by the fact that they allow for an 8-dimensional scalar decomposition when using a combination of the GLV/GLS algorithms. Besides lowering the number of doublings required in a scalar multiplication this approach has the advantage of performing arithmetic operations in a 64-bit ground field making it an attractive candidate for embedded devices. We found cryptographically secure genus 2 curves which although susceptible to index calculus attacks aim for the standardized 112-bit security level. Our implementation results on both high-end architectures (Ivy Bridge) and low-end ARM platforms (Cortex-A8) highlight the practical benefits of this approach.