Joppe W. BosCraig CostelloHuseyin HisilKristin LauterBos, Joppe W.Lauter, KristinCostello, CraigHisil, Huseyin2025-10-0620160933-27901432-137810.1007/s00145-014-9188-72-s2.0-84955328642http://dx.doi.org/10.1007/s00145-014-9188-7https://gcris.yasar.edu.tr/handle/123456789/7358https://doi.org/10.1007/s00145-014-9188-7In 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.Englishinfo:eu-repo/semantics/openAccessHYPERELLIPTIC CURVES, ELLIPTIC-CURVES, SPEEDING-UP, DISCRETE LOGARITHMS, MULTIPLICATION, ENDOMORPHISMS, COMPUTATION, FACTORIZATION, ALGORITHM, JACOBIANSArticle