Joppe W. BosCraig CostelloHuseyin HisilKristin LauterT JohanssonPQ Nguyen2025-10-062013978-3-642-38348-9, 978-3-642-38347-20302-9743https://gcris.yasar.edu.tr/handle/123456789/7420In 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.EnglishHYPERELLIPTIC CURVES, DISCRETE LOGARITHMS, ELLIPTIC-CURVES, SPEEDING-UP, MULTIPLICATION, ENDOMORPHISMS, FACTORIZATION, COMPUTATION, ALGORITHM, JACOBIANSConference Object