Joppe W. BosCraig CostelloHüseyin HişilKristin Estella LauterBos, Joppe W.Lauter, KristinCostello, CraigHisil, Huseyin2025-10-0620139789819698936, 9789819698042, 9789819698110, 9789819698905, 9789819512324, 9783032026019, 9783032008909, 9783031915802, 9789819698141, 97830319841369783642383489978364238347216113349, 030297430933-27901432-13781611-33490302-974310.1007/978-3-642-38348-9_122-s2.0-84883437294https://www.scopus.com/inward/record.uri?eid=2-s2.0-84883437294&doi=10.1007%2F978-3-642-38348-9_12&partnerID=40&md5=8240c0ca6e2c8317ac26c074231a27eahttps://gcris.yasar.edu.tr/handle/123456789/10080https://doi.org/10.1007/978-3-642-38348-9_12In 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.Englishinfo:eu-repo/semantics/openAccessElliptic Curve, Genus 2 Curves, Intel Core I7, Kummer Surface, Modular Arithmetic, Scalar Multiplication, Security Level, Artificial Intelligence, Computer Science, Public Key CryptographyElliptic curve, Genus 2 curves, Intel core i7, Kummer surface, Modular arithmetic, Scalar multiplication, Security level, Artificial intelligence, Computer science, Public key cryptographyConference Object