Joppe W. BosCraig CostelloHüseyin HişilKristin Estella Lauter2025-10-06201614321378, 093327900933-27901432-137810.1007/s00145-014-9188-7https://www.scopus.com/inward/record.uri?eid=2-s2.0-84955328642&doi=10.1007%2Fs00145-014-9188-7&partnerID=40&md5=cb24360ec3280c973ff29a9a35c1af5bhttps://gcris.yasar.edu.tr/handle/123456789/9846In 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. © 2016 Elsevier B.V. All rights reserved.EnglishPublic Key Cryptography, Elliptic Curve, Genus 2 Curves, Intel Core I7, Kummer Surface, Modular Arithmetic, Scalar Multiplication, Security Level, CryptographyPublic key cryptography, Elliptic curve, Genus 2 curves, Intel core i7, Kummer surface, Modular arithmetic, Scalar multiplication, Security level, CryptographyArticle