Joppe W. BosCraig CostelloHüseyin HişilKristin Estella Lauter2025-10-0620139789819698936, 9789819698042, 9789819698110, 9789819698905, 9789819512324, 9783032026019, 9783032008909, 9783031915802, 9789819698141, 978303198413616113349, 0302974310.1007/978-3-642-40349-1_19https://www.scopus.com/inward/record.uri?eid=2-s2.0-84890775778&doi=10.1007%2F978-3-642-40349-1_19&partnerID=40&md5=adb2e0bd875ccdfd04539aa99df3811ehttps://gcris.yasar.edu.tr/handle/123456789/10134This 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. © 2013 Springer-Verlag Berlin Heidelberg. © 2025 Elsevier B.V. All rights reserved.EnglishCryptography, Differentiation (calculus), Digital Arithmetic, Encryption Algorithms, Arithmetic Operations, Doublings, Embedded Device, Extension Field, Genus 2 Curves, Ground Field, Index Calculus, Performance, Scalar Multiplication, Security LevelCryptography, Differentiation (calculus), Digital arithmetic, Encryption algorithms, Arithmetic operations, Doublings, Embedded device, Extension field, Genus 2 curves, Ground field, Index calculus, Performance, Scalar multiplication, Security levelConference Object