Thomaz OliveiraJulio C. López-HernándezHüseyin HişilArmando Faz-HernandezFrancisco Rodríguez-HenríquezLópez, JulioFaz-Hernández, ArmandoOliveira, ThomazHışıl, HüseyinRodríguez-Henríquez, FranciscoC. Adams , J. Camenisch2025-10-0620189789819698936, 9789819698042, 9789819698110, 9789819698905, 9789819512324, 9783032026019, 9783032008909, 9783031915802, 9789819698141, 97830319841369783319725659978331972564216113349, 030297431611-33490302-974310.1007/978-3-319-72565-9_92-s2.0-85041833783https://www.scopus.com/inward/record.uri?eid=2-s2.0-85041833783&doi=10.1007%2F978-3-319-72565-9_9&partnerID=40&md5=327257e1949804c75899899a3d6ae883https://gcris.yasar.edu.tr/handle/123456789/9635https://doi.org/10.1007/978-3-319-72565-9_9In the RFC 7748 memorandum the Internet Research Task Force specified a Montgomery-ladder scalar multiplication function based on two recently adopted elliptic curves “curve25519” and “curve448”. The purpose of this function is to support the Diffie-Hellman key exchange algorithm that will be included in the forthcoming version of the Transport Layer Security cryptographic protocol. In this paper we describe a ladder variant that permits to accelerate the fixed-point multiplication function inherent to the Diffie-Hellman key pair generation phase. Our proposal combines a right-to-left version of the Montgomery ladder along with the pre-computation of constant values directly derived from the base-point and its multiples. To our knowledge this is the first proposal of a Montgomery ladder procedure for prime elliptic curves that admits the extensive use of pre-computation. In exchange of very modest memory resources and a small extra programming effort the proposed ladder obtains significant speedups for software implementations. Moreover our proposal fully complies with the RFC 7748 specification. A software implementation of the X25519 and X448 functions using our pre-computable ladder yields an acceleration factor of roughly 1.20 and 1.25 when implemented on the Haswell and the Skylake micro-architectures respectively. © 2018 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/closedAccessDiffie-hellman Protocol, Elliptic Curve Scalar Multiplication, Montgomery Ladder, Rfc 7748, Computer Architecture, Cryptography, Geometry, Public Key Cryptography, Cryptographic Protocols, Diffie-hellman Key Exchange, Diffie-hellman Protocol, Internet Research Task Forces, Montgomery, Rfc 7748, Scalar Multiplication, Transport Layer Security, LaddersComputer architecture, Cryptography, Geometry, Public key cryptography, Cryptographic protocols, Diffie-Hellman key exchange, Diffie-Hellman protocol, Internet research task forces, Montgomery, RFC 7748, Scalar multiplication, Transport layer security, LaddersMontgomery LadderRfc 7748Elliptic Curve Scalar MultiplicationDiffie-Hellman ProtocolConference Object