Parametrizations for Families of ECM-Friendly Curves

Alexandre Gélin (1) , Thorsten Kleinjung (2) , Arjen K. Lenstra (2)

1 ALMASTY - ALgorithms for coMmunicAtion SecuriTY
2 LACAL - Laboratory for Cryptologic Algorithms

We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factoriza-tion method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.

Domaines: Cryptographie et sécurité [cs.CR]

Alexandre Gélin, Thorsten Kleinjung, Arjen K. Lenstra. Parametrizations for Families of ECM-Friendly Curves. ISSAC 2017 The 42nd International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.165--171, ⟨10.1145/3087604.3087606⟩. ⟨hal-01568343⟩