Parametrizations for Families of ECM-Friendly Curves

Abstract : 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.
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Submitted on : Tuesday, July 25, 2017 - 11:03:24 AM
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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⟩

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