On the non-idealness of cyclotomic families of pairing-friendly elliptic curves

2013/04/26 by Min Sha, Sha, Min
Computer Science · Mathematics · #14H52 #Coding theory and cryptography #Combinatorics #Computer science #Condensed matter physics #Cryptography and Data Security #Cryptography and Residue Arithmetic #Cyclotomic polynomial #Degree (music) #Elliptic curve #Embedding #FOS: Mathematics #Ideal (ethics) #Law #Mathematical analysis #Mathematics #Number Theory (math.NT) #Pairing #Physics #Political science #Polynomial #Primary 11T71 #Prime (order theory) #Pure mathematics #Secondary 11T22 #Superconductivity #math.NT #msc:11T22 #msc:11T71 #msc:14H52

paper · pdf · doi:10.48550/arxiv.1304.7169

openalex publication_date 2013/04/26 · arxiv created 2014/04/17 · arxiv updated 2014/04/18 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/08

Abstract

Let k=2^mpⁿ for an odd prime p and integers m≥ 0 and n≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φ_k(x). Our bounds imply that none of these families are ideal.

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