2016/05/08 by Keiji Okano, Okano, Keiji
Computer Science · Mathematics · #Coding theory and cryptography #Computer science #Cryptography and Data Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #Degree (music) #Discrete mathematics #Elliptic curve #Embedding #FOS: Computer and information sciences #FOS: Mathematics #Ideal (ethics) #Mathematics #Number Theory (math.NT) #Pairing #Physics #Pure mathematics #Set (abstract data type) #cs.CR #math.NT
paper · pdf · doi:10.48550/arxiv.1605.02328
13 pages
arxiv created 2016/05/08 · openalex publication_date 2016/05/08 · arxiv updated 2016/05/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Pairing-based cryptographic schemes require so-called pairing-friendly elliptic curves, which have special properties. The set of pairing-friendly elliptic curves that are generated by given polynomials form a complete family. Although a complete family with a ρ-value of 1 is the ideal case, there is only one such example that is known, this was given by Barreto and Naehrig. We prove that there are no ideal families with embedding degree 3, 4, or 6 and that many complete families with embedding degree 8 or 12 are nonideal, even if we chose noncyclotomic families.