Journal of the Korea Institute of Information Security & Cryptology (정보보호학회논문지)

Korea Institute of Information Security and Cryptology (한국정보보호학회)
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A generating method of CM parameters of pairing-friendly abelian surfaces using Brezing-Weng family

Brezing-Weng 다항식족을 이용한 페어링 친화 아벨 곡면의 CM 파라미터 생성법

  • Received : 2015.03.31
  • Accepted : 2015.04.27
  • Published : 2015.06.30
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Abstract

Brezing and Weng proposed a method to generate CM parameters of pairing-friendly elliptic curves using polynomial representations of a number field, and Freeman generalized the method for the case of abelian varieties. In this paper we derive explicit formulae to find a family of polynomials used in Brezing-Weng method especially in the case of abelian surfaces, and present some examples generated by the proposed method.

Brezing과 Weng은 페어링 친화 타원곡선의 CM 파라미터들을 수체(number field)의 다항식 표현을 이용하여 생성하는 방법을 제안하였고, Freeman은 그 방법을 아벨 다양체(abelian variety)의 경우로 일반화 시켰다. 본 논문에서는 특히 단순 아벨 곡면(simple abelian surface)의 경우에 대해 Brezing-Weng 방법에서 사용되는 다항식족(polynomial family)을 구하는 새로운 공식들을 유도하고, 이를 이용하여 CM 파라미터들을 생성할 수 있음을 보인다.

Keywords

수식논문이라 구축이불가합니다.

References

  1. D. Freeman, "A generalized Brezing-Weng algorithm for constructing pairing-friendly ordinary abelian varieties," Algorithmic Number Theory, LNCS vol. 5029, pp. 60-73, Oct. 2008.
  2. D. Freeman, P. Stevenhagen and M. Streng, "Abelian varieties with prescribed embedding degree," Pairing-Based Cryptography - Pairing 2008, LNCS vol. 5011, pp. 60-73, May. 2008.
  3. D. Freeman, M. Scott and E. Teske, "A Taxonomy of Pairing-Friendly Elliptic Curves," J. Cryptology vol. 23, no. 2, pp. 224-280, Apr. 2010. https://doi.org/10.1007/s00145-009-9048-z
  4. K. Yoon, "A new method of choosing primitive elements for Brezing-Weng families of pairing-friendly elliptic curves," J. Mathmatical Cryptology vol 9, no. 1, pp. 1-9, Mar. 2015. https://doi.org/10.1515/jmc-2013-0017
  5. K. Yoon, "Construction de courbes elliptiques et de surfaces abeliennes adaptees a la cryptographie a couplage," PhD thesis, Universite de Caen Basse-Normandie Nov. 2013.