Free storage basis conversion over finite fields
Yıl: 2017 Cilt: 41 Sayı: 1 Sayfa Aralığı: 96 - 109 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022
Free storage basis conversion over finite fields
Öz: Representation of a field element plays a crucial role in the efficiency of field arithmetic. If an efficient representation of a field element in one basis exists, then field arithmetic in the hardware and/or software implementations becomes easy. Otherwise, a basis conversion to an efficient one is searched for easier arithmetic. However, this conversion often brings a storage problem for transition matrices associated with these bases. In this paper, we study this problem for conversion between normal and polynomial bases in the extension field Fqp over Fq where q = p n . We construct transition matrices that are of a special form. This provides free storage basis conversion algorithms between normal and polynomial bases, which is crucial from the implementation point of view.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Akleylek S. On the representation of finite fields. PhD, Middle East Technical University, Ankara, Turkey, 2010.
- [2] Akleylek S, Cenk M, Ozbudak F. Polynomial multiplication over binary fields using Charlier polynomial represen- ¨ tation with low space complexity. In: Gong G, Gupta KC, editors. 11th International Conference on CryptologyINDOCRYPT 2010 in India; 1215 December 2010; Hyderabad, India. Berlin, Germany: Springer, 2010, pp. 227-237.
- [3] Gashkov SB, Bolotov AA, Burtsev AA, Zhebet SY, Frolov AB. On hardware and software implementation of arithmetic in finite fields of characteristic 7 for calculation of Pairings. J Math Sci-Univ Toky 2010; 168: 49-75.
- [4] Gathen JVZ. Irreducible trinomials over finite fields. Math Comput 2002; 72: 1987-2000.
- [5] Guajardo J, Paar C. Itoh-Tsujii inversion in standard basis and its application in Cryptography and Codes. Design Code Cryptogr 2002; 25: 207-216.
- [6] Hankerson D, Menezes A, Vanstone S. Guide to Elliptic Curve Cryptography. New York, NY, USA: Springer Science & Business Media, 2006.
- [7] Kaliski BS, Yin YL. Storage efficient finite fields basis conversion. In: Tavares S, Meijer H, editors. Proceedings of the Selected Areas in Cryptography-SAC 98; 1718 August 1998; Kingston, ON, Canada. Berlin, Germany: Springer-Verlag, 1999, pp. 81-93.
- [8] Lidl R, Niederreiter H. Introduction to Finite Fields and Its Applications. Cambridge, UK: Cambridge University Press, 1997.
- [9] Menezes A, Blake I, Gao X, Mullen R, Vanstone S, Yaghobian T. Applications of Finite Fields. Boston, MA, USA: Kluwer Academic, 1993.
- [10] Muchtadi-Alamsyah I, Yuliawan F. Basis conversion in composite field. International Journal of Mathematics and Computation 2013; 11-17.
- [11] Ozbudak F, Akleylek S, Cenk M. A new representation of elements in binary fields with subquadratic space ¨ complexity multiplication of polynomials. Ieice T Fund Electr 2013; 96-A: 2016-2024.
- [12] Schwarz S. Irreducible polynomials over finite fields with linearly independent roots. Math Slovaca 1988; 38: 147-158.
- [13] Sial MR, Akyıldız E. Storage free basis conversion over composite finite fields of odd characteristics. Proceedings of 6th International Conference on Information Security and Cryptology-ISCTURKEY; 2021 September 2013; Ankara, Turkey. 2013, pp. 199-204.
APA | AKYILDIZ E, HAROLD N, SINAK A (2017). Free storage basis conversion over finite fields. , 96 - 109. |
Chicago | AKYILDIZ Ersan,HAROLD Ndangang Yampa,SINAK AHMET Free storage basis conversion over finite fields. (2017): 96 - 109. |
MLA | AKYILDIZ Ersan,HAROLD Ndangang Yampa,SINAK AHMET Free storage basis conversion over finite fields. , 2017, ss.96 - 109. |
AMA | AKYILDIZ E,HAROLD N,SINAK A Free storage basis conversion over finite fields. . 2017; 96 - 109. |
Vancouver | AKYILDIZ E,HAROLD N,SINAK A Free storage basis conversion over finite fields. . 2017; 96 - 109. |
IEEE | AKYILDIZ E,HAROLD N,SINAK A "Free storage basis conversion over finite fields." , ss.96 - 109, 2017. |
ISNAD | AKYILDIZ, Ersan vd. "Free storage basis conversion over finite fields". (2017), 96-109. |
APA | AKYILDIZ E, HAROLD N, SINAK A (2017). Free storage basis conversion over finite fields. Turkish Journal of Mathematics, 41(1), 96 - 109. |
Chicago | AKYILDIZ Ersan,HAROLD Ndangang Yampa,SINAK AHMET Free storage basis conversion over finite fields. Turkish Journal of Mathematics 41, no.1 (2017): 96 - 109. |
MLA | AKYILDIZ Ersan,HAROLD Ndangang Yampa,SINAK AHMET Free storage basis conversion over finite fields. Turkish Journal of Mathematics, vol.41, no.1, 2017, ss.96 - 109. |
AMA | AKYILDIZ E,HAROLD N,SINAK A Free storage basis conversion over finite fields. Turkish Journal of Mathematics. 2017; 41(1): 96 - 109. |
Vancouver | AKYILDIZ E,HAROLD N,SINAK A Free storage basis conversion over finite fields. Turkish Journal of Mathematics. 2017; 41(1): 96 - 109. |
IEEE | AKYILDIZ E,HAROLD N,SINAK A "Free storage basis conversion over finite fields." Turkish Journal of Mathematics, 41, ss.96 - 109, 2017. |
ISNAD | AKYILDIZ, Ersan vd. "Free storage basis conversion over finite fields". Turkish Journal of Mathematics 41/1 (2017), 96-109. |