DOI QR코드

DOI QR Code

On a construction of resilient functions using a hyperelliptic curve with genus 2

종수 2인 초타원곡선을 이용한 균형상관면역함수의 생성에 관한 연구

  • 최춘수 (단국대학교 첨단과학부) ;
  • 이민섭 (단국대학교 첨단과학부)
  • Published : 2003.10.01

Abstract

In [3], J. H. Cheon and S. T Chee proposed a method to generate boolean functions with good properties using a poly-nomials of degree 3 over a finite field $F_{2n}$. In this paper, we propose a method generating resilient functions with high nonlinearity from polynomials of degree 5 over a finite field $F_$2^n$$(n$\leq$14).

유한체 F$_{2}$sup n// 위에서 정의되는 다항식을 이용하여 암호학적으로 좋은 성질을 갖는 부울함수를 생성하는 방법으로 3차 다항식을 이용하여 균형상관면역함수를 생성하는 방법이 [3]에서 제안되었다. 이 논문에서는 n$\leq$14일 때 5차 다항식을 이용하여 비선형치가 높은 균형상관면역함수를 생성하는 방법을 제안하고, 예를 제시한다.

Keywords

References

  1. Proc. of Asiacrypto'94 semi-bent functions S.T.Chee;S.J.Lee;K.J.Kim
  2. Advances in Cryptology-CRYPTO 2001,LNCS v.2139 Nonlinear Vector Resilient Function J.H.Cheon
  3. ICISE 2000,LNCS 2015 v.2139 Elliptic Curves and Resilient Functions J.H.Cheon;S.T.Chee
  4. An algebraic approach to boolean functions J.H.Cheon;J.H.Silverman
  5. To be appeared in J. of Applied Math and Computing v.13 Isomorphism classes of hyperelliptic curves of genus 2 over F₂ for even n C.S.Choi;M.S.Rhee
  6. Fast Evaluation Weights and Nonlinearity of Rotation-Symmetric Functions T.M.Cusick;P.Stanica
  7. Finite fields, Encyclopedia of Math. and its application v.20 R.Lidl;H.Niederreiter
  8. Applications of Finite Fields A. Menezes
  9. Elliptic Curve Public Key Cryptosystems A. Menezes
  10. Isomorphism Classes of Genus 2 Hyperelliptic Curves over Finite Fields A.Menezes;L.Encinas;J.Masque
  11. Technical Report CORR-96-19, CACR An elementary introduction to hyperelliptic curves A.Menezes;Y.Wu;R.Zuccherato
  12. Annals of Discrete Mathematics v.30 Roots of affine polynomial G.Menichetti
  13. Adbances in Cryptology-Crypto 2000, LNCS v.1880 Nonlinearity bounds and consructions of resilient boolean functions P.Sarkar;S.Maitra https://doi.org/10.1007/3-540-44598-6_32
  14. Technical Report No. 93-1 Highly monlinear balanced Boolean functions satisfying high degree propagation criterion J.Seberry;X.M.Zhang;Y.Zheng
  15. Advances in Cryptology-Eurocrypt'93,LNCS v.765 On constructions and nonlinearity of correlation immune functions J.Seberry;X.M.Zhang;Y.Zheng
  16. Information and Computation 119(1) Nonlinearity and Propagation Characteristics of Balanced Boolean functions J.Seberry;X.M.Zhang;Y.Zheng
  17. IEEE Trans. Information Theory v.30 Correlation immunity of nonlinear combining functions for cryptographic applications T.Siegenthaler https://doi.org/10.1109/TIT.1984.1056949