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

  • 제11권6호
  • /
  • Pages.105-113
  • /
  • 2001
  • /
  • 1598-3986(pISSN)
  • /
  • 2288-2715(eISSN)
한국정보보호학회 (Korea Institute of Information Security and Cryptology)
권호 표지
DOI QR코드

DOI QR Code

타원곡선상의 고속 곱셈연산을 위한 새로운 분해 알고리즘

A new decomposition algorithm of integer for fast scalar multiplication on certain elliptic curves

  • 박영호 (고려대학교 정보보호기술연구센터) ;
  • 김용호 (고려대학교 정보보호기술연구센터) ;
  • 임종인 (세명대학교 컴퓨터수리정보학과) ;
  • 김창한 (세명대학교 컴퓨터수리정보학과) ;
  • 김용태 (광주교육대학교 수학교육학과)
  • 발행 : 2001.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

최근에 Gallant, Lambert, Vanstone은 소수체 위에 정의된 타원곡선이 효율적으로 계산 가능한 자기준동형을 가질 때 스칼라 곱을 가속화하는 방법을 제안하였다. 이 방법은 실제로 자기준동형의 특성다항식의 고유치를 사용하여 스칼라를 분해하는데 기반을 두고 있다. 본 논문에서는 그러한 타원곡선의 자기준동형 환의 원소를 이용하여 스칼라를 분해하는 개선된 알고리즘을 제안한다. 이 알고리즘은 Gallant 등의 알고리즘보다 속도면에서 효율적이며 분해성분들의 구체적인 상한 값을 줄 수 있다.

Recently, Gallant, Lambert arid Vanstone introduced a method for speeding up the scalar multiplication on a family of elliptic curves over prime fields that have efficiently-computable endomorphisms. It really depends on decomposing an integral scalar in terms of an integer eigenvalue of the characteristic polynomial of such an endomorphism. In this paper, by using an element in the endomorphism ring of such an elliptic curve, we present an alternate method for decomposing a scalar. The proposed algorithm is more efficient than that of Gallant\`s and an upper bound on the lengths of the components is explicitly given.

키워드

참고문헌

  1. Math. of Comp. v.61 no.203 Elliptic curves and Primality Proving A.O.L. Atkin;F. Morain
  2. London Mathematical Society Lecture Note Series v.265 Elliptic Curves in Cryptography Ian Blake;Gadiel Seroussi;Nigel Smart
  3. Computaional Perspectives on Number theory Ellpitic and modular curves over finite fields and related computaional issues N. Elkies
  4. Advances in Cryptology-Crypto '2001 Faster Point Multiplication on Elliptic Curves R. Gallant;R. Lambert;S. Vanstone
  5. Advances in Cryptology-Crypto '91 CM-curves with good cryptographic properties N. Koblitz
  6. Journal of Cryptology Fast multiplication in elliptic curves over small fields of characterostoc twp V. Muller
  7. Advances in Cryptology-Crypto '92 Efficient multiplication on certain non-supersingular elliptic curves W. Meier;O. Staffelbach
  8. IEEE Trans. Info. Theory v.39 Reducting elliptic curves logarithms to logarithms in a finite field A. Menezes;T. Okamoto;S. Vanstone
  9. J. Ramanujan Math. Soc. v.15 The canonical lift of an ordinary elliptic curve over a finite field and its point counting T. Satoh
  10. J. Theorie des Nombres de Bordeaux v.7 Counting points on elliptic curves over finite fields R. Schoof
  11. Proc. 2nd Manitoba Conference on Numerical Mathematics Five number theoretic algorithms D. Shanks
  12. Advanced Topics in the Arithmetic of Elliptic Curves J.H. Silverman
  13. Journal of Cryptology Elliptic curve cryptosystems over small fields of odd characteristic N. Smart
  14. Advances in Cryptology-Crypto '97 An improved algorithm for arithmetic on a family of elliptic curves J. Solinas
  15. Design. Codes and Cryptography Efficient arithmetic on Koblitz curves J. Solinas
  16. Algebraic Number Theory I. Stewart;D. Tall
  17. Une approche geometrique des algorithmes de reduction es reseaux en petite dimension B. Vallee