DOI QR코드

DOI QR Code

ON THE PUBLIC KEY CRYPTOSYSTEMS OVER CLASS SEMIGROUPS OF IMAGINARY QUADRATIC NON-MAXIMAL ORDERS

Kim, Young-Tae;Kim, Chang-Han

  • Published : 2006.07.01

Abstract

In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class SEMIGROUPS of imaginary quadratic orders which were given by Zanardo and Zannier [8], and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to cryptography in the class semigroup of imaginary quadratic non-maximal order and revisit the cryptosystem of Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity as their secret key, in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon [5]'s.鳭醜谂Á䰉ê뒀곬麐Ā夏1㔰⸱㠳⸱㌷⸲ㄵЂȂȌ蠀ʏ蘢ꠒꠑ ͧ[2004년 뽧툌ࡕꠑȆ᧽Ʈऀƞ[2004년도 한국비블리아학회 추계학술발표회] 기획주제: 지식관리와 표현(knowledge Management and Representation) 날짜: 2004년 11월 19일(금) 13:00~ 20일(토) 12:00 장소: 대구대학교 강당 ※ 자세한 사항은 한국비블리아학회 홈페이지(http://society.kisti.re.kr/~kbslis )를 참조하십시오.Ā吀쐃Ā〇x樁ऌ؂̀숃㤁DȀ섋䨀㈰〴駭验蓫辄⃭閜귬麑볭閙谠闪뢰鷭验⃫낏⃬뚔蓭閙ꃫ난鳭验Ȁ셊ऀ胫ꚬ送Yༀㄵ〮ㄸ㌮ㄳ㜮㈱㔸̃㘀ĂಈȀĀ辆⌀ƨሀƨᄀऀः最Ǖ岭淇醻㳕姖谀₿柒ఈ唀ƨᄂؙﴀȂ툀Ǖ岭淇醻㳕姖貲鐀 尀尀 ㈀  㓕姖貱䒳쐀⃕岭淇醻㳕姖谀⃈ᖮネᷖ谀₼ༀ⃍钬쓕姂₼᳔峖谀 尀尀∀₹簀⃂?榲좲⸀ હ컇䀀₭Âﰀ⃌㣅簀₽胐솴?붲좲⸀਀਀਀⨀⨀ ㈀  㒱䒳쐀⃍钬쓕姂₼᳔岳Ö谀₱粻㣈᳍鰀₼ༀ⃀곈Ҵ崀⃅䢰됀 ⨀⨀਀ ਀㄀⺬ᰀ⃍尀⃇簀⃂? 㨀 ㈀  㒱䐀 ㄀テ퐀 ㈀㇇簀₺꧆铇簀縀 ㄀テ퐀 ㈀㋇簀₮ࣆ铇簀 ਀਀㈀⸀€ᰀ⃍尀⃇ꔀ⃁谀 㨀€붽膳Õ妭倀⃈ᖼӀ냆퀀€ᖲ豈 ਀਀㌀⸀₱粻㣍ࢸ嶹좬က 㨀 ㈀  㒱䐀 ㄀テ퐀  㧇簀⃑ꃆ铇簀 ਀ ਀㐀⸀⃀곈Ҵ嶹좬က 㨀 ㈀  㒱䐀 ㄀テ퐀 ㄀㣇簀₮ࣆ铇簀 ਀ ਀㔀⸀⃈᳍鲼⦼销㨀⃇磑ケ㜀⃀쇅탁ᰀ₱粻㣈ᇂ᠀₼ༀ⃀곈Ҵ巇䐀⃕栀਀ਠ㬀⃇郁㣕尀⃀곕淇䀀⃕岭淇醻㳕姖谀⃖䣓飇瓉쀀⠀栀琀琀瀀

Keywords

class semigroup;power of ideals;key exchange system

References

  1. D. Cox, Primes of the form $x^2\;+\;ny^2$, Wiley, New York, 1989
  2. J. Buchmann and H. C. Williams, A key-exchange system based on imaginary quadratic fields, J. Cryptology 1 (1988), 107-118 https://doi.org/10.1007/BF02351719
  3. W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. on Inform. Theory 22 (1976), 472-492
  4. C. F. Gauss, Disquisitiones Arithmeticae , translated by Clarke A. A., SpringerVerlag, New York, 1986
  5. H. Kim and S. Moon, Public-Key Cryptosystems based on Class Semigroups of Imaginary Quadratic Non-maximal Orders, ASISP 2003, LNCS 2727 (2003), 488-497 https://doi.org/10.1007/3-540-45067-X_42
  6. Y. Kim, On the structures of class semiqroups of quadratic non-maximal orders, Honam Mathematical Journal 26 (2004), no. 3, 247-256
  7. P. Zanardo and U. Zannier, The class semigroup of orders in number fields, Math. Proc. Camb.Phil. Soc. 115 (1994), 379-391
  8. Michael J. Jacobson, Jr., The security of cryptosystems based on class semigroups of imaginary quadratic non-maximal orders ASISP 2004, LNCS 3108 (2004), 149-156