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

Kim, Young-Tae;Kim, Chang-Han

• Published : 2006.07.01
• 51 3

#### 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⸲ㄵЂȂȌ蠀ʏ蘢ꠒꠑ ͧ[2004년 뽧툌ࡕꠑȆ᧽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

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