Volume 61 Issue 2 (2011) - Годишник на ТУ - София - Технически ...

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Proposition 3.8 For any n ≥ 2 in the semiring of idempotent elementsID (E An ) there is a chain of ideals ID 0 ⊂ ID 1 ⊂ · · · ⊂ ID n−2 ⊂ ID n−1 .Note that ID n−2 = ID (E An ) \{i} is a maximal ideal of this semiring.4 ConclusionIn the present paper the endomorphism semiring of a finite semilattice of aspecial type is investigated. The main results are Theorem 3.1 which gives thestructure of the center of the semiring of nonconstant endomorphisms and Theorem3.4 where we prove that idempotent elements formed a commutative subsemiringof the endomorphism semiring.References[1] Anderson A., Belnap N. (1975), Entailment, the Logic of Relevanceand Necessity, vol. I, Princeton Univ. Press, Princeton, 1975.[2] El Bashir R., Hurt J., Jan˘ca˘rík A., Kepka T. (2001), Simple commutativesemirings, J. Algebra 236 (2001), 277 – 306.[3] Golan J. (1999), Semirings and Their Applications, Kluwer, Dordrecht,1999.[4] Gratzer G. (2011), Lattice Theory: Foundation, Birkhäuser SpringerBasel AG, 2011.[5] Jeẑek J., Kepka T., Maròti M. (2009), The endomorphism semiring ofa semilattice, Semigroup Forum, 78 (2009), 21 – 26.[6] Kala V., Kepka T. (2008), A note on finitely generated ideal-simplecommutative semirings, Comment.Math.Univ.Carolin., 49, 1 (2008), 1 – 9.[7] Monico C. (2004), On finite congruence-simple semirings, J. Algebra271 (2004) 846 – 854.[8] Moore E. H. (1902), A definition of abstract groups, Trans. Amer.Math. Soc, 3 (1902), 485 – 492.[9] Trendafilov I., Vladeva D. (2011), The endomorphism semiring of afinite chain, Proc. Techn. Univ.-Sofia, 61 (2011).[10] Trendafilov I., Vladeva D. (2011), Endomorphism semirings withoutzero of a finite chain, Proc. Techn. Univ.-Sofia, 61 (2011).[11] Zumbrägel J. (2008), Classification of finite congruence-simplesemirings with zero, J. Algebra Appl. 7 (2008) 363 – 377.Authors: Ivan Trendafilov, assoc. prof., Department "Algebra andgeometry", FAMI, TU–Sofia, e-mail: ivan_d_trendafilov@abv.bgDimitrinka Vladeva, assoc. prof., Department "Mathematicsand physics", LTU, Sofia, e-mail: d_vladeva@abv.bgПостъпила на 05.12.2011Рецензент доц. д-р Георги Бижев28
Годишник на Технически Университет - София, т. 61, кн.2, 2011Proceedings of the Technical University - Sofia, v. 61, book 2, 2011ÊÐÈÏÒÎÑÈÑÒÅÌÀ Ñ ÎÒÊÐÈÒ ÊËÞ×, ÎÑÍÎÂÀÍÀÍÀ ÏÎËÓÏÐÚÑÒÅÍÈ ÎÒ ÅÍÄÎÌÎÐÔÈÇÌÈ ÍÀÊÐÀÉÍÀ ÏÎËÓÐÅØÅÒÊÀ ÎÒ ÑÏÅÖÈÀËÅÍ ÂÈÄÌàðèàíà Äóð÷åâàÐåçþìå: Â òàçè ñòàòèÿ ïîêàçâàìå êàê ïîëóïðúñòåíèòå îòåíäîìîðôèçìè íà êðàéíà ïîëóðåøåòêà ìîãàò äà áúäàò èçïîëçâàíè êàòîïëàòôîðìà íà êðèïòîñèñòåìà, îñíîâàíà íà äåéñòâèÿ íà ïîëóãðóïà.Ïîêàçàíà å è êîíêðåòíà ïîëóãðóïîâà îïåðàöèÿ, ïîñòðîåíà ñ ïîìîùòàíà ïîëóïðúñòåíèòå îò åíäîìîðôèçìè.Êëþ÷îâè äóìè: êðèïòîñèñòåìà ñ îòêðèò êëþ÷, ïðîòîêîë íà Die-Hellman, äåéñòâèå íà ïîëóãðóïà, ïîëóïðúñòåí îò åíäîìîðôèçìèòå íà êðàéíàïîëóðåøåòêà.PUBLIC KEY CRYPTOSYSTEM BASED ONENDOMORPHISM SEMIRINGS OF A FINITESEMILATTICE OF A SPECIAL TYPEMariana DurchevaAbstract: In this paper we illustrate how endomorphism semirings of a nitesemilattice can be used as a platform of a cryptosystem, based on semigroup actions.A concrete practical semigroup action built from endomorphism semiringsis presented.Keywords: public key cryptosystem, Die-Hellman protocol, semigroup actions,endomorphism semiring of a nite semilattice.1. INTRODUCTIONCryptographic protocols are small programs designed to ensure secure communicationsvia a public channel. The Discrete Logarithm Problem (DLP) is on thebase of many cryptographic protocols.Let G be a cyclic group and g a generator of G. Given an element h of G theDiscrete Logarithm Problem is the problem of nding an integer t such that g t = h(see [10]).© 2011 Publishing House of Technical University of Sofia29All rights reserved ISSN 1311-0829
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Fig.1 Block structure of proposed o
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pends on the results of the thermal
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Laskin and Wang presented a detaile
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Figure 2: Temperature dependence of
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An additional analysis obtained at
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