Lecture 25: Pairing Based Cryptography
|
|
- Mabel Rose
- 6 years ago
- Views:
Transcription
1 6.897 Special Topics in Cyptogaphy Instucto: Ran Canetti May 5, 2004 Lectue 25: Paiing Based Cyptogaphy Scibe: Ben Adida 1 Intoduction The field of Paiing Based Cyptogaphy has exploded ove the past 3 yeas [cy, DBS04]. The cental idea is the constuction of a mapping between two useful cyptogaphic goups which allows fo new cyptogaphic schemes based on the eduction of one poblem in one goup to a diffeent, usually easie poblem in the othe goup. In many eseach papes, the fist of these two goups is efeed to as a Gap Goup, whee the Decisional Diffie Helman poblem [Bon98] is easy (because it educes to an easy poblem in the second goup), but the Computational Diffie Helman poblem emains had. The known implementations of these paiings the Weil and Tate paiings involve faily complex mathematics. Fotunately, they can be dealt with abstactly, using only the goup stuctue and mapping popeties. Many inteesting schemes have been built based puely on abstact bilinea maps. 2 Bilinea Maps The majo paiing based constuct is the bilinea map. Conside two goups G 1 and G 2 of pime ode. Fo claity, we denote G 1 using additive notation and G 2 using multiplicative notation, even though the goup opeations in G 1 and G 2 may well be vey diffeent fom the well known aithmetic addition and multiplication. (Sometimes G 1 is also witten multiplicatively in the liteatue.) We conside P and Q two geneatos of G 1, and we wite a times {}}{ ap = P + P P We now conside the mapping e as follows: e : G 1 G 1 G 2 (Note that we do not know how to build a self bilinea map, G 1 G 1 G 1. This would be uite poweful.) Useful bilinea maps have thee popeties: Bilineaity P, Q G 1, a, b Z, e(ap, bq) = e(p, Q) ab 17 1
2 Non Degeneacy If eveything maps to the identity, that s obviously not inteesting: P G 1, P = 0 e(p, P ) = G 2 (e(p, P ) geneates G 2 ) In othe wods: P = 0 e(p, P ) = 1 Computability e is efficiently computable. We can find G 1 and G 2 whee these popeties hold: the Weil and Tate paiings pove the existence of such constuctions. Typically, G 1 is an elliptic cuve goup and G 2 is a finite field. 3 Complexity Implications The constuction of a bilinea map comes with a numbe of complexity implications. Theoem 1 The Discete Log Poblem in G 1 is no hade than the Discete Log Poblem in G 2. Poof 1 Conside Q = ap (still using additive notation), though a is unknown. Solving the Discete Log Poblem involves discoveing a fo a given P and a andom Q. We note: e(p, Q) = e(p, ap ) = e(p, P ) a Thus, we can educe the Discete Log Poblem in G 1 to the Discete Log Poblem in G 2. Given P G 1 and a andom Q G 1, and noting that the mapping e is easily computable, we can compute log P (Q) as follows: 1. detemine P = e(p, P ) 2. detemine Q = e(p, Q) 3. detemine a = log P (Q ) in G a is also log P (Q). Theoem 2 The Decisional Diffie Helman [Bon98] is easy in G 1. Poof 2 Solving the DDH poblem involves distinguishing: P, ap, bp, cp with a, b, c R Z, and P, ap, bp, abp with a, b R Z If we define P, A, B, C as the fou values given to the distinguishe, the distinguishe functions as follows: 17 2
3 1. Detemine v 1 = e(a, B) and v 2 = e(p, C) 2. If v 1 = v 2, then the tuple is of the type P, ap, bp, abp. Indeed, assume C = abp, then: e(a, B) = e(ap, bp ) = e(p, P ) ab = e(p, abp ) = e(p, C) Since we know the mapping e is non degeneate, the euality e(a, B) = e(p, C) is euivalent to c = ab. The distinguishe can gain a significant advantage in deciding DDH given the mapping e. 4 Cyptogaphic Schemes The application of bilinea maps leads to numeous inteesting cyptogaphic schemes. 4.1 One Round, 3 paty Key Ageement Scheme In 2000, Joux intoduced a scheme fo one ound, 3 paty key ageement based on bilinea maps [Jou00]. Key ageement schemes based on Diffie Helman [DH76] ae well known, but all euie moe than one ound of exchanged data. In the Joux scheme, assume the above notation and existence of a bilinea map between goups G 1 and G 2 with P a geneato of G 1. Thee paties A, B, C espectively have secets a, b, c Z. The potocol functions as follows: 1. A B, C: ap 2. B A, C: bp 3. C A, B: cp 4. Note that steps 1, 2, 3 ae done in one ound of paallel message exchanges. 5. A computes e(bp, cp ) a = e(p, P ) abc. 6. B computes e(ap, cp ) b = e(p, P ) abc. 7. C computes e(ap, bp ) c = e(p, P ) abc. 8. Note that steps 5, 6, 7 ae done in paallel. 9. All paties have the same shaed key K = e(p, P ) abc G 2. This potocol is contingent on the BDH assumption. Definition The Bilinea Diffie Helman (BDH) Assumption consides the computation of e(p, P ) abc given P, ap, bp, cp to be had. 4.2 Identity Based Encyption In 1984, Shami imagined a public key encyption scheme whee any publicy known sting (e.g. someone s addess) could be used as a public key [Sha85]. In this scheme, 17 3
4 the coesponding pivate key is deliveed to the pope owne of this sting (e.g. the ecipient of the addess) by a tusted pivate key geneato. This key geneato must veify the use s identity befoe deliveing a pivate key, of couse, though this veification is essentially the same as that euied fo issuing a cetificate in a typical Public Key Infastuctue (PKI). Thus, an Identity Based Encyption Scheme enables the deployment of a public key cyptosystem without the pio setup of a PKI: a use poves his identity in a lazy way, only once he needs his pivate key to decypt a message sent to him. In 2001, Boneh and Fanklin devised the fist pactical implementation of such an Identity Based Encyption scheme [BF01]. Thei appoach uses bilinea maps and elies on the BDH Assumption and the Random Oacle model. Setup the usual G 1 and G 2 with a bilinea mapping e : G 1 G 1 G 2 and P a geneato a system wide secet key s R Z. a coesponding system wide public key P pub = sp. Encypt We want to encypt a message m to public key A using the system wide settings fom above. The encyption function is: Enc(P pub, A, m) = P, M H 2 (g A ), R Z g A = e(q A, P pub ) Q A = H 1 (A) H 1 : { 0, 1} G 1, a andom oacle H 2 : G 2 { 0, 1}, a andom oacle Decypt We want to decypt a ciphetext c = (u, v) encypted with public key sting A. The secet key is deliveed to the owne of A as d A = sq A, with Q A defined as above: Q A = H 1 (A). We define: Dec(u, v, d A ) = v H 2 (e(d A, u)) = v H 2 (e(sh 1 (A), P )) = v H 2 (e(h 1 (A), P ) s ) = v H 2 (e(q A, sp ) ) = v H 2 (e(q A, P pub ) ) = v H 2 (g A ) = (m H 2 (g A )) H 2 (g A ) = m 17 4
5 This scheme is not CCA2 secue, but can be made so with the Fujisaki Okamoto constuction [FO99], which assumes the Random Oacle model nothing futhe than what we aleady assume. Refeences [BF01] Dan Boneh and Matt Fanklin. Identity based encyption fom the Weil paiing. Lectue Notes in Compute Science, 2139:213??, [Bon98] Dan Boneh. The decisional diffie hellman poblem. In Thid Algoithmic Numbe Theoy Symposium, pages Spinge Velag, [cy] Paiing based cypto lounge. available at infomatica/paulobaeto/pblounge.html. [DBS04] Ratna Dutta, Rana Baua, and Palash Saka. Paiing based cyptogaphy : A suvey. Cyptology epint Achive, Repot 2004/064, iac.og/. [DH76] [FO99] Whitfield Diffie and Matin E. Hellman. New diections in cyptogaphy. IEEE Tansactions on Infomation Theoy, IT 22(6): , Eiichio Fujisaki and Tatsuaki Okamoto. Secue integation of asymmetic and symmetic encyption schemes. Lectue Notes in Compute Science, 1666: , [Jou00] Antoine Joux. A one ound potocol fo tipatite diffie hellman. In Poceedings of the 4th Intenational Symposium on Algoithmic Numbe Theoy, pages Spinge Velag, [Sha85] Adi Shami. Identity based cyptosystems and signatue schemes. In Cypto 84, LNCS Vol. 196, pages Spinge,
Fixed Argument Pairing Inversion on Elliptic Curves
Fixed Agument Paiing Invesion on Elliptic Cuves Sungwook Kim and Jung Hee Cheon ISaC & Dept. of Mathematical Sciences Seoul National Univesity Seoul, Koea {avell7,jhcheon}@snu.ac.k Abstact. Let E be an
More informationKey Establishment Protocols. Cryptography CS 507 Erkay Savas Sabanci University
Key Establishment Potocols Cyptogaphy CS 507 Ekay Savas Sabanci Univesity ekays@sabanciuniv.edu Key distibution poblem Secuity of the keys Even if the cyptogaphic algoithms & potocols ae cyptogaphically
More information10/04/18. P [P(x)] 1 negl(n).
Mastemath, Sping 208 Into to Lattice lgs & Cypto Lectue 0 0/04/8 Lectues: D. Dadush, L. Ducas Scibe: K. de Boe Intoduction In this lectue, we will teat two main pats. Duing the fist pat we continue the
More informationSecret Exponent Attacks on RSA-type Schemes with Moduli N = p r q
Secet Exponent Attacks on RSA-type Schemes with Moduli N = p q Alexande May Faculty of Compute Science, Electical Engineeing and Mathematics Univesity of Padebon 33102 Padebon, Gemany alexx@uni-padebon.de
More informationNew problems in universal algebraic geometry illustrated by boolean equations
New poblems in univesal algebaic geomety illustated by boolean equations axiv:1611.00152v2 [math.ra] 25 Nov 2016 Atem N. Shevlyakov Novembe 28, 2016 Abstact We discuss new poblems in univesal algebaic
More informationarxiv: v1 [math.co] 1 Apr 2011
Weight enumeation of codes fom finite spaces Relinde Juius Octobe 23, 2018 axiv:1104.0172v1 [math.co] 1 Ap 2011 Abstact We study the genealized and extended weight enumeato of the - ay Simplex code and
More informationConstruction and Analysis of Boolean Functions of 2t + 1 Variables with Maximum Algebraic Immunity
Constuction and Analysis of Boolean Functions of 2t + 1 Vaiables with Maximum Algebaic Immunity Na Li and Wen-Feng Qi Depatment of Applied Mathematics, Zhengzhou Infomation Engineeing Univesity, Zhengzhou,
More informationUsing Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu
Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of
More informationCALCULATING THE NUMBER OF TWIN PRIMES WITH SPECIFIED DISTANCE BETWEEN THEM BASED ON THE SIMPLEST PROBABILISTIC MODEL
U.P.B. Sci. Bull. Seies A, Vol. 80, Iss.3, 018 ISSN 13-707 CALCULATING THE NUMBER OF TWIN PRIMES WITH SPECIFIED DISTANCE BETWEEN THEM BASED ON THE SIMPLEST PROBABILISTIC MODEL Sasengali ABDYMANAPOV 1,
More informationComputer Security Laboratory Concordia Institute for Information Systems Engineering Concordia University, Montreal (QC), Canada
2005 Intenational Confeence on Wieless Netwoks, Communications and Mobile Computing Impoving the Diffie-Heliman Secue Key Exchange P. Bhattachaya, M. Debbabi and H. Otok Compute Secuity Laboatoy Concodia
More informationConcurrent Blind Signatures without Random Oracles
Concuent Blind Signatues without Random Oacles Aggelos Kiayias Hong-Sheng Zhou Abstact We pesent a blind signatue scheme that is efficient and povably secue without andom oacles unde concuent attacks utilizing
More informationE E E. Aggelos Kiayias. Cryptography. Primitives and Protocols. Notes by S. Pehlivanoglu, J. Todd, and H.S. Zhou
P1 P2 P3 E E E IV C1 C2 C3 Aggelos Kiayias Cyptogaphy Pimitives and Potocols Notes by S. Pehlivanoglu, J. Todd, and H.S. Zhou CONTENTS 1 Contents 2 1 Intoduction To begin discussing the basic popeties
More informationCryptography. Primitives and Protocols. Aggelos Kiayias
P1 P2 P3 E E E IV C1 C2 C3 Aggelos Kiayias Cyptogaphy Pimitives and Potocols Based on notes by G. Panagiotakos, S. Pehlivanoglu, J. Todd, K. Samai, T. Zachaias and H.S. Zhou CONTENTS 1 Contents 1 Intoduction
More informationProvable Security in Cryptography
Povable Secuity in Cyptogaphy Thomas Baignèes EPFL http://lasecwww.epfl.ch May 29, 2007 (ve. 25) These lectue notes ae a compilation of some of my eadings while I was pepaing two lectues given at EPFL
More informationE E E. Aggelos Kiayias. Cryptography. Primitives and Protocols. Based on notes by S. Pehlivanoglu, J. Todd, K. Samari, T. Zacharias and H.S.
P1 P2 P3 E E E IV C1 C2 C3 Aggelos Kiayias Cyptogaphy Pimitives and Potocols Based on notes by S. Pehlivanoglu, J. Todd, K. Samai, T. Zachaias and H.S. Zhou CONTENTS 1 Contents 1 Intoduction 4 1.1 Flipping
More informationNew Finding on Factoring Prime Power RSA Modulus N = p r q
Jounal of Mathematical Reseach with Applications Jul., 207, Vol. 37, o. 4, pp. 404 48 DOI:0.3770/j.issn:2095-265.207.04.003 Http://jme.dlut.edu.cn ew Finding on Factoing Pime Powe RSA Modulus = p q Sadiq
More information6 PROBABILITY GENERATING FUNCTIONS
6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to
More informationNon-Transferable Proxy Re-Encryption Scheme
Title Non-Tansfeable Poxy Re-Encyption Scheme Autho(s) He, Y; Chim, TW; Hui, CK; Yiu, SM Citation The 5th IFIP Intenational Confeence on New Technologies, Mobility and Secuity (NTMS 12), Istanbul, Tukey,
More informationInverting the nal exponentiation of Tate pairings on ordinary elliptic curves using faults
Inveting the nal exponentiation of Tate paiings on odinay elliptic cuves using faults Ronan Lashemes 1,2, Jacques Founie 1, and Louis Goubin 2 1 CEA-TechReg, Gadanne, Fance onan.lashemes@cea.f, jacques.founie@cea.f
More informationSome RSA-based Encryption Schemes with Tight Security Reduction
Some RSA-based Encyption Schemes with Tight Secuity Reduction Kaou Kuosawa 1 and Tsuyoshi Takagi 2 1 Ibaaki Univesity, 4-12-1 Nakanausawa, Hitachi, Ibaaki, 316-8511, Japan kuosawa@cis.ibaaki.ac.jp 2 Technische
More informationLecture 18: Graph Isomorphisms
INFR11102: Computational Complexity 22/11/2018 Lectue: Heng Guo Lectue 18: Gaph Isomophisms 1 An Athu-Melin potocol fo GNI Last time we gave a simple inteactive potocol fo GNI with pivate coins. We will
More informationProbablistically Checkable Proofs
Lectue 12 Pobablistically Checkable Poofs May 13, 2004 Lectue: Paul Beame Notes: Chis Re 12.1 Pobablisitically Checkable Poofs Oveview We know that IP = PSPACE. This means thee is an inteactive potocol
More informationA more efficient secure event signature protocol for massively multiplayer online games based on P2P Dapeng Li1, a, Liang Hu1,b, and JianFeng Chu1,c
Intenational Foum on Mechanical, Contol and Automation (IFMCA 2016) A moe efficient secue event signatue potocol fo massively multiplaye online games based on P2P Dapeng Li1, a, Liang Hu1,b, and JianFeng
More information9.1 The multiplicative group of a finite field. Theorem 9.1. The multiplicative group F of a finite field is cyclic.
Chapte 9 Pimitive Roots 9.1 The multiplicative goup of a finite fld Theoem 9.1. The multiplicative goup F of a finite fld is cyclic. Remak: In paticula, if p is a pime then (Z/p) is cyclic. In fact, this
More informationIntroduction Common Divisors. Discrete Mathematics Andrei Bulatov
Intoduction Common Divisos Discete Mathematics Andei Bulatov Discete Mathematics Common Divisos 3- Pevious Lectue Integes Division, popeties of divisibility The division algoithm Repesentation of numbes
More informationApplication of Parseval s Theorem on Evaluating Some Definite Integrals
Tukish Jounal of Analysis and Numbe Theoy, 4, Vol., No., -5 Available online at http://pubs.sciepub.com/tjant/// Science and Education Publishing DOI:.69/tjant--- Application of Paseval s Theoem on Evaluating
More informationSolving Some Definite Integrals Using Parseval s Theorem
Ameican Jounal of Numeical Analysis 4 Vol. No. 6-64 Available online at http://pubs.sciepub.com/ajna///5 Science and Education Publishing DOI:.69/ajna---5 Solving Some Definite Integals Using Paseval s
More informationOn the ratio of maximum and minimum degree in maximal intersecting families
On the atio of maximum and minimum degee in maximal intesecting families Zoltán Lóánt Nagy Lale Özkahya Balázs Patkós Máté Vize Septembe 5, 011 Abstact To study how balanced o unbalanced a maximal intesecting
More informationChapter 3: Theory of Modular Arithmetic 38
Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences
More informationPairing Inversion via Non-degenerate Auxiliary Pairings
Paiing Invesion via Non-degeneate Auxiliay Paiings Seunghwan Chang 1, Hoon Hong 2, Eunjeong Lee 1, and Hyang-Sook Lee 3 1 Institute of Mathematical Sciences, Ewha Womans Univesity, Seoul, S. Koea schang@ewha.ac.k,
More informationON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION. 1. Introduction. 1 r r. r k for every set E A, E \ {0},
ON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION E. J. IONASCU and A. A. STANCU Abstact. We ae inteested in constucting concete independent events in puely atomic pobability
More informationOn the ratio of maximum and minimum degree in maximal intersecting families
On the atio of maximum and minimum degee in maximal intesecting families Zoltán Lóánt Nagy Lale Özkahya Balázs Patkós Máté Vize Mach 6, 013 Abstact To study how balanced o unbalanced a maximal intesecting
More informationDivisibility. c = bf = (ae)f = a(ef) EXAMPLE: Since 7 56 and , the Theorem above tells us that
Divisibility DEFINITION: If a and b ae integes with a 0, we say that a divides b if thee is an intege c such that b = ac. If a divides b, we also say that a is a diviso o facto of b. NOTATION: d n means
More informationA STUDY OF HAMMING CODES AS ERROR CORRECTING CODES
AGU Intenational Jounal of Science and Technology A STUDY OF HAMMING CODES AS ERROR CORRECTING CODES Ritu Ahuja Depatment of Mathematics Khalsa College fo Women, Civil Lines, Ludhiana-141001, Punjab, (India)
More informationEnumerating permutation polynomials
Enumeating pemutation polynomials Theodoulos Gaefalakis a,1, Giogos Kapetanakis a,, a Depatment of Mathematics and Applied Mathematics, Univesity of Cete, 70013 Heaklion, Geece Abstact We conside thoblem
More informationMultiple Criteria Secretary Problem: A New Approach
J. Stat. Appl. Po. 3, o., 9-38 (04 9 Jounal of Statistics Applications & Pobability An Intenational Jounal http://dx.doi.og/0.785/jsap/0303 Multiple Citeia Secetay Poblem: A ew Appoach Alaka Padhye, and
More informationRELIABILITY is an important concept in the design
Poceedings of the Wold Congess on Engineeing 0 Vol I WCE 0, July -, 0, London, U.K. Reliability Measues in Ciculant Netwok *Inda Rajasingh, Bhaati Rajan, and R. Sundaa Rajan Abstact Reliability and efficiency
More informationAQI: Advanced Quantum Information Lecture 2 (Module 4): Order finding and factoring algorithms February 20, 2013
AQI: Advanced Quantum Infomation Lectue 2 (Module 4): Ode finding and factoing algoithms Febuay 20, 203 Lectue: D. Mak Tame (email: m.tame@impeial.ac.uk) Intoduction In the last lectue we looked at the
More informationOn a Hyperplane Arrangement Problem and Tighter Analysis of an Error-Tolerant Pooling Design
On a Hypeplane Aangement Poblem and Tighte Analysis of an Eo-Toleant Pooling Design Hung Q Ngo August 19, 2006 Abstact In this pape, we fomulate and investigate the following poblem: given integes d, k
More informationEfficient Multiplication in for Elliptic Curve Cryptography
Efficient Multiplication in fo Elliptic Cuve Cyptogaphy JC Bajad, L Imbet, C Nège and T Plantad Laboatoie d Infomatique de Robotique et de Micoélectonique de Montpellie LIRMM, ue Ada, 3439 Montpellie cedex
More informationDesign and Analysis of Password-Based Key Derivation Functions
Design and Analysis of Passwod-Based Key Deivation Functions Fances F. Yao 1 and Yiqun Lisa Yin 2 1 Depatment of Compute Science City Univesity of Hong Kong Kowloon, Hong Kong Email: csfyao@cityu.edu.hk
More informationCALCULUS II Vectors. Paul Dawkins
CALCULUS II Vectos Paul Dawkins Table of Contents Peface... ii Vectos... 3 Intoduction... 3 Vectos The Basics... 4 Vecto Aithmetic... 8 Dot Poduct... 13 Coss Poduct... 21 2007 Paul Dawkins i http://tutoial.math.lama.edu/tems.aspx
More informationPerturbation to Symmetries and Adiabatic Invariants of Nonholonomic Dynamical System of Relative Motion
Commun. Theo. Phys. Beijing, China) 43 25) pp. 577 581 c Intenational Academic Publishes Vol. 43, No. 4, Apil 15, 25 Petubation to Symmeties and Adiabatic Invaiants of Nonholonomic Dynamical System of
More informationStanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012
Stanfod Univesity CS59Q: Quantum Computing Handout 8 Luca Tevisan Octobe 8, 0 Lectue 8 In which we use the quantum Fouie tansfom to solve the peiod-finding poblem. The Peiod Finding Poblem Let f : {0,...,
More informationNOTE. Some New Bounds for Cover-Free Families
Jounal of Combinatoial Theoy, Seies A 90, 224234 (2000) doi:10.1006jcta.1999.3036, available online at http:.idealibay.com on NOTE Some Ne Bounds fo Cove-Fee Families D. R. Stinson 1 and R. Wei Depatment
More informationLocalization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix
Jounal of Sciences, Islamic Republic of Ian (): - () Univesity of Tehan, ISSN - http://sciencesutaci Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matix H Ahsani
More informationLifting Private Information Retrieval from Two to any Number of Messages
Lifting Pivate Infomation Retieval fom Two to any umbe of Messages Rafael G.L. D Oliveia, Salim El Rouayheb ECE, Rutges Univesity, Piscataway, J Emails: d746@scaletmail.utges.edu, salim.elouayheb@utges.edu
More informationAuchmuty High School Mathematics Department Advanced Higher Notes Teacher Version
The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!
More informationAnonymity-enhanced Pseudonym System
JAIST Reposi https://dspace.j Title Anonymity-enhanced Pseudonym System Autho(s)Tamua, Yuko; Miyaji, Atsuko Citation Lectue Notes in Compute Science, 2 47 Issue Date 2003 Type Jounal Aticle Text vesion
More informationAnonymous return route information for onion based mix-nets
Anonymous etun oute infomation fo onion based mix-nets ABSTRACT Yoshifumi Manabe NTT Communication Science Laboatoies NTT Copoation Atsugi Kanagawa 239-0198 Japan manabeyoshifumi@labnttcojp This pape poposes
More informationMeasure Estimates of Nodal Sets of Polyharmonic Functions
Chin. Ann. Math. Se. B 39(5), 08, 97 93 DOI: 0.007/s40-08-004-6 Chinese Annals of Mathematics, Seies B c The Editoial Office of CAM and Spinge-Velag Belin Heidelbeg 08 Measue Estimates of Nodal Sets of
More informationLecture 16 Root Systems and Root Lattices
1.745 Intoduction to Lie Algebas Novembe 1, 010 Lectue 16 Root Systems and Root Lattices Pof. Victo Kac Scibe: Michael Cossley Recall that a oot system is a pai (V, ), whee V is a finite dimensional Euclidean
More informationPushdown Automata (PDAs)
CHAPTER 2 Context-Fee Languages Contents Context-Fee Gammas definitions, examples, designing, ambiguity, Chomsky nomal fom Pushdown Automata definitions, examples, euivalence with context-fee gammas Non-Context-Fee
More informationOn decompositions of complete multipartite graphs into the union of two even cycles
On decompositions of complete multipatite gaphs into the union of two even cycles A. Su, J. Buchanan, R. C. Bunge, S. I. El-Zanati, E. Pelttai, G. Rasmuson, E. Spaks, S. Tagais Depatment of Mathematics
More informationDesign and Analysis of Password-Based Key Derivation Functions
Design and Analysis of Passwod-Based Key Deivation Functions 245 Fances F. Yao 1 and Yiqun Lisa Yin 2 1 Depatment of Compute Science, City Univesity of Hong Kong, Kowloon, Hong Kong csfyao@cityu.edu.hk
More informationHOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?
6th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS? Cecília Sitkuné Göömbei College of Nyíegyháza Hungay Abstact: The
More informationThe Archimedean Circles of Schoch and Woo
Foum Geometicoum Volume 4 (2004) 27 34. FRUM GEM ISSN 1534-1178 The Achimedean Cicles of Schoch and Woo Hioshi kumua and Masayuki Watanabe Abstact. We genealize the Achimedean cicles in an abelos (shoemake
More informationJournal of Inequalities in Pure and Applied Mathematics
Jounal of Inequalities in Pue and Applied Mathematics COEFFICIENT INEQUALITY FOR A FUNCTION WHOSE DERIVATIVE HAS A POSITIVE REAL PART S. ABRAMOVICH, M. KLARIČIĆ BAKULA AND S. BANIĆ Depatment of Mathematics
More informationA Comparison and Contrast of Some Methods for Sample Quartiles
A Compaison and Contast of Some Methods fo Sample Quatiles Anwa H. Joade and aja M. Latif King Fahd Univesity of Petoleum & Mineals ABSTACT A emainde epesentation of the sample size n = 4m ( =, 1, 2, 3)
More informationCentral Coverage Bayes Prediction Intervals for the Generalized Pareto Distribution
Statistics Reseach Lettes Vol. Iss., Novembe Cental Coveage Bayes Pediction Intevals fo the Genealized Paeto Distibution Gyan Pakash Depatment of Community Medicine S. N. Medical College, Aga, U. P., India
More informationGoodness-of-fit for composite hypotheses.
Section 11 Goodness-of-fit fo composite hypotheses. Example. Let us conside a Matlab example. Let us geneate 50 obsevations fom N(1, 2): X=nomnd(1,2,50,1); Then, unning a chi-squaed goodness-of-fit test
More informationQuasi-Randomness and the Distribution of Copies of a Fixed Graph
Quasi-Randomness and the Distibution of Copies of a Fixed Gaph Asaf Shapia Abstact We show that if a gaph G has the popety that all subsets of vetices of size n/4 contain the coect numbe of tiangles one
More informationA Bijective Approach to the Permutational Power of a Priority Queue
A Bijective Appoach to the Pemutational Powe of a Pioity Queue Ia M. Gessel Kuang-Yeh Wang Depatment of Mathematics Bandeis Univesity Waltham, MA 02254-9110 Abstact A pioity queue tansfoms an input pemutation
More informationOvercoming Weak Expectations
Ovecoming Weak Expectations Yevgeniy Dodis Depatment of Compute Science New Yok Univesity Email: dodis@cs.nyu.edu (Invited Pape) Yu Yu Institute fo Intedisciplinay Infomation Sciences Tsinghua Univesity,
More informationTHE MAXIMUM SIZE OF A PARTIAL SPREAD II: UPPER BOUNDS
THE MAXIMUM SIZE OF A PARTIAL SPREAD II: UPPER BOUNDS ESMERALDA NĂSTASE MATHEMATICS DEPARTMENT XAVIER UNIVERSITY CINCINNATI, OHIO 4507, USA PAPA SISSOKHO MATHEMATICS DEPARTMENT ILLINOIS STATE UNIVERSITY
More informationOn a quantity that is analogous to potential and a theorem that relates to it
Su une quantité analogue au potential et su un théoème y elatif C R Acad Sci 7 (87) 34-39 On a quantity that is analogous to potential and a theoem that elates to it By R CLAUSIUS Tanslated by D H Delphenich
More informationSurveillance Points in High Dimensional Spaces
Société de Calcul Mathématique SA Tools fo decision help since 995 Suveillance Points in High Dimensional Spaces by Benad Beauzamy Januay 06 Abstact Let us conside any compute softwae, elying upon a lage
More informationMore Efficient Oblivious Transfer Extensions with Security for Malicious Adversaries
Moe Efficient Oblivious Tansfe Extensions with Secuity fo Malicious Advesaies Gilad Ashaov Yehuda Lindell Thomas Schneide Michael Zohne Hebew Univesity Ba-Ilan Univesity Damstadt Damstadt EUROCRYPT 2015
More informationDuality between Statical and Kinematical Engineering Systems
Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.
More informationResearch Article On Alzer and Qiu s Conjecture for Complete Elliptic Integral and Inverse Hyperbolic Tangent Function
Abstact and Applied Analysis Volume 011, Aticle ID 697547, 7 pages doi:10.1155/011/697547 Reseach Aticle On Alze and Qiu s Conjectue fo Complete Elliptic Integal and Invese Hypebolic Tangent Function Yu-Ming
More informationFUSE Fusion Utility Sequence Estimator
FUSE Fusion Utility Sequence Estimato Belu V. Dasaathy Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500 belu.d@dynetics.com Sean D. Townsend Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500
More informationMAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS
The 8 th Intenational Confeence of the Slovenian Society fo Non-Destuctive Testing»pplication of Contempoay Non-Destuctive Testing in Engineeing«Septembe 1-3, 5, Potoož, Slovenia, pp. 17-1 MGNETIC FIELD
More informationOn the Computation of the Optimal Ate Pairing at the 192-bit Security Level
On the Computation of the Optimal Ate Paiing at the 192-bit Secuity Level Loubna Ghammam 1 and Emmanuel Fouotsa 2 (1) IRMAR, UMR CNRS 6625, Univesité Rennes 1, Campus de Beaulieu 35042 Rennes cedex, Fance.
More informationAnalytical Solutions for Confined Aquifers with non constant Pumping using Computer Algebra
Poceedings of the 006 IASME/SEAS Int. Conf. on ate Resouces, Hydaulics & Hydology, Chalkida, Geece, May -3, 006 (pp7-) Analytical Solutions fo Confined Aquifes with non constant Pumping using Compute Algeba
More informationONE-POINT CODES USING PLACES OF HIGHER DEGREE
ONE-POINT CODES USING PLACES OF HIGHER DEGREE GRETCHEN L. MATTHEWS AND TODD W. MICHEL DEPARTMENT OF MATHEMATICAL SCIENCES CLEMSON UNIVERSITY CLEMSON, SC 29634-0975 U.S.A. E-MAIL: GMATTHE@CLEMSON.EDU, TMICHEL@CLEMSON.EDU
More informationCOLLAPSING WALLS THEOREM
COLLAPSING WALLS THEOREM IGOR PAK AND ROM PINCHASI Abstact. Let P R 3 be a pyamid with the base a convex polygon Q. We show that when othe faces ae collapsed (otated aound the edges onto the plane spanned
More informationChaos and bifurcation of discontinuous dynamical systems with piecewise constant arguments
Malaya Jounal of Matematik ()(22) 4 8 Chaos and bifucation of discontinuous dynamical systems with piecewise constant aguments A.M.A. El-Sayed, a, and S. M. Salman b a Faculty of Science, Aleandia Univesity,
More information15.081J/6.251J Introduction to Mathematical Programming. Lecture 6: The Simplex Method II
15081J/6251J Intoduction to Mathematical Pogamming ectue 6: The Simplex Method II 1 Outline Revised Simplex method Slide 1 The full tableau implementation Anticycling 2 Revised Simplex Initial data: A,
More informationTurán Numbers of Vertex-disjoint Cliques in r- Partite Graphs
Univesity of Wyoming Wyoming Scholas Repositoy Honos Theses AY 16/17 Undegaduate Honos Theses Sping 5-1-017 Tuán Numbes of Vetex-disjoint Cliques in - Patite Gaphs Anna Schenfisch Univesity of Wyoming,
More information1. INTRODUCTION FAST ELLIPTIC CURVE CRYPTOGRAPHY USING OPTIMAL DOUBLE-BASE CHAINS
FAST ELLIPTIC CURVE CRYPTOGRAPHY USING OPTIMAL DOUBLE-BASE CHAINS Voapong Suppakitpaisan, Hioshi Imai Gaduate School of Infomation Science and Technology, The Univesity of Tokyo Tokyo, Japan 11-00 m t
More informationEncapsulation theory: radial encapsulation. Edmund Kirwan *
Encapsulation theoy: adial encapsulation. Edmund Kiwan * www.edmundkiwan.com Abstact This pape intoduces the concept of adial encapsulation, wheeby dependencies ae constained to act fom subsets towads
More informationQUANTUM ALGORITHMS IN ALGEBRAIC NUMBER THEORY
QUANTU ALGORITHS IN ALGEBRAIC NUBER THEORY SION RUBINSTEIN-SALZEDO Abstact. In this aticle, we discuss some quantum algoithms fo detemining the goup of units and the ideal class goup of a numbe field.
More informationCHARIOT: Cloud-Assisted Access Control for the Internet of Things
CHARIOT: Cloud-Assisted Access Contol fo the Intenet of Things Clémentine Gitti Euecom Sophia Antipolis, Fance gitti@euecom.f Melek Önen Euecom Sophia Antipolis, Fance onen@euecom.f Refik Molva Euecom
More informationComputers and Mathematics with Applications
Computes and Mathematics with Applications 58 (009) 9 7 Contents lists available at ScienceDiect Computes and Mathematics with Applications jounal homepage: www.elsevie.com/locate/camwa Bi-citeia single
More informationANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE
THE p-adic VALUATION OF STIRLING NUMBERS ANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE Abstact. Let p > 2 be a pime. The p-adic valuation of Stiling numbes of the
More informationTANTON S TAKE ON CONTINUOUS COMPOUND INTEREST
CURRICULUM ISPIRATIOS: www.maa.og/ci www.theglobalmathpoject.og IOVATIVE CURRICULUM OLIE EXPERIECES: www.gdaymath.com TATO TIDBITS: www.jamestanton.com TATO S TAKE O COTIUOUS COMPOUD ITEREST DECEMBER 208
More informationarxiv: v1 [math.co] 4 May 2017
On The Numbe Of Unlabeled Bipatite Gaphs Abdullah Atmaca and A Yavuz Ouç axiv:7050800v [mathco] 4 May 207 Abstact This pape solves a poblem that was stated by M A Haison in 973 [] This poblem, that has
More informationThe Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
More informationAustralian Intermediate Mathematics Olympiad 2017
Austalian Intemediate Mathematics Olympiad 207 Questions. The numbe x is when witten in base b, but it is 22 when witten in base b 2. What is x in base 0? [2 maks] 2. A tiangle ABC is divided into fou
More informationA pathway to matrix-variate gamma and normal densities
Linea Algeba and its Applications 396 005 317 38 www.elsevie.com/locate/laa A pathway to matix-vaiate gamma and nomal densities A.M. Mathai Depatment of Mathematics and Statistics, McGill Univesity, 805
More informationLecture 7. Public Key Cryptography (Diffie-Hellman and RSA)
Lectue 7 Pulic Key Cytogahy (Diffie-Hellman and RSA) 1 Pulic Key Cytogahy Asymmetic cytogahy Invented in 1974-1978 (Diffie-Hellman and Rivest-Shami- Adleman) Two keys: ivate (SK), ulic (PK) Encytion: with
More informationChannel matrix, measurement matrix and collapsed matrix. in teleportation
Channel matix, measuement matix and collapsed matix in telepotation XIN-WEI ZHA, JIAN-XIA QI and HAI-YANG SONG School of Science, Xi an Univesity of Posts and Telecommunications, Xi an, 71011, P R China
More informationA Simple Model of Communication APIs Application to Dynamic Partial-order Reduction
Simple Model of Communication PIs pplication to Dynamic Patial-ode Reduction Cistian Rosa Stephan Mez Matin Quinson VOCS 2010 22/09/2010 1 / 18 Motivation Distibuted lgoithms ae had to get ight: lack of
More informationConsensus Determining with Dependencies of Attributes with Interval Values
Jounal of Univesal Compute Science, vol. 13, no. (007), 39-344 submitted: 31/7/06, accepted: 15/1/07, appeaed: 8//07 J.UCS Consensus Detemining with Dependencies of Attibutes with Inteval Values Michal
More informationTHE NUMBER OF TWO CONSECUTIVE SUCCESSES IN A HOPPE-PÓLYA URN
TH NUMBR OF TWO CONSCUTIV SUCCSSS IN A HOPP-PÓLYA URN LARS HOLST Depatment of Mathematics, Royal Institute of Technology S 100 44 Stocholm, Sweden -mail: lholst@math.th.se Novembe 27, 2007 Abstact In a
More informationFall 2014 Randomized Algorithms Oct 8, Lecture 3
Fall 204 Randomized Algoithms Oct 8, 204 Lectue 3 Pof. Fiedich Eisenband Scibes: Floian Tamè In this lectue we will be concened with linea pogamming, in paticula Clakson s Las Vegas algoithm []. The main
More informationH.W.GOULD West Virginia University, Morgan town, West Virginia 26506
A F I B O N A C C I F O R M U L A OF LUCAS A N D ITS SUBSEQUENT M A N I F E S T A T I O N S A N D R E D I S C O V E R I E S H.W.GOULD West Viginia Univesity, Mogan town, West Viginia 26506 Almost eveyone
More informationAsymptotically Lacunary Statistical Equivalent Sequence Spaces Defined by Ideal Convergence and an Orlicz Function
"Science Stays Tue Hee" Jounal of Mathematics and Statistical Science, 335-35 Science Signpost Publishing Asymptotically Lacunay Statistical Equivalent Sequence Spaces Defined by Ideal Convegence and an
More informationAn upper bound on the number of high-dimensional permutations
An uppe bound on the numbe of high-dimensional pemutations Nathan Linial Zu Luia Abstact What is the highe-dimensional analog of a pemutation? If we think of a pemutation as given by a pemutation matix,
More informationFunctions Defined on Fuzzy Real Numbers According to Zadeh s Extension
Intenational Mathematical Foum, 3, 2008, no. 16, 763-776 Functions Defined on Fuzzy Real Numbes Accoding to Zadeh s Extension Oma A. AbuAaqob, Nabil T. Shawagfeh and Oma A. AbuGhneim 1 Mathematics Depatment,
More information