KISS: A Bit Too Simple. Greg Rose
|
|
- Bertina Pamela Harrell
- 6 years ago
- Views:
Transcription
1 KI: A Bit Too impl Grg Ros ggr@qualcomm.com
2 Outli KI radom umbr grator ubgrators Efficit attack N KI ad attack oclusio PAGE 2
3 O approach to PRNG scurity "A radom umbr grator is lik sx: Wh it's good, its odrful; Ad h it's bad, it's still prtty good." Add to that, i li ith my rcommdatios o combiatio grators; "Ad if it's bad, try a tosom or thrsom. -- Gorg Marsaglia, quotig himslf (1999) PAGE 3
4 KI a Psudo-Radom Numbr Grator Kp it impl tupid Marsaglia ad Zama, Florida tat U, 1993 Marsaglia posts vrsio to sci.crypt, 1998/99, took off Nvr said it as scur! Good thig, too But othrs sm to thik it is. #dfi z (z=36969*(z&65535)(z>>16)) #dfi (=18000*(&65535)(>>16)) #dfi MW ((z<<16) ) #dfi HR3 (jsr^=(jsr<<17), jsr^=(jsr>>13), jsr^=(jsr<<5)) #dfi ONG (jcog=69069*jcog ) #dfi KI ((MW^ONG)HR3) PAGE 4
5 KI diagram z M W O N G H R 3 K I PAGE 5
6 Multiply With arry subgrator z ad 16 bits radom lookig, 32 bits of stat Multiply by costat (18000, rsp), add carry from prvious multiplicatio Priods about ad to log cycls ach To bad valus (0 ad somthig ls) rpat forvr Larg stats go ito smallr os aftr o updat z oly affcts high ordr bits. PAGE 6
7 Liar ogrutial subgrator Wll studid, priod 2 32, sigl log cycl Lo ordr bits form smallr liar cogrutial grators I particular, LB gos PAGE 7
8 3-hift Rgistr subgrator Liar, but ot lik LFR Authors assum log priod, but rog LBs of output form o of 64 LFRs Priods rag from 1 to (ot !) a rcovr iitial stat from 32 coscutiv LBs asily Biary matrix multiplicatio PAGE 8
9 Attack ida Divid ad oqur Rgistrs ar updatd idpdtly of ach othr, th combid o try to gt rid of ffcts of o or mor rgistrs O of thm is alrady partly go! Exploit aksss (g. Liarity of HR3, lo ordr bits of ONG) Guss ad Dtrmi Guss (that is, try all possibilitis) for som valus, th Driv othr valus Vrify hthr still cosistt PAGE 9
10 What do ko at th start? z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 10
11 Guss z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 11
12 Guss LB of ONG (01010 or ) z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 12
13 Dtrmi LB squc from HR3 z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 13
14 Vrify LB squc from HR3 is LFR z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 14
15 Dtrmi half of ONG z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 15
16 Guss top half of ONG z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 16
17 Dtrmi lo half of z z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 17
18 Dtrmi high half of z from lo half z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 18
19 Ad vrify z M W O N G Gussd Dtrmid No ko H R 3 K I PAGE 19
20 Ho much ork? Domiatd by tryig, o avrag, 589,823,999 valus for Ad for ach o, usig Brlkamp-Massy algorithm to chck hthr th cadidat for HR3 is LFR Altrativly, ca chck parity quatios. F hours o laptop. PAGE 20
21 Nr KI ci.crypt 2011 postig by Marsaglia Lookig for logr ad logr cycls Priod > 10 40,000,000 tat is ridiculously larg ( bit ords) Agai combis multipl compots for scurity b32mw (2 22 ords) H R 3 O N G PAGE 21
22 N KI static usigd log Q[ ],carry=0; usigd log b32mw(void) {usigd log t,x; static it j= ; j=(j1)& ; x=q[j]; t=(x<<28)carry; carry=(x>>4)-(t<x); rtur (Q[j]=t-x); } #dfi NG ( cg=69069*cg13579 ) #dfi X ( xs^=(xs<<13), xs^=(xs>>17), xs^=(xs<<5) ) #dfi KI ( b32mw()ngx ) PAGE 22
23 omplmtd Multiply With arry Larg circular buffr ith carry variabl Extrmly log priod tat valus ar usd dirctly for output a b ru backard Aftr o rotatio through buffr, ca chck cosistcy asily (usd i attack) By itslf has o cryptographic strgth at all output is stat PAGE 23
24 Attack o N KI impl divid ad coqur Guss stat of ONG ad HR3 Ru grator forard slightly mor tha a full rotatio of b32mw s buffr If 3 outputs ar mutually cosistt, must hav gussd corrctly Ru backard to rcovr full iitial stat Equivalt to 2 63 ky stup opratios But th ky is hug, so is th ky stup opratio PAGE 24
25 oclusio M & Z ovrstimatd th priod by about a factor of 10 KI is ot scur Nd about 70 ords of gratd output a apply attack to uko (but biasd) plaitxt Rplac B-M stp ith fast corrlatio attack till surprisigly fficit Do t us KI if you d scurity! PAGE 25
Worksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationLectures 9 IIR Systems: First Order System
EE3054 Sigals ad Systms Lcturs 9 IIR Systms: First Ordr Systm Yao Wag Polytchic Uivrsity Som slids icludd ar xtractd from lctur prstatios prpard by McCllla ad Schafr Lics Ifo for SPFirst Slids This work
More informationAPPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
More informationProbability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationln x = n e = 20 (nearest integer)
H JC Prlim Solutios 6 a + b y a + b / / dy a b 3/ d dy a b at, d Giv quatio of ormal at is y dy ad y wh. d a b () (,) is o th curv a+ b () y.9958 Qustio Solvig () ad (), w hav a, b. Qustio d.77 d d d.77
More informationDiscrete Fourier Transform (DFT)
Discrt Fourir Trasorm DFT Major: All Egirig Majors Authors: Duc guy http://umricalmthods.g.us.du umrical Mthods or STEM udrgraduats 8/3/29 http://umricalmthods.g.us.du Discrt Fourir Trasorm Rcalld th xpotial
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationProblem Value Score Earned No/Wrong Rec -3 Total
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING ECE6 Fall Quiz # Writt Eam Novmr, NAME: Solutio Kys GT Usram: LAST FIRST.g., gtiit Rcitatio Sctio: Circl t dat & tim w your Rcitatio
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray ad Hido Mabuchi 5 Octobr 4 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls
More informationDiscrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform
Discrt Fourir Trasform Dfiitio - T simplst rlatio btw a lt- squc x dfid for ω ad its DTFT X ( ) is ω obtaid by uiformly sampli X ( ) o t ω-axis btw ω < at ω From t dfiitio of t DTFT w tus av X X( ω ) ω
More informationClass #24 Monday, April 16, φ φ φ
lass #4 Moday, April 6, 08 haptr 3: Partial Diffrtial Equatios (PDE s First of all, this sctio is vry, vry difficult. But it s also supr cool. PDE s thr is mor tha o idpdt variabl. Exampl: φ φ φ φ = 0
More informationLECTURE 13 Filling the bands. Occupancy of Available Energy Levels
LUR 3 illig th bads Occupacy o Availabl rgy Lvls W hav dtrmid ad a dsity o stats. W also d a way o dtrmiig i a stat is illd or ot at a giv tmpratur. h distributio o th rgis o a larg umbr o particls ad
More informationNumerov-Cooley Method : 1-D Schr. Eq. Last time: Rydberg, Klein, Rees Method and Long-Range Model G(v), B(v) rotation-vibration constants.
Numrov-Cooly Mthod : 1-D Schr. Eq. Last tim: Rydbrg, Kli, Rs Mthod ad Log-Rag Modl G(v), B(v) rotatio-vibratio costats 9-1 V J (x) pottial rgy curv x = R R Ev,J, v,j, all cocivabl xprimts wp( x, t) = ai
More informationChapter 6 Folding. Folding
Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl
More informationSolution to 1223 The Evil Warden.
Solutio to 1 Th Evil Ward. This is o of thos vry rar PoWs (I caot thik of aothr cas) that o o solvd. About 10 of you submittd th basic approach, which givs a probability of 47%. I was shockd wh I foud
More informationDiscrete Fourier Transform. Nuno Vasconcelos UCSD
Discrt Fourir Trasform uo Vascoclos UCSD Liar Shift Ivariat (LSI) systms o of th most importat cocpts i liar systms thory is that of a LSI systm Dfiitio: a systm T that maps [ ito y[ is LSI if ad oly if
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationLaw of large numbers
Law of larg umbrs Saya Mukhrj W rvisit th law of larg umbrs ad study i som dtail two typs of law of larg umbrs ( 0 = lim S ) p ε ε > 0, Wak law of larrg umbrs [ ] S = ω : lim = p, Strog law of larg umbrs
More informationDigital Signal Processing, Fall 2006
Digital Sigal Procssig, Fall 6 Lctur 9: Th Discrt Fourir Trasfor Zhg-Hua Ta Dpartt of Elctroic Systs Aalborg Uivrsity, Dar zt@o.aau.d Digital Sigal Procssig, I, Zhg-Hua Ta, 6 Cours at a glac MM Discrt-ti
More informationChapter Taylor Theorem Revisited
Captr 0.07 Taylor Torm Rvisitd Atr radig tis captr, you sould b abl to. udrstad t basics o Taylor s torm,. writ trascdtal ad trigoomtric uctios as Taylor s polyomial,. us Taylor s torm to id t valus o
More informationA Review of Complex Arithmetic
/0/005 Rviw of omplx Arithmti.do /9 A Rviw of omplx Arithmti A omplx valu has both a ral ad imagiary ompot: { } ad Im{ } a R b so that w a xprss this omplx valu as: whr. a + b Just as a ral valu a b xprssd
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Part B: Trasform Mthods Chaptr 3: Discrt-Tim Fourir Trasform (DTFT) 3. Discrt Tim Fourir Trasform (DTFT) 3. Proprtis of DTFT 3.3 Discrt Fourir Trasform (DFT) 3.4 Paddig with Zros ad frqucy Rsolutio 3.5
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationH2 Mathematics Arithmetic & Geometric Series ( )
H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic
More informationEconomics 201b Spring 2010 Solutions to Problem Set 3 John Zhu
Economics 20b Spring 200 Solutions to Problm St 3 John Zhu. Not in th 200 vrsion of Profssor Andrson s ctur 4 Nots, th charactrization of th firm in a Robinson Cruso conomy is that it maximizs profit ovr
More informationu r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C
Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin
More informationStatistics 3858 : Likelihood Ratio for Exponential Distribution
Statistics 3858 : Liklihood Ratio for Expotial Distributio I ths two xampl th rjctio rjctio rgio is of th form {x : 2 log (Λ(x)) > c} for a appropriat costat c. For a siz α tst, usig Thorm 9.5A w obtai
More informationFigure 2-18 Thevenin Equivalent Circuit of a Noisy Resistor
.8 NOISE.8. Th Nyquist Nois Thorm W ow wat to tur our atttio to ois. W will start with th basic dfiitio of ois as usd i radar thory ad th discuss ois figur. Th typ of ois of itrst i radar thory is trmd
More information(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More informationDFT: Discrete Fourier Transform
: Discrt Fourir Trasform Cogruc (Itgr modulo m) I this sctio, all lttrs stad for itgrs. gcd m, = th gratst commo divisor of ad m Lt d = gcd(,m) All th liar combiatios r s m of ad m ar multils of d. a b
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More information10. Joint Moments and Joint Characteristic Functions
0 Joit Momts ad Joit Charactristic Fctios Followig sctio 6 i this sctio w shall itrodc varios paramtrs to compactly rprst th iformatio cotaid i th joit pdf of two rvs Giv two rvs ad ad a fctio g x y dfi
More informationA Simple Proof that e is Irrational
Two of th most bautiful ad sigificat umbrs i mathmatics ar π ad. π (approximatly qual to 3.459) rprsts th ratio of th circumfrc of a circl to its diamtr. (approximatly qual to.788) is th bas of th atural
More informationOption 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.
Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray 7 Octobr 3 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls Dscrib th dsig o
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationMONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx
MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of
More informationSession : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationThe calculation method for SNE
Elctroic Supplmtary Matrial (ESI) for RSC Advacs. This joural is Th Royal Socity of Chmistry 015 Th ulatio mthod for SNE (1) Slct o isothrm ad o rror fuctio (for xampl, th ERRSQ rror fuctio) ad gt th solvr
More informationSeptember 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
More informationHow many neutrino species?
ow may utrio scis? Two mthods for dtrmii it lium abudac i uivrs At a collidr umbr of utrio scis Exasio of th uivrs is ovrd by th Fridma quatio R R 8G tot Kc R Whr: :ubblcostat G :Gravitatioal costat 6.
More informationChapter 4 - The Fourier Series
M. J. Robrts - 8/8/4 Chaptr 4 - Th Fourir Sris Slctd Solutios (I this solutio maual, th symbol,, is usd for priodic covolutio bcaus th prfrrd symbol which appars i th txt is ot i th fot slctio of th word
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More informationDerivation of a Predictor of Combination #1 and the MSE for a Predictor of a Position in Two Stage Sampling with Response Error.
Drivatio of a Prdictor of Cobiatio # ad th SE for a Prdictor of a Positio i Two Stag Saplig with Rspos Error troductio Ed Stak W driv th prdictor ad its SE of a prdictor for a rado fuctio corrspodig to
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationINTRODUCTION TO SAMPLING DISTRIBUTIONS
http://wiki.stat.ucla.du/socr/id.php/socr_courss_2008_thomso_econ261 INTRODUCTION TO SAMPLING DISTRIBUTIONS By Grac Thomso INTRODUCTION TO SAMPLING DISTRIBUTIONS Itro to Samplig 2 I this chaptr w will
More informationThomas J. Osler. 1. INTRODUCTION. This paper gives another proof for the remarkable simple
5/24/5 A PROOF OF THE CONTINUED FRACTION EXPANSION OF / Thomas J Oslr INTRODUCTION This ar givs aothr roof for th rmarkabl siml cotiud fractio = 3 5 / Hr is ay ositiv umbr W us th otatio x= [ a; a, a2,
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationANOVA- Analyisis of Variance
ANOVA- Aalii of Variac CS 700 Comparig altrativ Comparig two altrativ u cofidc itrval Comparig mor tha two altrativ ANOVA Aali of Variac Comparig Mor Tha Two Altrativ Naïv approach Compar cofidc itrval
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 301 Signals & Systms Prof. Mark Fowlr ot St #21 D-T Signals: Rlation btwn DFT, DTFT, & CTFT 1/16 W can us th DFT to implmnt numrical FT procssing This nabls us to numrically analyz a signal to find
More informationIntegration by Parts
Intgration by Parts Intgration by parts is a tchniqu primarily for valuating intgrals whos intgrand is th product of two functions whr substitution dosn t work. For ampl, sin d or d. Th rul is: u ( ) v'(
More informationChapter 3 Fourier Series Representation of Periodic Signals
Chptr Fourir Sris Rprsttio of Priodic Sigls If ritrry sigl x(t or x[] is xprssd s lir comitio of som sic sigls th rspos of LI systm coms th sum of th idividul rsposs of thos sic sigls Such sic sigl must:
More informationStrongly Connected Components
Strongly Connctd Componnts Lt G = (V, E) b a dirctd graph Writ if thr is a path from to in G Writ if and is an quivalnc rlation: implis and implis s quivalnc classs ar calld th strongly connctd componnts
More informationECE594I Notes set 6: Thermal Noise
C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More information15/03/1439. Lectures on Signals & systems Engineering
Lcturs o Sigals & syms Egirig Dsigd ad Prd by Dr. Ayma Elshawy Elsfy Dpt. of Syms & Computr Eg. Al-Azhar Uivrsity Email : aymalshawy@yahoo.com A sigal ca b rprd as a liar combiatio of basic sigals. Th
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More information( ) = is larger than. the variance of X V
Stat 400, sectio 6. Methods of Poit Estimatio otes by Tim Pilachoski A oit estimate of a arameter is a sigle umber that ca be regarded as a sesible value for The selected statistic is called the oit estimator
More informationOn the Hamiltonian of a Multi-Electron Atom
On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationFrequency Response & Digital Filters
Frquy Rspos & Digital Filtrs S Wogsa Dpt. of Cotrol Systms ad Istrumtatio Egirig, KUTT Today s goals Frquy rspos aalysis of digital filtrs LTI Digital Filtrs Digital filtr rprstatios ad struturs Idal filtrs
More informationBipolar Junction Transistors
ipolar Juctio Trasistors ipolar juctio trasistors (JT) ar activ 3-trmial dvics with aras of applicatios: amplifirs, switch tc. high-powr circuits high-spd logic circuits for high-spd computrs. JT structur:
More informationThey must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.
37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam
More informationA GENERALIZED RAMANUJAN-NAGELL EQUATION RELATED TO CERTAIN STRONGLY REGULAR GRAPHS
#A35 INTEGERS 4 (204) A GENERALIZED RAMANUJAN-NAGELL EQUATION RELATED TO CERTAIN STRONGLY REGULAR GRAPHS B d Wgr Faculty of Mathmatics ad Computr Scic, Eidhov Uivrsity of Tchology, Eidhov, Th Nthrlads
More informationChapter (8) Estimation and Confedence Intervals Examples
Chaptr (8) Estimatio ad Cofdc Itrvals Exampls Typs of stimatio: i. Poit stimatio: Exampl (1): Cosidr th sampl obsrvatios, 17,3,5,1,18,6,16,10 8 X i i1 17 3 5 118 6 16 10 116 X 14.5 8 8 8 14.5 is a poit
More informationECEN 655: Advanced Channel Coding Spring Lecture 7 02/04/14. Belief propagation is exact on tree-structured factor graphs.
ECEN 655: Advaced Chael Codig Sprig 014 Prof. Hery Pfister Lecture 7 0/04/14 Scribe: Megke Lia 1 4-Cycles i Gallager s Esemble What we already kow: Belief propagatio is exact o tree-structured factor graphs.
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationHow many neutrons does this aluminium atom contain? A 13 B 14 C 27 D 40
alumiium atom has a uclo umbr of 7 ad a roto umbr of 3. How may utros dos this alumiium atom cotai? 3 4 7 40 atom of lmt Q cotais 9 lctros, 9 rotos ad 0 utros. What is Q? calcium otassium strotium yttrium
More informationOrdinary Differential Equations
Basi Nomlatur MAE 0 all 005 Egirig Aalsis Ltur Nots o: Ordiar Diffrtial Equatios Author: Profssor Albrt Y. Tog Tpist: Sakurako Takahashi Cosidr a gral O. D. E. with t as th idpdt variabl, ad th dpdt variabl.
More informationComputing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
More informationn n ee (for index notation practice, see if you can verify the derivation given in class)
EN24: Computatioal mthods i Structural ad Solid Mchaics Homwork 6: Noliar matrials Du Wd Oct 2, 205 School of Egirig Brow Uivrsity I this homwork you will xtd EN24FEA to solv problms for oliar matrials.
More informationOutline. Ionizing Radiation. Introduction. Ionizing radiation
Outli Ioizig Radiatio Chaptr F.A. Attix, Itroductio to Radiological Physics ad Radiatio Dosimtry Radiological physics ad radiatio dosimtry Typs ad sourcs of ioizig radiatio Dscriptio of ioizig radiatio
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationLinear Algebra Existence of the determinant. Expansion according to a row.
Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationAbstract Interpretation: concrete and abstract semantics
Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationComparison of Simple Indicator Kriging, DMPE, Full MV Approach for Categorical Random Variable Simulation
Papr 17, CCG Aual Rport 11, 29 ( 29) Compariso of Simpl Idicator rigig, DMPE, Full MV Approach for Catgorical Radom Variabl Simulatio Yupg Li ad Clayto V. Dutsch Ifrc of coditioal probabilitis at usampld
More informationElectrochemistry L E O
Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationCS 332: Algorithms. Linear-Time Sorting. Order statistics. Slide credit: David Luebke (Virginia)
1 CS 332: Algorithms Liear-Time Sortig. Order statistics. Slide credit: David Luebke (Virgiia) Quicksort: Partitio I Words Partitio(A, p, r): Select a elemet to act as the pivot (which?) Grow two regios,
More informationPhysics 302 Exam Find the curve that passes through endpoints (0,0) and (1,1) and minimizes 1
Physis Exam 6. Fid th urv that passs through dpoits (, ad (, ad miimizs J [ y' y ]dx Solutio: Si th itgrad f dos ot dpd upo th variabl of itgratio x, w will us th sod form of Eulr s quatio: f f y' y' y
More informationSUMMER 17 EXAMINATION
(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr
More informationIterative Methods of Order Four for Solving Nonlinear Equations
Itrativ Mods of Ordr Four for Solvig Noliar Equatios V.B. Kumar,Vatti, Shouri Domii ad Mouia,V Dpartmt of Egirig Mamatis, Formr Studt of Chmial Egirig Adhra Uivrsity Collg of Egirig A, Adhra Uivrsity Visakhapatam
More informationWant to go a-courtin but not allowed to dance? Well then, try this once popular party game as a way to get to know each other.
fiddl, piano party gam, circl danc Want to go a-courtin but not allowd to danc? Wll thn, try this onc popular party gam as a way to gt to know ach othr. Ky G, first not do(g) Squar/Circl Danc d d d d d
More information3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More informationLecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
More informationRecurrence Relations
Recurrece Relatios Aalysis of recursive algorithms, such as: it factorial (it ) { if (==0) retur ; else retur ( * factorial(-)); } Let t be the umber of multiplicatios eeded to calculate factorial(). The
More informationIdeal crystal : Regulary ordered point masses connected via harmonic springs
Statistical thrmodyamics of crystals Mooatomic crystal Idal crystal : Rgulary ordrd poit masss coctd via harmoic sprigs Itratomic itractios Rprstd by th lattic forc-costat quivalt atom positios miima o
More informationReview Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2
MATHEMATIS --RE Itgral alculus Marti Huard Witr 9 Rviw Erciss. Evaluat usig th dfiitio of th dfiit itgral as a Rima Sum. Dos th aswr rprst a ara? a ( d b ( d c ( ( d d ( d. Fid f ( usig th Fudamtal Thorm
More informationSTIRLING'S 1 FORMULA AND ITS APPLICATION
MAT-KOL (Baja Luka) XXIV ()(08) 57-64 http://wwwimviblorg/dmbl/dmblhtm DOI: 075/МК80057A ISSN 0354-6969 (o) ISSN 986-588 (o) STIRLING'S FORMULA AND ITS APPLICATION Šfkt Arslaagić Sarajvo B&H Abstract:
More informationCPU Frequency Tuning for Optimizing the Energy. David Brayford 1
CPU Frqucy Tuig or Optimizig th Ergy to Solutio. David Brayord Brayord@lrz.d 1 Cost o Larg HPC Systms Computr Hardwar HPC systm, cabls, data archivig systm tc. Buildig Th availability ad pric o ral stat.
More information