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1、#CiscoLive#CiscoLiveFrederic DetienneDistinguished EngineerBRKSEC-3129Public Key CryptographyFrom RSA and EC to Post-Quantum 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveEnter your personal notes hereCisco Webex App 3Questions?Use Cisco Webex App to chat with the speake
2、r after the sessionFind this session in the Cisco Live Mobile AppClick“Join the Discussion”Install the Webex App or go directly to the Webex spaceEnter messages/questions in the Webex spaceHowWebex spaces will be moderated by the speaker until June 9,2023.12343https:/ 2023 Cisco and/or its affiliate
3、s.All rights reserved.Cisco PublicBRKSEC-3129Agenda 2023 Cisco and/or its affiliates.All rights reserved.Cisco PublicA Brief IntroductionMODP:Multiplicative Group of Integers Modulo PECC:Elliptic Curve CryptographyEnters The Quantum ComputerLattice Based CryptographyConclusion and RecommendationsBRK
4、SEC-31294 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveToday is a bout making math fun!5BRKSEC-3129Introduction 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveCryptographic Mechanisms7BRKSEC-3129EncryptionData Authentication(HMAC)Key Establis
5、hmentHashingSignaturesRandom NumberGeneration 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveToday-Suite B8BRKSEC-3129Key Establishment ECDHDigital SignaturesECDSAHashingSHA-2AuthenticatedEncryptionAES-GCMAuthenticationHMAC-SHA-2EntropySP800-90ProtocolsTLSv1.2,IKEv2,IPsec
6、,MACSecHashes and HMACsFocus on SHA-2 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveWhat is a Cryptographic Hash Function10BRKSEC-3129Legitimate MessageHashHashFunctionAny LengthFixed LengthEasy&Fastvery hardIllegitimate MessageHashHashFunctionvery hardPre-image resistan
7、ce(message can not be found from hash)Legitimate MessageHashHashFunctionSecond pre-image resistance(legitimate message and hash are imposed;find new message)Fixed length outputAvalanche effect(small change in message,big change in hash)*!#%HashFunctionEasy&FastBogus Message 1Some HashHashFunctionUnc
8、hangedvery hardCollision resistance(attacker gets to select message 1 and 2;hash must match)Bogus Message 2Legitimate MessageLegitimate MesSage 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveThe MerkleDamgrd Construction11BRKSEC-3129IVFBlock 1Block 2Block 3FFFPadN.DataFin
9、HSymmetric Encryption Algorithms:One Time Pad&AES 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveOne Time Pad13BRKSEC-3129MM1 10 00 01 11 10 01 11 11 1 Pad011000101Cypher111110010A One Time Pad(here using XOR)A Pad is a truly random truly random sequence of numbersPad is
10、used as encryption and decryption key through modular additionmodular additionThe Pad must be as long as the messageas long as the messageThe Pad must be used ONLY ONCEONLY ONCEIf used properly,this is the strongest possible strongest possible encryption scheme 2023 Cisco and/or its affiliates.All r
11、ights reserved.Cisco Public#CiscoLiveOne Time Pad-example14BRKSEC-3129H HE EL LL LO Omessagemessage74111114+231221011key=3016132125m+kmod 26416132125(m+k)mod 26E EQ QN NV VZ ZciphertextciphertextE EQ QN NV VZ Zciphertextciphertext416key=-194111114c-kmod 2674111114(c-k)mod 26H HE EL L
12、L LO Omessagemessage 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveIssue 1 Key Length15BRKSEC-3129H HE EL LL LO Omessagemessage74111114+231221011key=3016132125m+kmod 26416132125(m+k)mod 26E EQ QN NV VZ ZciphertextciphertextKey must have the same size as message Key excha
13、nge is a problem!Use high quality Deterministic Random Bit Generator(DRBG)Select Carefully 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveIssue 2 Key Re-use&Known Plain Text Attack16BRKSEC-3129H HE EL LL LO Omessagemessage74111114+231221011key=3016132125m+kmod 26416132125
14、(m+k)mod 26E EQ QN NV VZ ZciphertextciphertextH HE EL LL LO Oknown messageknown message416132125ciphertext-74111114known message=-31221011c-mmod 26231221011(c-m)mod 26=KEYKEYAssumption#1:Attacker knows some plain text(e.g.injection,guess,)Assumption#2:Attacker can wiretap ciphertextConclusion:Attack
15、er can compute the key easily DO NOT REUSE KEY!2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLive65439Block Cipher Mode of Operation(ECB,CBC,counter)17BRKSEC-3129Penguin source:Wikipedia123145915ENCENCENCENCENC12314ENC72608ENCENCENCENCIV12314IVIVIV+1 IV+2 IV+3 IV+412314ENCEN
16、CENCENCENC61231453397DRBG seeded by IV Parallel encryption pipelines.Efficient implementation possibleOne Time Pad depends on IVMake IV unique to ensure unique padm=c=c=c=c=m=m=m=CTRCBCECB 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveAES GCM18BRKSEC-3129GF(2128)Polynomi
17、al x128+x7+x2+x+1GHASH(H,A,C)=Xm+n+1u,v bits in Am,PnWeak but fast HMACEncrypted HMAC Very strong!ICV can be 8,12 or 16 bytesAES Based PRNGgenerate padSecure CTR DRBGOne Time PadAlgorithmGalois HMACOne Time PadParallelization possibleFed from Initialization VectorAES GCM in summaryAES is more secure
18、 than 3DESAES-CTR CAN be much faster(implementation)GMAC consumes less than SHA-2(or even SHA-1)MODPMultiplicative Group of Integers Modulo P 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveRSA20BRKSEC-3129Rivest,Shamir,Adleman(1977)Patented but expired=no more royaltyPubl
19、ic key cryptosystemVariable key length(usually 512-2048 bits)Based on the(current)difficulty of factoring very large numbers 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveModular Arithmetic21BRKSEC-3129Modulo is like a clockb bx xmod n=rmod n=r also written as b bx x r(m
20、od n)r(mod n)b is the basex is the exponentn is the modulusr is the remainderKnowing b,x&n,it is very easy to compute rvery easy to compute rKnowing x,r&n,it is veryvery difficult to compute b=difficult to compute b=x x r mod nr mod n aka the RSA problemKnowing b,r&n,it is very difficult to compute
21、x=logvery difficult to compute x=logb b(r)mod n(r)mod n aka the discrete log problem0 1 2 3 4 5 6 7 8 9 10 11mod 40unless there are trapdoorsunless there are trapdoors 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveEncryption with Modular Arithmetic22BRKSEC-312
22、9AliceBobcTakes n n&e e from Bob(we assume m n)Computes c=mc=me emod nmod nComputes m=cm=cd dmod nmod nm=cdmod n=(me)dmod n=medmod n=m1mod n=mBob has reversed the operation!Bob knows d but nobody elseWe have an encryption schemeSelects three numbers n,d&en,d&en n&e e are publicpublic,d d is secretse
23、crete,d e,d are chosen such as eded 1 mod n 1 mod nMust send a private message mmTo decrypt,the attacker would need to compute m=e e c mod nc mod n RSA ProblemRSA ProblemAttacker can not guess m m just knowing c,n and ec,n and e 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#Cisco
24、LiveSignature with Modular Arithmetic23BRKSEC-3129AliceBobTakes n n&e e from BobComputes m=m=c ce emod nmod nm=cemod n=(md)emod n=mdemod n=m1mod n=m mod n=mBob must have sent the c,mc,mComputes c=mc=md dmod nmod n(we assume m n)Selects three numbers n,d&en,d&en n&e e are publicpublic,d d is secretse
25、crete,d e,d are chosen such as eded 1 mod n 1 mod nMust send a signed message mmc,mAttacker can not guess d d just knowing m,n and em,n and eNow how can we find such e,d and n?To forge the signature,the attacker would need to computed d=log=logmm(c)mod n(c)mod n Discrete Logarithm ProblemDiscrete Lo
26、garithm Problem 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveRegular Exponentiation Dichotomy to reverse24BRKSEC-3129 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveMODP breaks dichotomy25BRKSEC-3129 2023 Cisco and/or its affiliates.All right
27、s reserved.Cisco Public#CiscoLiveAbout Prime Numbers26BRKSEC-3129A number is prime if it can be divided by one or itselfA number is composite is it can be divided by 2 or more prime numbersFactorization is a hard problemFactorization is a hard problem.Best algorithm yields Fundamental Theorem of Ari
28、thmetic:a given number has a single factorizationEuclids theorems:there are infinitely many primesinfinitely many primesprime density(ratio of primes per composite up to x)is 1/ln(x)density drops off rapidly in the beginning but very slowly after a few powers of 10(x)=x/ln(x):number of primes xEuler
29、s(n)function or Euleurs totient#of integers in 1,n that are relatively prime to n:|k 2,n|GCD(k,n)=1|,12 numbers are coprime if they share no factor other than 1.Property:n1,n2n1,n2,GCD(,GCD(n1,n2n1,n2)=1)=1 (n1*n2n1*n2)=)=(n1n1)*)*(n2n2)Totient is multiplicativeif x is prime if x is prime (n n)=n)=n
30、-1 1 since 1n-1 coprime with n and n divisible by itselfEulers theorem:mm(n n)1(mod 1(mod n n)if)if mm and and n n are coare co-primeprime.picture:Khan Academy 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveRSA keys finding e,d,ne,d,n|m|meded m(mod n)m(mod n)27BRKSEC-3129
31、Choose two distinct prime numbers p,qp,q and hide them forever!n=p.qn is hard to factor if p&q are very large(n)=n-(p+q-1)p&q are prime (p)=p-1(q)=q-1(n)=(pq)=(p)(q)=(p-1)(q-1)=n-(p+q-1)Final steps1k=1 (m(n)k 1k(mod n)mk(n)1(mod n)1m=m m mk(n)m(mod n)mk(n)+1 m(mod n)we look for e,d,n such that med m
32、k(n)+1 m(mod n)eded=k=k (n n)+1)+1 d=d=k k (n n)+1)+1e e=k k(n n (p p+q q1)1)+1 1e eSelect e e,small integer and k k such that GCD(d,(n)=1(i.e.d&(n)are co-prime)e e is usually 3 or 65537adjust k k to make d d an integerm arbitrary messagen the moduluse the public keyd the private keyEuler theorem 20
33、23 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveDH Diffie-Hellman28BRKSEC-3129LengthAliceBobApub,(g,p)BpubThe group definitionSelect a generator g g and a modulus p pPick a random number a aKeep a a secret!Compute A Apubpub=g ga amod pmod pUsing the same g g and p p as Alice
34、Pick a random number b bKeep b b secret!Compute B Bpubpub=g gb bmod pmod pSecretBob=(Apub)bmod pSecretAlice=(Bpub)a mod pSecret=ga.bmod pAttacker can not guess a aAttacker can not guess b bECCElliptic Curve Cryptography 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveWhat
35、is an elliptic curve?30BRKSEC-3129A curve of general equation y y2 2=x=x3 3+ax+b+ax+bIt MUST be a smooth curveIts discriminant MUST BE NON ZERO:The Elliptic Curve is the set of pointsThe Elliptic Curve is the set of pointsthat satisfy the equation of the curve(ie.that“belong”to the curve)Plus a spec
36、ial point at infinity that we call O(the letter O)D=4A3+27B2 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveElliptic Curve Addition31BRKSEC-3129OPQ-RP+Q=RLet P and Q be two points on the curveA line(P,Q)cuts the curve at a third point RIf the line is parallel to the Y axi
37、s,this point is OIf the line is tangent to the curve,the tangent point is counted twiceThe group operator+is defined such asP+Q+R=O;O is the identityThe x-axis symmetric opposite(“conjugate”)point from-R is R=P+Q=2(+)=(-)-2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveThe
38、 scalar multiplication n*P32BRKSEC-3129OP-RR=2P-RR=3PLets start with P+P=2*PFor drawing(P,P)draw a tangent to the curve R(O,R)cuts in P+P=2PThis is a scalar multiplication The multiplication of a point by a scalar(integer)Algebraically:One can derive3P=2P+P,4P=2(2P),5P=4P+P,=32+2=2 2=(-)-2023 Cisco
39、and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveFast Forward the finite fields Fm&F2k33BRKSEC-3129Remember modulo arithmeticGalois Field=Finite FieldLet E be an elliptic curve defined over a finite field Fm(modulo m):E(Fm):U(x,y)in FE(Fm):U(x,y)in FmmxFxFmm|y|y2 2=x=x3 3+ax+b,a,b in
40、F+ax+b,a,b in Fmm E(Fm)is the set of points whose coordinates belong to FmxFmand satisfy the equation+point at infinityThe set along group operations(+,x)seen before form an Abelian Group under multiplication a field.For cryptography,m should be a prime numberIt seems(seemed?)seems(seemed?)more comp
41、utationally efficient if m=2m=2k k-1 1 yielding the notation F F2 2k kMultiplication supposed to be more efficient very important for ECDH and ECDSIn this case,the Koblitz curve is used:y y2 2+xy=x+xy=x3 3+ax+ax2 2+1+1 where a=0a=0 or a=1a=1For cryptography,k should be a prime numberm should remain
42、a prime it would be called a Mersenne PrimeThere is debate about the actual security and efficiency of these curvesThere is debate about the actual security and efficiency of these curves!The order of a group order of a group G G is the cardinalitycardinality of that group written ordord(G)(G)or|G|G
43、|.The order of a point point P P in a group in a group G G is the value n such that n*P=O written ordord(p)(p)or|p|p|mod 40 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveExample Curve34BRKSEC-3129E(R):y2=x3+x+2E(F11):y2=x3+x+2|E(F11)|=16(i.e.15+O)2023 Cisco an
44、d/or its affiliates.All rights reserved.Cisco Public#CiscoLiveExample on F31 Complexity Increases35BRKSEC-3129m=25-1=31E(F31):y2=x3+x+2|E(F31)|=24 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveThe same on F127 Complexity Further Increases36BRKSEC-3129m=27-1=127E(F127):y2
45、=x3+x+2|E(F127)|=1362*P=P+PLet P be 40,623*P=2*P+P4*P=3*P+P5*P=4*P+P6*P7*P8*PDifficult problem:Difficult problem:Knowing E&P,what is n n for this point?n*PEasy to compute on Easy to compute on F Fmm 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveECDH Elliptic Curve Diffie
46、-Hellman37BRKSEC-3129LengthAliceBobApub,(P,f(x),m)BpubThe curve definition f fand point P PSelect a curve f and a point P on the curvePick a random number aKeep a secret!Compute Apub=a*PUsing the same curve f and point PPick a random number bKeep b secret!Compute Bpub=b*PSecretInit=a*BpubSecret=a*b*
47、PAttacker can not guess a aAttacker can not guess b bSecretResp=b*Apub 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveRepresentation of Elliptic Curves38BRKSEC-3129Elliptic curve domain parameters(p,a,b,G,n,h)for a curve over a prime field Fp(m,f(x),a,b,G,n,h)for a curve
48、over a binary field F2mWherep p is the prime modulusG G is the generator(base point)of the curven n is the order of G.i.e n*G=On*G=Oa,b a,b are the coefficient of y y2 2+xyxy=x=x3 3+ax+b(mod p)+ax+b(mod p)Who defines elliptic curves?National Institute of Standards and Technology(NIST)American Nation
49、al Standard Institute(ANSI)Agence Nationale pour la Securit des SystmesInformatiques(ANSSI)Institute of Electrical and Electronics Engineers(IEEE)CerticomBrainpool ECCP-256 from NIST routinesEnters theQuantum Computer 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveTodays
50、Cryptography Temporal DefenseTIME PROTECTS PUBLIC KEYS(Until Y2Q)TIME PROTECTS PUBLIC KEYS(Until Y2Q)Public Key=Prime 1 x Prime 2=Prime 1 x Prime 2BRKSEC-312940 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveShors Factoring AlgorithmProblem:For a given“N”find a“p”between“
51、1”and“N”that divides“N”N=p1*p2PeterShorPart AClassicReduction of factoring problem to period finding problemPart BQuantumSolve period finding problem using Quantum Fourier Transform(Adjust it to taste if its wrong)(Probabilistic Algorithm)Shors algo converts exponential complexity Shors algo convert
52、s exponential complexity toto polynomial complexitypolynomial complexityxN Nxwhere N is the number of bitsBRKSEC-312941Lattice Based CryptographyLBC,LWE,NTRU 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveVectorsa1a2ana a=b1b2bnb b=OperationFormulaResult typeadditiona a+b
53、 b=(a1+b1,a2+b2)VectorScalar multiplicationx.a a=x.a1+x.anVectorInner producta a.b b=a1b1+anbnScalar(number)Commonly denoted or We will use v v or a a3.a3.a-5.a5.aa ab ba+a+b bBRKSEC-312943 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveThis is not a lattice44BRKSEC-3129
54、2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveWhat is a Lattice?A periodic“grid”in All integerinteger linear combinatons of n n basis vectors b b1 1,b,b2 2,b,bn nBasis B B=b b1 1,b bmmLattice =1,45BRKSEC-3129 2023 Cisco and/or its affiliates.All rights reserved.Cisco Pub
55、lic#CiscoLiveGood Basis,Bad Basis46BRKSEC-3129B=b b1 1,b b2 2:good basisShort,almost perpendicular vectorsB=b b1 1,b b2 2:bad basisLong,not very perpendicular vectors 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveNot a basis47BRKSEC-3129B=b b1 1,b b2 2:not a basisThe lat
56、tices do not overlap fully 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveShort Vectors is a Hard Problem48BRKSEC-3129Given this base,what is the shortest possible non-trivial vector?Surprise!2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveClose
57、st Vector Problem is a Hard Problem49BRKSEC-3129What is the closest lattice vector to y?Babais round-off algorithm:=.1.Theorem:12 In clear:Better base Closer vectory y 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveSISSIS=0 with short 0Average case SVP(Shortest Vector Pro
58、blem)=:=0Short Integer Solution&Learning With Errors50LWELWE(,=+)vs.(,)Average case BDD(Bounded Distance Decision)=mod BRKSEC-3129These are other ways to define a lattice 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveGoldreich,Goldwasser,Halevi Cryptosystem51BRKSEC-3129A
59、liceBobcTakes V V from BobComputes l l=m m*VVGenerates an error vector r r(n)Computes c c=l l+r rGenerates V V(nxn),a good basisPublishes VV(nxn),a bad basisMust send a private message mmEve can not guess m m because of the Closest Vector Problem(bad basis)Example Only!Quantum secure but broken l th
60、e lattice vectorc c=l l+r rthe cyphertextApplies Babai on(V V,c c)finds l l(good basis accuracy)Computes m=l l*VV-1 1Bob has reversed the operation!We have an encryption scheme 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveNIST Post Quantum Algorithm SelectionSelected Al
61、gorithms 202252BRKSEC-3129TypeTypeNameNameMathMathPub Key Encr and Key ExchangeCRYSTALS-KYBERLattice LWE(CVP)Digital SignatureCRYSTAL-DILITHIUMLattice LWE(CVP)Digital SignatureFALCONLattice NTRU(SVP)+FFTDigital SignatureSPHINCS+Stateless hash-basedRef:https:/csrc.nist.gov/Projects/post-quantum-crypt
62、ography/selected-algorithms-2022In Summary 2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveMain Public-Key Cryptographic Primitives54BRKSEC-3129KeyGenPublic KeyPrivate KeySignPrivate KeyMessageSignatureVerifyPrivate KeySignatureValid/InvalidMessageKey ExchangeShared KeyLoc
63、al nonceRemote nonceEncryptPublic KeyMessageCyphertext 2023 Cisco and/or its affiliates.All rights reserved.Cisco PublicBusiness OutcomeCrypto is not broken;it evolves and so do attackers.These are good news!The more research,the more insight.Lattice-based cryptography is Post-Quantum ready55BRKSEC-
64、3129Evolve your systems as new recommended algorithms are released!2023 Cisco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveA Short Bibliography56BRKSEC-3129NIST SP 800-90A:Recommendations for Random Number Generation Using Deterministic Random Bit GeneratorsNIST SP 800-38D:Recomme
65、ndation for Block Cipher Modes of Operation:Galois/Counter Mode(GCM)and GMACNIST SP 800-56A(R2):Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography(i.e.DH,ECDH+key derivation methods)NIST 800-131Ar1:Transitions:Recommendations fro Transitioning the Use of Cryptographic Algorith
66、ms and Key LengthsNIST FIPS 140-2:Security Requirements for Cryptographic ModulesNIST FIPS 186-4:Digital Signature Standard(DSS)(DSA,RSA(PKCS#1),ECDSA,)NIST FIPS 180-4:Secure Hash Standard(SHA-1,SHA-256,SHA-512)NIST Routines:https:/www.nsa.gov/ia/_files/nist-routines.pdf(Curve P-192,P-224,P-256 etc.
67、)Safe Curves:http:/safecurves.cr.yp.toTranscript Collision Attacks:Breaking authentication in TLS,IKE and SSH:http:/www.mitls.org/downloads/transcript-collisions.pdfSimons institute:https:/simons.berkeley.edu/workshops/schedule/10563https:/simons.berkeley.edu/workshops/lattices-2020-boot-camp 2023 C
68、isco and/or its affiliates.All rights reserved.Cisco Public#CiscoLiveFill out your session surveys!Attendees who fill out a minimum of four session surveys and the overall event survey will get Cisco Live-branded socks(while supplies last)!57BRKSEC-3129These points help you get on the leaderboard an
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71、points for attending this session!for attending this session!Open the Cisco Events App.Click on Cisco Live Challenge in the side menu.Click on View Your Badges at the top.Click the+at the bottom of the screen and scan the QR code:How:123460 2023 Cisco and/or its affiliates.All rights reserved.Cisco PublicBRKSEC-3129#CiscoLive