EXPRESSO: Artigo

From: Subject: EXPRESSO: Artigo Date: Sat, 18 Jan 2003 00:54:15 -0000 MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_000_0268_01C2BE8C.1F836980"; type="text/html" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 This is a multi-part message in MIME format. ------=_NextPart_000_0268_01C2BE8C.1F836980 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://segundasedicoes.expresso.pt/revista/artigos/interior.asp?edicao=1506&id_artigo=ES35593 EXPRESSO: Artigo

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=20

8/9/2001

Matem=E1tica

Cibersegredos inviol=E1veis =

A seguran=E7a do com=E9rcio = electr=F3nico est=E1=20 assegurada por um m=E9todo matem=E1tico inovador: uma chave = p=FAblica que=20 permite encerrar as mensagens num cofre, mas um cofre que = s=F3 se abre=20 com outra chave, esta secreta.

Texto de Nuno Crato

Tem receio de=20 enviar o n=FAmero do seu cart=E3o de cr=E9dito pela = Internet? H=E1 uma=20 compra de livro ou disco que n=E3o fez porque o vendedor = requeria o=20 uso de um Visa ou MasterCard? Pois n=E3o est=E1 sozinho = nessa=20 desconfian=E7a. Muitos portugueses e muitas pessoas em todo = o mundo=20 n=E3o beneficiam ainda das grandes vantagens do com=E9rcio = electr=F3nico=20 por receios de seguran=E7a. No entanto, a circula=E7=E3o de = informa=E7=E3o=20 confidencial pela Internet =E9 das mais seguras que at=E9 = hoje se=20 constru=EDram. Com alguns cuidados b=E1sicos, tais como = evitar=20 comerciantes desconhecidos e n=E3o enviar informa=E7=E3o = confidencial por=20 e-mail directo (n=E3o cifrado), o mundo do com=E9rcio = electr=F3nico est=E1=20 ao alcance dos seus dedos.

Ronald Rivest

A=20 Internet abriu possibilidades com que ainda h=E1 poucos anos = n=E3o se=20 sonhava. Tornou-se uma gigantesca biblioteca p=FAblica e = abriu aos=20 cidad=E3os do mundo o acesso ao com=E9rcio internacional, = r=E1pido e=20 seguro. Quer comprar aquele manual t=E9cnico que n=E3o = encontra nas=20 livrarias e de cujo t=EDtulo exacto j=E1 n=E3o se recorda? = Quer obter=20 aquele CD de Bob Dylan que n=E3o consegue encontrar? =C9 = coleccionador e=20 pretende adquirir uma b=FAssola do s=E9culo XIX? Tudo isso = pode fazer=20 pela Internet, que lhe d=E1 ainda acesso a v=E1rias redes = internacionais=20 de alfarrabistas onde, por tuta e meia, talvez encontre = aquela=20 esgotad=EDssima autobiografia de Max Planck que gostaria de = ler. Quem=20 sabe, tal como aconteceu com o autor destas linhas, pode ser = que=20 haja um alfarrabista na Nova Zel=E2ndia que lha venda pela=20 Internet.

Mas ser=E1 seguro enviar o nosso n=FAmero de = cart=E3o de=20 cr=E9dito atrav=E9s desses bits e bytes que circulam sabe = Deus por onde?=20 Como podem a Amazon e outras cadeias de com=E9rcio = electr=F3nico=20 garantir que os dados n=E3o chegam a m=E3os menos = escrupulosas, ao=20 teclado de algum computador da Cochinchina? =C9 verdade que = dizem que=20 a informa=E7=E3o segue cifrada, mas, se a minha mensagem =E9 = codificada=20 com uma chave que enviam para o meu computador, n=E3o podem = alguns=20 lar=E1pios descobrir essa chave?

Adi Shamir

A=20 pergunta faz todo o sentido. Durante mil=E9nios, os segredos = das=20 comunica=E7=F5es apoiaram-se em sistemas de cifra baseados = numa chave=20 dita sim=E9trica, que permitia cifrar e decifrar as = mensagens. Os=20 interlocutores acordavam nessa chave. Diziam, por exemplo: o = A=20 escreve-se B, o B escreve-se C, e por a=ED adiante. Sendo = assim,=20 quando queriam dizer BOM DIA, escreviam CPN EJB. A chave que = permite=20 cifrar esta mensagem =E9 a mesma que, invertida, a permite = decifrar. A=20 seguran=E7a da comunica=E7=E3o estava baseada na = possibilidade de manter=20 secreta a chave. Se ela era roubada ou descoberta ap=F3s = tentativas=20 v=E1rias...

A comunica=E7=E3o cifrada atrav=E9s da = Internet baseia-se=20 num princ=EDpio inovador que =E9 o da chave assim=E9trica. = Trata-se de uma=20 aut=EAntica revolu=E7=E3o em criptografia, talvez mesmo a = mais importante=20 desde o aparecimento de mensagens cifradas. O sistema, que = est=E1=20 incorporado nos =ABbrowsers=BB, em alguns sistemas de = correio=20 electr=F3nico e, =E9 claro, nas comunica=E7=F5es = interbanc=E1rias, baseia-se=20 numa proposta de Ronald Rivest, Adi Shamir e Leonard = Adleman, tr=EAs=20 investigadores do Massachusetts Institute of Technology que, = em=20 1977, avan=E7aram um m=E9todo de cifra que veio a ser = conhecido pelas=20 suas iniciais: RSA.

Leonard Adleman, que com Ronald = Riverst e=20 Adi Shamir, todos investigadores do MIT, propuseram em = 1977 o=20 sistema de cifra RSA. Descobriu-se recentemente que = James=20 Ellis e Clifford Cocks, investigadores de criptografia = dos=20 servi=E7os secretos do Governo ingl=EAs, tinham = inventado o mesmo=20 sistema poucos anos antes, mas mantiveram o processo=20 confidencial

Com=20 esse sistema, o receptor da mensagem, o vendedor da = Internet, por=20 exemplo, constr=F3i uma chave que consiste em dois n=FAmeros = grandes (N,=20 e). Envia esses dois n=FAmeros para o computador do cliente = e pouco se=20 preocupa com o seu secretismo. Pode mesmo, se quiser, = public=E1-los no=20 jornal. O computador do cliente, por seu turno, rescreve a = mensagem=20 que pretende enviar em forma num=E9rica (habitualmente, = seguindo os=20 c=F3digos ASCII dos computadores), obtendo um terceiro = n=FAmero (M), e=20 aplica depois uma f=F3rmula simples: eleva M =E0 pot=EAncia = e, divide o=20 resultado por N e calcula o resto, obtendo o n=FAmero C, que = envia=20 pela Internet.

O espantoso =E9 que esse n=FAmero C, que =E9 = a mensagem=20 cifrada, contendo, por exemplo, o n=FAmero do cart=E3o de = cr=E9dito, pode=20 ser visto por qualquer pessoa, porque, mesmo na posse da = chave=20 p=FAblica (os n=FAmeros N, e), a mensagem n=E3o =E9 = decifr=E1vel. A raz=E3o=20 desse facto =E9 que a fun=E7=E3o matem=E1tica que = transformou o n=FAmero M no=20 n=FAmero C n=E3o =E9 biun=EDvoca: ela transforma o n=FAmero = original num=20 n=FAmero perfeitamente determinado, mas outros n=FAmeros = poderiam ter=20 produzido o mesmo resultado, pelo que nenhum pirata da = Internet fica=20 a conhecer o nosso cart=E3o de cr=E9dito.

Como pode ent=E3o o receptor da mensagem = descodific=E1-la?=20 =C9 que este, que emitiu a chave p=FAblica, sabe como a = construiu:=20 escolheu N como o produto de dois n=FAmeros primos (apenas = divis=EDveis=20 pela unidade e por eles pr=F3prios), digamos p e q, e n=E3o = os revelou a=20 ningu=E9m. Conhecendo-os, calcula um outro n=FAmero d, de = tal forma que=20 (ed - 1) seja divis=EDvel por (p - 1)(q - 1). Eleva ent=E3o = o n=FAmero=20 cifrado C =E0 pot=EAncia d, divide-o por N e calcula o resto = da divis=E3o=20 inteira. Esse resto =E9 a mensagem original M. Milagre? = N=E3o. =C9 apenas=20 a aplica=E7=E3o engenhosa de um resultado da teoria dos = n=FAmeros,=20 conhecido como Teorema de Euler.

O que torna este sistema praticamente = inviol=E1vel =E9 que=20 a factoriza=E7=E3o de um n=FAmero no produto dos seus primos = =E9=20 extraordinariamente morosa quando esses n=FAmeros s=E3o = grandes. Obter o=20 produto de dois n=FAmeros =E9 f=E1cil. Mas, mesmo sabendo = que um dado=20 n=FAmero =E9 o produto de dois primos p e q, encontrar esses = dois=20 factores pode n=E3o ser nada simples - e sem os conhecer a = mensagem =E9=20 indecifr=E1vel.

O novo livro de Simon Singh, = autor=20 conhecido dos leitores portugueses atrav=E9s de =ABA = Solu=E7=E3o do=20 =DAltimo Teorema de Fermat=BB, =E9 uma viagem = fascinante pelo mundo=20 da criptografia, onde tamb=E9m se explica em pormenor = o sistema=20 RSA. Para saber mais sobre este m=E9todo, o leitor = pode=20 igualmente consultar www.rsa.com/rsalabs

Basta que=20 o n=FAmero N seja grande e que os seus factores p e q sejam = bem=20 escolhidos, para que o tempo de computa=E7=E3o necess=E1rio = =E0 factoriza=E7=E3o=20 seja extraordinariamente elevado. T=E3o elevado que se torna = impratic=E1vel a qualquer ciber-pirata tentar a proeza. Se = cada um dos=20 factores tiver 100 d=EDgitos, por exemplo, e um computador = conseguir=20 efectuar um milh=E3o de milh=F5es de tentativas por segundo, = ainda assim=20 a idade estimada para o Universo n=E3o seria suficiente para = garantir=20 que tal computador conseguisse descobrir os factores primos = desse=20 n=FAmero.

Como sempre, a cada avan=E7o das t=E9cnicas = de=20 criptografia sucede-se um avan=E7o nas t=E9cnicas de = criptoan=E1lise. O=20 sistema RSA tem sido sujeito a amea=E7as variadas de = matem=E1ticos, que=20 procuram algoritmos para a decifra=E7=E3o da chave privada = d, passando=20 ou n=E3o pela factoriza=E7=E3o da chave p=FAblica N nos seus = factores=20 primos. Os sucessos que t=EAm sido obtidos colocam = restri=E7=F5es =E0=20 escolha dos componentes do sistema e t=EAm obrigado os = peritos a=20 utilizar aperfei=E7oamentos v=E1rios para refor=E7ar a = seguran=E7a do=20 sistema, nomeadamente n=FAmeros grandes nas chaves do RSA. = At=E9 ao=20 momento, a matem=E1tica n=E3o conseguiu fornecer nenhuma = forma de=20 decifra=E7=E3o que funcione contra o RSA. O com=E9rcio = electr=F3nico=20 continua a ser muito mais seguro do que esconder dinheiro = debaixo do=20 colch=E3o.

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Helvetica, Sans-serif } .actualiz-data { FONT-SIZE: 9px; COLOR: #cc0000; LINE-HEIGHT: 9px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif } .actualiz-txt { FONT-WEIGHT: bold; FONT-SIZE: 12px; LINE-HEIGHT: 10px; FONT-FAMILY: = "Times New Roman", Times, serif } .assi-frases { FONT-SIZE: 70%; LINE-HEIGHT: 100%; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; TEXT-ALIGN: right } .breves { FONT-SIZE: 70%; LINE-HEIGHT: 90%; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .espacolinhas2px { LINE-HEIGHT: 2px } .espacolinhas2 { LINE-HEIGHT: 2pt } .espacolinhas4 { LINE-HEIGHT: 4pt } .espacolinhas6 { LINE-HEIGHT: 6pt } .espacolinhas8 { LINE-HEIGHT: 8px } .espacolinhas10 { LINE-HEIGHT: 10px } .espacolinhas14 { LINE-HEIGHT: 14px } .legenda { FONT-WEIGHT: bold; FONT-SIZE: 70%; LINE-HEIGHT: 120%; FONT-FAMILY: = Arial, Helvetica, sans-serif } .link { TEXT-DECORATION: none } .link:hover { TEXT-DECORATION: underline } .link-k { COLOR: #000000; TEXT-DECORATION: none } .link-k:hover { COLOR: #000000; TEXT-DECORATION: underline } .link-k-visited { COLOR: #000000; TEXT-DECORATION: none } .link-k-visited:hover { COLOR: #000000; TEXT-DECORATION: underline } .link-k-visited:visited { COLOR: #999999 } .link-w { COLOR: #ffffff; TEXT-DECORATION: none } .link-w:hover { COLOR: #ffffff; TEXT-DECORATION: underline } .link-r { COLOR: #000000; TEXT-DECORATION: none } .link-r:hover { COLOR: #000000; TEXT-DECORATION: underline } .par- { MARGIN-TOP: 0pt; MARGIN-BOTTOM: 8pt } .par-0 { MARGIN-TOP: 0pt; MARGIN-BOTTOM: 0pt } .par-assifim { FONT-WEIGHT: bold; FONT-SIZE: 75%; FONT-FAMILY: Arial, Helvetica, = sans-serif; TEXT-ALIGN: right } .par-subtitle { FONT-SIZE: 110%; PADDING-TOP: 6pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .par-subsubtitle { FONT-SIZE: 11px; PADDING-TOP: 6pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .texto-cita { FONT-SIZE: 14px; FONT-STYLE: italic; FONT-FAMILY: "Times New Roman", = Times, serif } .texto-cita-interior { FONT-SIZE: 15px; FONT-STYLE: italic; FONT-FAMILY: "Times New Roman", = Times, serif } .bar-caixa-r { FONT-SIZE: 11px; COLOR: #ffffff; LINE-HEIGHT: 18px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #336699 } .titulo-caixa-gr { FONT-SIZE: 100%; TEXT-TRANSFORM: uppercase; COLOR: #ffffff; = LINE-HEIGHT: 120%; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif; LETTER-SPACING: -1px } .titulo-caixa-med { FONT-SIZE: 90%; TEXT-TRANSFORM: uppercase; COLOR: #ffffff; LINE-HEIGHT: = 120%; FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif; = LETTER-SPACING: -1px } .texto-caixa-big { FONT-SIZE: 400%; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif } .texto-caixa-gr { FONT-SIZE: 300%; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif } .bar-art-rel { FONT-SIZE: 11px; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .copyright { FONT-SIZE: 8px; LINE-HEIGHT: 10px; FONT-FAMILY: verdana, Arial, = Helvetica, sans-serif } .edicao-data { FONT-SIZE: 11px; LINE-HEIGHT: 10px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .txt-dec-none-w { COLOR: white; TEXT-DECORATION: none } .tit-revista-gr { FONT-SIZE: 250%; COLOR: #cc6600; LINE-HEIGHT: 85%; FONT-FAMILY: "Times = New Roman", Times, serif } .tit-revista { FONT-SIZE: 190%; COLOR: #cc6600; LINE-HEIGHT: 90%; FONT-FAMILY: "Times = New Roman", Times, serif } .tit-revista-preto { FONT-SIZE: 190%; LINE-HEIGHT: 90%; FONT-FAMILY: "Times New Roman", = Times, serif } .tit-antevisao { FONT-SIZE: 12px; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .tit-momentos { FONT-SIZE: 12px; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .tit-qualvida { FONT-WEIGHT: bold; FONT-SIZE: 140%; LINE-HEIGHT: 100%; FONT-FAMILY: = "Times New Roman", Times, serif } .tit-tendencias { FONT-WEIGHT: bold; FONT-SIZE: 140%; LINE-HEIGHT: 100%; FONT-FAMILY: = "Times New Roman", Times, serif } .tit-rev-opi { FONT-WEIGHT: bold; FONT-SIZE: 105%; LINE-HEIGHT: 100%; FONT-FAMILY: = "Times New Roman", Times, serif } .tit-semana { FONT-SIZE: 11px; VERTICAL-ALIGN: middle; TEXT-TRANSFORM: uppercase; = FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif; = LETTER-SPACING: -1px } .txt-antevisao { FONT-SIZE: 16px; LINE-HEIGHT: 11px; FONT-FAMILY: "Times New Roman", = Times, serif } .antetit-primeira-momentos { FONT-WEIGHT: bold; FONT-SIZE: 10px; TEXT-TRANSFORM: uppercase; = LINE-HEIGHT: 10px; FONT-FAMILY: "Times New Roman", Times, serif } .antetit-art-momentos { FONT-WEIGHT: bold; FONT-SIZE: 13px; TEXT-TRANSFORM: uppercase; = LINE-HEIGHT: 13px; FONT-FAMILY: "Times New Roman", Times, serif } .antetit-revista { FONT-SIZE: 75%; TEXT-TRANSFORM: uppercase; COLOR: #933d00; LINE-HEIGHT: = 140%; FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif } .antetitgr-revista { FONT-SIZE: 90%; TEXT-TRANSFORM: uppercase; COLOR: #933d00; LINE-HEIGHT: = 140%; FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif } .postitulo-revista { FONT-WEIGHT: bold; FONT-SIZE: 110%; COLOR: #999999; LINE-HEIGHT: 140%; = FONT-FAMILY: "Times New Roman", Times, serif } .assi-rev-opiniao { FONT-SIZE: 16px; LINE-HEIGHT: 11px; FONT-FAMILY: "Times New Roman", = Times, serif } .assi-revista { FONT-WEIGHT: bold; FONT-SIZE: 60%; LINE-HEIGHT: 11px; FONT-FAMILY: = verdana, Arial, Helvetica, Sans-serif } .barra-semana { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #003366 } .destaque-opiniao-rev { FONT-WEIGHT: bold; FONT-SIZE: 11px; COLOR: #cc6600; LINE-HEIGHT: 13px; = FONT-FAMILY: Arial, Helvetica, sans-serif } .dias-antevisao { FONT-WEIGHT: bold; FONT-SIZE: 10px; FONT-FAMILY: "Times New Roman", = Times, serif } .dias-antevisao-primeira-letra { FONT-WEIGHT: bold; FONT-SIZE: 16px; FONT-FAMILY: "Times New Roman", = Times, serif } .entrada-revista { FONT-SIZE: 14px; LINE-HEIGHT: 15px; FONT-FAMILY: Arial, Helvetica, = Sans-serif } .legenda-revista { FONT-WEIGHT: bold; FONT-SIZE: 9px; COLOR: #cc6600; LINE-HEIGHT: 10px; = FONT-FAMILY: Verdana, Arial, Helvetica, sans-serif } .link-rev { COLOR: #cc6600; TEXT-DECORATION: none } .link-rev:hover { COLOR: #cc6600; TEXT-DECORATION: underline } .numero-antevisao { FONT-SIZE: 50px; COLOR: #cc6600; LINE-HEIGHT: 40px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -3px } .pratos-ementa { FONT-WEIGHT: bold; FONT-SIZE: 12px; COLOR: #999999; LINE-HEIGHT: 12px; = FONT-FAMILY: "Times New Roman", Times, serif } .semana-antevisao { FONT-SIZE: 10px; COLOR: #ffffff; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #cc6600 } .bar-opiniao { FONT-SIZE: 11px; COLOR: #ffffff; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #336699 } .antetit-opiniao { FONT-SIZE: 10px; COLOR: #003366; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .tit-opiniao { FONT-SIZE: 18px; COLOR: #666633; LINE-HEIGHT: 18px; FONT-STYLE: italic; = FONT-FAMILY: "Times New Roman", Times, serif } .destaque-opiniao { FONT-WEIGHT: bold; FONT-SIZE: 12px; COLOR: #003366; LINE-HEIGHT: 14px; = FONT-FAMILY: Arial, Helvetica, sans-serif } .orelha-opiniao { FONT-SIZE: 10px; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .assi-opiniao { FONT-SIZE: 11px; LINE-HEIGHT: 9px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .orelha-pais { FONT-SIZE: 100%; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; BACKGROUND-COLOR: #336699 } .tit-semana-pais { FONT-SIZE: 16px; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif; LETTER-SPACING: -1px } .orelha-economia { FONT-SIZE: 100%; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; BACKGROUND-COLOR: #336699 } .legenda-sobdesc { FONT-SIZE: 9px; COLOR: #000000; LINE-HEIGHT: 9px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif } .subirdescer { FONT-SIZE: 17px; COLOR: #003366; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px } .orelha-inter { FONT-SIZE: 105%; COLOR: #003366; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .orel-intern { FONT-SIZE: 10px; COLOR: #003366; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .assi-vidas { FONT-SIZE: 11px; VERTICAL-ALIGN: middle; FONT-FAMILY: "Arial Black", = Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px } .barra-vidas { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #990066 } .barra-vidas-assinatura { FONT-SIZE: 11px; COLOR: #000000; LINE-HEIGHT: 16px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #eaeaea } .barra-vidas-opiniao { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #666666 } .entrada-vidas { FONT-SIZE: 15px; LINE-HEIGHT: 11pt; FONT-FAMILY: Arial, Helvetica, = sans-serif } .orel-vidas { FONT-SIZE: 12px; COLOR: #006699; LINE-HEIGHT: 10px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, sans-serif } .tit-breves-vidas { FONT-SIZE: 11px; LINE-HEIGHT: 13px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, sans-serif; LETTER-SPACING: -1px } .tit-gente-vidas { FONT-WEIGHT: bold; FONT-SIZE: 16px; LINE-HEIGHT: 12px; FONT-FAMILY: = Arial, Helvetica, sans-serif } .tit-caixa-vidas { FONT-SIZE: 12px; TEXT-TRANSFORM: uppercase; LINE-HEIGHT: 16px; = FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif } .tit-orel-vidas { FONT-SIZE: 12px; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .titulo-vidas { FONT-SIZE: 24px; LINE-HEIGHT: 20px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .orelha-cartaz { FONT-SIZE: 10px; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .antetit-cartaz { FONT-SIZE: 12px; TEXT-TRANSFORM: uppercase; COLOR: #336699; = LINE-HEIGHT: 10px; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif } .assi-cartaz { FONT-SIZE: 11px; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .bar-seccao-cartaz { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #003366 } .entrada-cartaz { FONT-SIZE: 14px; LINE-HEIGHT: 15px; FONT-FAMILY: Arial, Helvetica, = Sans-serif } .tit-evento-cartaz { FONT-SIZE: 11px; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: 0px } .tit-evento-assinatura-cartaz { FONT-SIZE: 10px; LINE-HEIGHT: 10px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .legenda-cartaz { FONT-WEIGHT: bold; FONT-SIZE: 11px; LINE-HEIGHT: 12px; FONT-FAMILY: = Arial, Helvetica, sans-serif } .orel-cartaz { FONT-SIZE: 10px; COLOR: #ffffff; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .thead-cartaz { FONT-SIZE: 10px; COLOR: #ffffff; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .texto-caixas-cartaz { FONT-SIZE: 10px; FONT-FAMILY: Arial, Helvetica, sans-serif } .tit-cartaz { FONT-SIZE: 24px; LINE-HEIGHT: 20px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .tit-cartaz-arti { FONT-SIZE: 28px; LINE-HEIGHT: 22px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .tit-cartaz-class { FONT-SIZE: 11px; FONT-FAMILY: "Arial Black", Arial, Helvetica, = Sans-serif; LETTER-SPACING: -1px } .caixa-pesquisa { FONT-SIZE: 11px; VERTICAL-ALIGN: middle; LINE-HEIGHT: 11pt; = FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif; = LETTER-SPACING: -1px } .ablack-9-9 { FONT-SIZE: 9px; COLOR: #000000; LINE-HEIGHT: 9px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif } .ablack-10-b2 { FONT-SIZE: 10px; COLOR: #003366; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .arial-10-10 { FONT-SIZE: 10px; LINE-HEIGHT: 10px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .arial-11-11 { FONT-SIZE: 12px; LINE-HEIGHT: 12px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .arial-24-20 { FONT-SIZE: 24px; LINE-HEIGHT: 20px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .ablack-9-9-w-k { FONT-SIZE: 9px; COLOR: #ffffff; LINE-HEIGHT: 9px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #000000 } .ablack-10-b { FONT-SIZE: 10px; COLOR: #336699; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .ablack-10-w { FONT-SIZE: 10px; COLOR: #ffffff; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .ablack-10-10-r { FONT-SIZE: 10px; COLOR: #cc0033; LINE-HEIGHT: 10px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif } .ablack-10-11-w-b { FONT-SIZE: 10px; COLOR: #ffffff; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; BACKGROUND-COLOR: #003366 } .ablack-11-9-1 { FONT-SIZE: 11px; VERTICAL-ALIGN: middle; FONT-FAMILY: "Arial Black", = Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px } .ablack-11-11-1 { FONT-SIZE: 11px; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif; LETTER-SPACING: -1px } .ablack-11-11-1-gy { FONT-SIZE: 11px; COLOR: #999999; LINE-HEIGHT: 11px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px } .ablack-11-10-b { FONT-SIZE: 11px; COLOR: #003366; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial = Black", Arial, Helvetica, sans-serif } .ablack-12-10 { FONT-SIZE: 12px; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .ablack-12-10-b { FONT-SIZE: 12px; COLOR: #003366; LINE-HEIGHT: 10pt; FONT-FAMILY: "Arial = Black", Arial, Helvetica, sans-serif } .ablack-12-16-caps { FONT-SIZE: 12px; TEXT-TRANSFORM: uppercase; LINE-HEIGHT: 16px; = FONT-FAMILY: "Arial Black", Arial, Helvetica, Sans-serif } .ablack-15-15-1-w { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 15px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px } .ablack-12-12-1-w-b { FONT-SIZE: 12px; COLOR: #ffffff; LINE-HEIGHT: 15px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: 1px; = BACKGROUND-COLOR: #003366 } .ablack-15-15-1-w-b { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 17px; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif; LETTER-SPACING: -1px; = BACKGROUND-COLOR: #003366 } .ablack-50-40 { FONT-SIZE: 50px; LINE-HEIGHT: 40px; FONT-FAMILY: "Arial Black", Arial, = Helvetica, Sans-serif } .times-10-10 { FONT-SIZE: 10px; LINE-HEIGHT: 10px; FONT-FAMILY: "Times New Roman", = Times, serif } .times-b-10-10-caps { FONT-WEIGHT: bold; FONT-SIZE: 10pt; TEXT-TRANSFORM: uppercase; = LINE-HEIGHT: 10px; FONT-FAMILY: "Times New Roman", Times, serif } .times-b-12-10 { FONT-WEIGHT: bold; FONT-SIZE: 12px; LINE-HEIGHT: 10px; FONT-FAMILY: = "Times New Roman", Times, serif } .times-b-12-12-b { FONT-WEIGHT: bold; FONT-SIZE: 12px; COLOR: #336699; LINE-HEIGHT: 12px; = FONT-FAMILY: "Times New Roman", Times, serif } .times-b-12-12-gy { FONT-WEIGHT: bold; FONT-SIZE: 12px; COLOR: #999999; LINE-HEIGHT: 12px; = FONT-FAMILY: "Times New Roman", Times, serif } .times-13-13 { FONT-SIZE: 13px; LINE-HEIGHT: 13px; FONT-FAMILY: "Times New Roman", = Times, serif } .times-b-13-13-caps { FONT-WEIGHT: bold; FONT-SIZE: 13px; TEXT-TRANSFORM: uppercase; = LINE-HEIGHT: 13px; FONT-FAMILY: "Times New Roman", Times, serif } .arial-15-15 { FONT-SIZE: 15px; LINE-HEIGHT: 15px; FONT-FAMILY: Arial, Helvetica, = sans-serif } .arial-15-15-w-b { FONT-SIZE: 15px; COLOR: #ffffff; LINE-HEIGHT: 15px; FONT-FAMILY: Arial, = Helvetica, sans-serif; BACKGROUND-COLOR: #336699 } .times-16-11 { FONT-SIZE: 16px; LINE-HEIGHT: 11px; FONT-FAMILY: "Times New Roman", = Times, serif } .times-b-17-13 { FONT-WEIGHT: bold; FONT-SIZE: 17px; LINE-HEIGHT: 13px; FONT-FAMILY: = "Times New Roman", Times, serif } .times-18-12-w { FONT-SIZE: 18px; COLOR: #ffffff; LINE-HEIGHT: 12px; FONT-FAMILY: "Times = New Roman", Times, serif } .times-24-16-w { FONT-SIZE: 24px; COLOR: #ffffff; LINE-HEIGHT: 16px; FONT-FAMILY: "Times = New Roman", Times, serif } .times-28-28 { FONT-SIZE: 28px; LINE-HEIGHT: 28px; FONT-FAMILY: "Times New Roman", = Times, serif } .times-36-36 { FONT-SIZE: 36px; LINE-HEIGHT: 36px; FONT-FAMILY: "Times New Roman", = Times, serif } .times-i-12-12 { FONT-SIZE: 12px; LINE-HEIGHT: 12px; FONT-STYLE: italic; FONT-FAMILY: = "Times New Roman", Times, serif } .abril-high { FONT-SIZE: 75%; COLOR: #933d00; LINE-HEIGHT: 140%; FONT-FAMILY: "Arial = Black", Arial, Helvetica, Sans-serif } .abril-link { FONT-SIZE: 75%; COLOR: #003366; LINE-HEIGHT: 140%; 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