EXPRESSO: Revista - Qualidade de Vida

From: Subject: EXPRESSO: Revista - Qualidade de Vida Date: Sat, 18 Jan 2003 00:54:51 -0000 MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_000_02A1_01C2BE8C.34E4BD60"; type="text/html" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 This is a multi-part message in MIME format. ------=_NextPart_000_02A1_01C2BE8C.34E4BD60 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://segundasedicoes.expresso.pt/revista/qualidade/interior.asp?edicao=1508&id_artigo=ES36772 EXPRESSO: Revista - Qualidade de Vida

	EXPRESSO = ONLINE

REGISTO

1=AA&= nbsp;P=C1GINA

REVIST= A

OPINI=C3= O

PA=CDS

ECONO= MIA

= INTERNACIONAL

DESPO= RTO

VIDAS

CARTAZ<= /A>

PESQU= ISA

F=D3RUNS

PUBLICA=C7=D5ES

GUIAS

DOSSIERS

=CDNDIC= E

EDI=C7= =D5ES

CO= MENT=C1RIOS

=20

22/9/2001

Alice e Bob =

A = comunica=E7=E3o atrav=E9s=20 da Internet baseia-se em processos de codifica=E7=E3o que = asseguram a=20 privacidade das mensagens. A matem=E1tica garante que isso = =E9 poss=EDvel=20 sem que os intervenientes tenham de acordar numa chave = secreta=20 comum.

Texto de Nuno = Crato
Ilustra=E7=F5es de Fernando Guerreiro = Martins

Alice e Bob vivem=20 isolados e apenas podem comunicar atrav=E9s do correio. Mas = sabem que=20 o carteiro lhes l=EA todas as cartas. Alice tem uma mensagem = para Bob=20 e n=E3o quer que ela seja lida. Que =E9 que pode fazer? J=E1 = pensou em=20 fazer-lhe chegar um cofre com a mensagem, fechado a cadeado. = Mas=20 como lhe far=E1 chegar a chave? N=E3o pode enviar-lha dentro = do cofre,=20 pois assim Bob n=E3o o poder=E1 abrir. Depois de muito = pensar, tem uma=20 ideia. Envia-lhe o cofre fechado com um cadeado. Sabe que = Bob =E9=20 esperto e acabar=E1 por perceber a sua ideia.

Com mais umas voltas do correio e sem nunca = terem=20 trocado chaves, a mensagem chega ao destinat=E1rio, que abre = o cofre e=20 a l=EA. Como =E9 que o leitor acha que resolveram o = problema? Se gosta=20 de desafios l=F3gicos, pare aqui e pense um bocado.

=C9 simples... depois de ser descoberto. Bob = recebe o=20 cofre e fecha-o com um outro cadeado, de que tem a chave. = Devolve o=20 cofre a Alice por correio, desta vez fechado com os dois = cadeados.=20 Esta remove o seu cadeado, utilizando a chave em seu poder, = e faz=20 seguir de novo o cofre por correio. Bob, quando o recebe, = apenas tem=20 que utilizar a chave do seu cadeado para abrir o cofre e ler = a=20 mensagem. O carteiro fica a ver navios. Esta hist=F3ria = relata um=20 velho quebra-cabe=E7as e uma das suas solu=E7=F5es. E = inspirou tr=EAs jovens=20 norte-americanos, Whitefield Diffie, Martin Hellman e Ralph = Merkle,=20 a construir em 1976 um sistema de criptografia em que o = segredo da=20 comunica=E7=E3o =E9 assegurado por duas chaves, que os = intervenientes n=E3o=20 trocam entre si. Foi esta inven=E7=E3o que inspirou o = sistema RSA,=20 discutido na =ABRevista=BB de 8 de Setembro.

Alice e Bob s=E3o=20 personagens fict=EDcios, mas s=E3o nomes sistematicamente = utilizados=20 pelos especialistas de criptografia. =C9 mais colorido do = que falar=20 apenas no emissor e receptor, ou apenas em A e B. = Junta-se-lhes=20 habitualmente uma terceira personagem, representada na nossa = hist=F3ria pelo carteiro, que costuma receber o nome de Eva = - =ABEve=BB,=20 em ingl=EAs - e que representa aquela que se p=F5e =E0 = escuta - ou seja,=20 aquela que =ABeavesdrop=BB.

At=E9 =E0 descoberta de Diffie, Hellman e = Merkle, a=20 comunica=E7=E3o de mensagens cifradas exigia a troca da = chave da cifra.=20 Era preciso que Alice e Bob se encontrassem previamente e = acertassem=20 numa chave que apenas eles dois conhecessem. S=F3 isso lhes=20 permitiria, posteriormente, trocar mensagens =E0 dist=E2ncia = sem que=20 Eva, sempre =E0 escuta, conseguisse perceb=EA-las. Assim = funcionaram as=20 mensagens secretas desde os tempos de C=E9sar at=E9 aos = tempos modernos,=20 assim funcionaram espi=F5es, governos, generais, = conspiradores e=20 simples amantes. A chave poderia ser simples, mas era sempre = necess=E1rio que Alice e Bob acordassem =E0 partida todo o = processo de=20 codifica=E7=E3o e descodifica=E7=E3o das mensagens. = Habitualmente, toda a=20 informa=E7=E3o pode ser resumida num n=FAmero, possivelmente = muito grande,=20 pelo que se pode admitir que a chave consiste apenas nesse = tal=20 n=FAmero.

A ideia de Diffie, Hellman e Merkle =E9 pois = revolucion=E1ria. Segundo o esquema que propuseram, Alice e = Bob=20 come=E7am por acordar em dois n=FAmeros. E estes podem ser = p=FAblicos,=20 pois mesmo que Eva os consiga descobrir n=E3o poder=E1 vir a = conhecer a=20 chave. Cada um deles escolhe um outro n=FAmero, que mant=E9m = secreto.=20 Feitas algumas contas, ambos chegam a um mesmo resultado: um = n=FAmero=20 que mais ningu=E9m conhece e que ser=E1 a chave de = codifica=E7=E3o das suas=20 mensagens. O processo que inventaram =E9 relativamente = simples, embora=20 muito engenhoso, e encontra-se brevemente descrito na caixa = que=20 acompanha este texto. Tudo se passa de forma parecida com a = da=20 hist=F3ria dos dois cadeados. As chaves n=E3o s=E3o = trocadas, mas cada um=20 acaba por poder abrir o cofre, sem que o carteiro, Eva, o=20 consiga.

Numa analogia=20 feliz, Simon Singh, no seu livro =ABThe Code Book=BB, a que = j=E1 nos=20 referimos no =FAltimo artigo nesta =ABRevista=BB, diz que = tudo se passa=20 como se Alice e Bob quisessem criar uma tinta secreta, sem = que=20 ningu=E9m conhe=E7a todos os seus ingredientes. Come=E7a-se = por escolher=20 uma cor determinada e cada um leva um litro dessa cor numa = lata. Em=20 casa, Alice adiciona-lhe um litro de uma cor secreta, que = n=E3o revela=20 a ningu=E9m, nem mesmo ao parceiro. Bob faz o mesmo. Trocam = depois as=20 duas latas com as misturas, pouco lhes importando que Eva as = observe. Cada um leva para casa a lata com os dois litros de = tinta=20 que resultou da adi=E7=E3o da cor secreta do outro. = Novamente em casa,=20 Alice adiciona um litro da sua cor secreta =E0 lata que Bob = lhe deu.=20 Fica assim com tr=EAs litros de tinta: um ter=E7o da cor = original comum,=20 um ter=E7o da cor secreta de Bob e um ter=E7o da sua cor = secreta. Bob,=20 em casa, faz o mesmo com a lata que Alice lhe deu. O = resultado =E9 o=20 mesmo que Alice obteve, pois as componentes de cor s=E3o as = mesmas.=20 Nenhum revelou ao outro a sua cor secreta, mas ambos = acabaram com a=20 mesma cor final, sem que ningu=E9m, nem mesmo Eva, sempre = =E0 espreita e=20 conhecedora das tintas trocadas, a conseguisse = descobrir.

Nos sistemas de codifica=E7=E3o n=E3o = existem tintas, mas=20 sim n=FAmeros e a aplica=E7=E3o engenhosa de um ramo da = Matem=E1tica=20 conhecido por teoria dos n=FAmeros. Sem os avan=E7os de = criptografia n=E3o=20 seria poss=EDvel que o com=E9rcio e a comunica=E7=E3o pela = Internet fossem=20 t=E3o seguros como o s=E3o.


	O nascimento das chaves = p=FAblicas

O processo inventado por Diffie, = Hellman e=20 Merkle marca o nascimento da criptografia com chaves = p=FAblicas,=20 que funcionam em conjunto com chaves secretas que = nunca s=E3o=20 trocadas. Baseia-se na aritm=E9tica modular, que = consiste,=20 essencialmente, em trabalhar com os restos da = divis=E3o inteira=20 por um n=FAmero determinado, chamado m=F3dulo. O = melhor exemplo =E9=20 dado por um rel=F3gio. Se a dado momento o rel=F3gio = marcar 10h,=20 cinco horas depois que horas marca? O resultado, = obviamente, =E9=20 3h, o que equivale ao resto da divis=E3o inteira de = 10+5=3D15 por=20 12. Em matem=E1tica escreve-se 10+5=3D3 (mod 12), pois = 15=3D3 no=20 m=F3dulo de congru=EAncia 12 dos rel=F3gios = anal=F3gicos comuns. Com=20 essa nota=E7=E3o descrevemos abaixo o processo seguido = por Alice e=20 Bob, seguindo de perto um exemplo fornecido por Simon = Singh.=20 Os nossos dois amigos conseguem acordar numa chave=20 criptogr=E1fica comum sem nunca a trocarem em pessoa e = sem mais=20 ningu=E9m a poder conhecer.

COMENT=C1RIOS (1)

	ANTERIOR	TOPO
1=AA P=C1GINA REVISTA OPINI=C3O PA=CDS ECONOMIA <= SPAN=20 class=3Dablack-11-10-b>INTERNACIONAL DESPORTO VIDAS CARTAZ =

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