ll caso e lo pseudo-caso nei protocolli di sicurezza online

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/sites/default/files/styles/crop_image_style_16_18/public/2024-11/img_25816.jpg?h=6258bf7a&itok=J0DFHGlm);height:350px;" data-stellar-background-ratio="0.5"> <div class="overlay"></div> <div class="page-title"> <span>5 Novembre, 2024</span> <h2>ll caso e lo pseudo-caso nei protocolli di sicurezza online</h2> <span></span> </div> </div> </div> </section> </div> <div role="main" class="container-fluid pb-4 pt-4 paddding"> <div class="container paddding main-container js-quickedit-main-content "> <div class="row mx-0"> <section class="col-sm-12 col-md-8" class="top-space co-md-8 col-sm-12 animate-box" data-animate-effect="fadeInLeft"> <a id="main-content"></a> <div class="region region-content"> <div data-drupal-messages-fallback class="hidden"></div> <div id="fh5co-single-content" class="container-fluid pb-4 pt-4 paddding"> <p><strong>Pubblichiamo l'intervento del professor Stefano Marmi sull'ultimo numero di <a href="https://www.exlmagazine.it/">Exl</a>, il magazine edito dall'Unione Industriale Pisana a cui collaborano alcuni degli enti di ricerca e culturali di Pisa. </strong></p> <p> </p> <p><span><span><strong>di Stefano Marmi*</strong></span></span></p> <p> </p> <p><span><span>“Il mondo è governato dal caso. La casualità ci perseguita ogni giorno della nostra vita.” Così scrive lo scrittore Paul Auster, e certamente il caso gioca un ruolo fondamentale nel mondo digitale. Crittografia, algoritmi, simulazioni: tutte queste tecnologie si affidano alla casualità per funzionare correttamente. Ma cosa intendiamo esattamente per “caso”? E come possiamo distinguere tra casualità vera e propria e “pseudo-casualità”, ovvero un’apparenza di caso generata da processi deterministici?</span></span></p> <p><span><span>Immaginiamo il lancio di una moneta: un atto semplice che incarna l’idea di caso. La probabilità di ottenere testa o croce è del 50%, a patto che la moneta non sia truccata e che ogni lancio sia indipendente dagli altri. Ma questa casualità “perfetta” è davvero raggiungibile o si tratta di un’astrazione matematica? </span></span></p> <p><span><span>La risposta, sorprendentemente, dipende dall’osservatore. Un computer dotato di sensori sofisticati e di una potenza di calcolo illimitata potrebbe prevedere con certezza l’esito di un lancio di moneta. Conoscendo “esattamente” la velocità, la direzione e il momento angolare della moneta è possibile risolvere le equazioni deterministiche che governano la meccanica del sistema. Per un osservatore umano, invece, il lancio resta imprevedibile, un perfetto esempio di casualità.</span></span></p> <p><span><span>I matematici e gli informatici misurano la casualità quantificando la capacità di un osservatore di discernere tra essa e un processo deterministico. Un fenomeno è “pseudo-casuale” se appare inscindibile dal caso per un osservatore con capacità computazionali limitate.</span></span></p> <p><span><span>Questo concetto ha rivoluzionato la crittografia moderna. I protocolli di sicurezza online si basano su chiavi generate pseudo-casualmente, impossibili da prevedere per un attaccante, benché siano generate da algoritmi deterministici. La sicurezza di questi sistemi dipende dalla difficoltà computazionale nel distinguere queste chiavi pseudo-casuali da chiavi veramente casuali.</span></span></p> <p><span><span>Un esempio paradigmatico di stringa “pseudo-casuale” è la sequenza delle cifre decimali di pi greco: una successione deterministica che si ritiene esibisca proprietà statistiche simili a quelle di una sequenza casuale. Terence Tao, uno dei più brillanti matematici contemporanei, sostiene che il caso, in senso stretto, non esista in matematica e quello che spesso percepiamo come caso sia in realtà “pseudo-caso”. </span></span></p> <p><span><span>La principale motivazione e giustificazione per l’uso del caso nel calcolo è forse che la casualità esiste in natura, e quindi è possibile campionare fenomeni naturali e così costruire delle sorgenti di caso che possono essere impiegate nelle applicazioni. Tuttavia, esiste una discrepanza tra il tipo di input casuale richiesto quando progettiamo algoritmi e protocolli randomizzati e il tipo di dati casuali che possono essere trovati in natura. Un problema naturale e ampiamente studiato è il problema della costruzione di estrattori di casualità. L’introduzione di computer quantistici promette notevoli passi avanti in questa competizione tra ordine e caso.</span></span></p> <p><span><span>La distinzione pseudo-caso e caso è un viaggio alla scoperta dei confini tra ordine e caos, tra determinismo e imprevedibilità. La scienza, guidata dalla curiosità e dalla creatività, continua a esplorarla, e a innovare le tecnologie che impiegano il caso.</span></span></p> <p> </p> <p><span><span><strong><span><span>*Stefano Marmi</span></span></strong><span><span>, professore ordinario di Fisica matematica alla Scuola Normale Superiore. Con Marco Malvaldi è autore di <em>Caos. Raccontare la matematica</em>, edito da Il Mulino (2019).</span></span></span></span></p> <p> </p> </div> <section class="views-element-container block block-views block-views-blocknews-video-block-1 clearfix" id="block-views-block-news-video-block-1"> <div class="form-group"><div class="pb-4 view view-news-video view-id-news_video view-display-id-block_1 js-view-dom-id-3d6e5b9c0a84fea785ee208939b3ea7e7c0c548eb9d998799052e27fc0c50d66"> <div class="view-content"> <div class="container animate-box fadeInUp animated-fast"> <div> <div class="fh5co_heading fh5co_heading_border_bottom py-2 mb-4">Galleria video e immagini</div> </div> <div class="owl-carousel owl-theme owl-loaded owl-drag" id="slider2"> <a href="https://normalenews.sns.it/sites/default/files/2024-11/maxresdefault.jpg" title="Stefano Marmi" data-colorbox-gallery="gallery-news-10100-48TBFapFYB4" class="colorbox" data-cbox-img-attrs="{"alt":"Stefano Marmi"}"><img 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