From 787b8ff5a657b54e38372c5e08c922fcd828a0b1 Mon Sep 17 00:00:00 2001 From: Ezerous Date: Tue, 18 May 2021 14:38:00 +0300 Subject: [PATCH] feat: init hash functions --- .../2.1.hash-functions.tex | 14 ++++++-------- thesis.pdf | Bin 249915 -> 242951 bytes 2 files changed, 6 insertions(+), 8 deletions(-) diff --git a/chapters/2.theoretical-background/2.1.hash-functions.tex b/chapters/2.theoretical-background/2.1.hash-functions.tex index dec03af..f5a3158 100644 --- a/chapters/2.theoretical-background/2.1.hash-functions.tex +++ b/chapters/2.theoretical-background/2.1.hash-functions.tex @@ -1,18 +1,16 @@ \section{Συναρτήσεις κατακερματισμού} -% Παλιό από Drive -Οι κρυπτογραφικές συναρτήσεις κατακερματισμού (cryptographic hash functions) είναι ειδική κατηγορία συναρτήσεων κατακερματισμού σχεδιασμένες για χρήση στην κρυπτογραφία. Οι συναρτήσεις κατακερματισμού είναι μαθηματικές συναρτήσεις που δέχονται ως είσοδο δεδομένα τυχαίου μεγέθους και επιστρέφουν συμβολοσειρές σταθερού μήκους αναπαράστασης. +Οι \textbf{κρυπτογραφικές συναρτήσεις κατακερματισμού} (cryptographic hash functions) είναι ειδική κατηγορία συναρτήσεων κατακερματισμού σχεδιασμένες για χρήση στην κρυπτογραφία. Αποτελούν μαθηματικές συναρτήσεις που δέχονται ως είσοδο δεδομένα τυχαίου μεγέθους και επιστρέφουν συμβολοσειρές σταθερού μήκους. % TODO: insert diagram -Οι τιμές που επιστρέφει η συνάρτηση κατακερματισμού ονομάζονται τιμές κατακερματισμού (hash values ή πιο απλά hashes). Μια ιδανική κρυπτογραφική συνάρτηση κατακερματισμού έχει τις εξής βασικές ιδιότητες: +Οι τιμές που επιστρέφει η συνάρτηση κατακερματισμού ονομάζονται τιμές κατακερματισμού (hash values, digests ή απλά hashes). Μία ιδανική κρυπτογραφική συνάρτηση κατακερματισμού έχει τις εξής βασικές ιδιότητες: \begin{itemize} - \item Είναι ντετερμινιστική, έτσι η ίδια είσοδος παράγει πάντα την ίδια έξοδο. - \item Ο υπολογισμός των hashes για οποιοδήποτε μήνυμα είναι γρήγορος. - \item Δεν είναι εφικτό να βρεις την είσοδο από το hash, παρά μόνο δοκιμάζοντας όλα τα πιθανά μηνύματα. - \item Μία μικρή αλλαγή στο μήνυμα επιφέρει τόσο μεγάλες αλλαγές στο νέο παραγόμενο hash ώστε να φαίνεται ασυσχέτιστο με το παλιό. - \item Δεν είναι εφικτό να βρεθούν δύο διαφορετικές είσοδοι που δίνουν το ίδιο hash. + \item Είναι ντετερμινιστική, δηλαδή η ίδια είσοδος παράγει πάντα την ίδια έξοδο. + \item Είναι μη αντιστρέψιμη, δηλαδή είναι πρακτικά ανέφικτο να υπολογιστεί η είσοδος δεδομένης μιας εξόδου. + \item Είναι αμφιμονοσήμαντη (1-1), δηλαδή σε δύο διαφορετικές εισόδους αντιστοιχούν πάντα δύο εντελώς διαφορετικές έξοδοι. + \item Είναι αποδοτική, δηλαδή ο υπολογισμός του hash οποιασδήποτε εισόδου είναι γρήγορος. \end{itemize} 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