From bb41c02d7fc788d1ecd322ed50a206fd7f00da7a Mon Sep 17 00:00:00 2001 From: Peter Gerwinski <peter.gerwinski@hs-bochum.de> Date: Thu, 19 May 2022 13:31:46 +0200 Subject: [PATCH] Tafelbilder und Aufgabe 19.5.2022 --- 20220519/ad-202200519.txt | 85 +++++++++++++++++++++++++ 20220519/mathe-20220519-01-ringe.png | Bin 0 -> 157134 bytes 20220519/mathe-20220519-02-ringe.png | Bin 0 -> 131845 bytes 20220519/mathe-20220519-03-koerper.png | Bin 0 -> 63699 bytes 20220519/mathe-20220519-04-koerper.png | Bin 0 -> 92091 bytes 20220519/mathe-20220519-05-koerper.png | Bin 0 -> 107686 bytes 20220519/mathe-20220519-06-koerper.png | Bin 0 -> 128741 bytes 20220519/mathe-20220519.xcf.gz | Bin 0 -> 307690 bytes 8 files changed, 85 insertions(+) create mode 100644 20220519/ad-202200519.txt create mode 100644 20220519/mathe-20220519-01-ringe.png create mode 100644 20220519/mathe-20220519-02-ringe.png create mode 100644 20220519/mathe-20220519-03-koerper.png create mode 100644 20220519/mathe-20220519-04-koerper.png create mode 100644 20220519/mathe-20220519-05-koerper.png create mode 100644 20220519/mathe-20220519-06-koerper.png create mode 100644 20220519/mathe-20220519.xcf.gz diff --git a/20220519/ad-202200519.txt b/20220519/ad-202200519.txt new file mode 100644 index 0000000..d143ff0 --- /dev/null +++ b/20220519/ad-202200519.txt @@ -0,0 +1,85 @@ +Aufgabe +======= + +Implementieren Sie einen nichttrivialen Algorithmus +mit großen vorzeichenlosen ganzen Zahlen. + +"groß" = "größer als das, was der Computer normalerweise verarbeiten kann" + +Aufteilung in Teams: + + - Grundrechenarten (einschließlich modulo) mit großen Zahlen + + - Exponentiation modulo p --> Websuche + + - Faktorisierung mittels der Fermat-Methode + +Beispiele: + + - Faktorisierung der 7. Fermatschen Zahl + + - RSA + + - Diffie-Hellman, El-Gamal + + - Elliptische Kurven + +Damit sich die Teams nicht gegenseitig blockieren: + + - "Dummy"-Funktionen für 64-Bit-Zahlen schreiben, + um damit schon mal die Schnittstelle festzulegen. + + - Später dann die Dummy-FUnktionen gegen die richtigen austauschen. + +Beispiel: + + Interface: + + void add (void *s1, void *s2, void *sum) + { + /* egal */ + } + + void init_number (uint64_t x, void *e) + { + /* egal */ + } + + Dummy-Implementierung: + + void add (void *s1, void *s2, void *sum) + { + uint64_t *ps1 = s1; + uint64_t *ps2 = s2; + uint64_t *psum = sum; + *psum = *ps1 + *ps2; + } + + void init_number (uint64_t x, void *e) + { + uint64_t *pe = e; + *pe + x; + } + + Ideen: + + - "Schriftlich" rechnen. + Jede Ziffer ist ein Array-Element, + z.B. eine Ziffer in einem String + oder eine Zahl von 0 bis 999999999 in einer 32-Bit-Zahl + oder eine 32-Bit-Zahl + oder eine 64-Bit-Zahl + ... + + - Dynamische Allozierung des Speichers: + Die 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