Download e-book for kindle: Kryptographie in C und C++: Zahlentheoretische Grundlagen, by Michael Welschenbach

By Michael Welschenbach

ISBN-10: 3540644040

ISBN-13: 9783540644040

ISBN-10: 3642979971

ISBN-13: 9783642979972

Das Buch bietet einen umfassenden ?berblick ?ber die Grundlagen moderner kryptographischer Verfahren. Der Autor stellt ausf?hrlich deren programmtechnische Umsetzung dar, indem er ein Programmpaket als leistungsf?hige Erweiterung der Programmiersprachen C und C++ f?r Berechnungen mit gro?en Zahlen entwickelt. Das Buch pr?sentiert Funktionen und Methoden, die hinsichtlich theoretischer Fundierung, Stabilit?t und Performanz professionellen Anspr?chen gen?gen. Deren Anwendung wird an einer objektorientierten Implementierung des RSA-Kryptosystems demonstriert.
Die beiliegende CD-ROM bietet den Leserinnen und Lesern, denen es prim?r um den praktischen Einsatz der Programmfunktionen geht, einen intestine sortierten Baukasten f?r eigene Anwendungen.
Michael Welschenbach, Jahrgang 1956, hat Mathematik an der Universit?t K?ln studiert. Er leitet den Projektbereich Sichere Systeme bei debis Systemhaus info defense providers GmbH in Bonn. Er besch?ftigt sich seit dem Studium mit theoretischen und praktischen Aspekten der Kryptographie; sein besonderes Interesse gilt dabei den Fragen der Implementierung.

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Additional info for Kryptographie in C und C++: Zahlentheoretische Grundlagen, Computer-Arithmetik mit großen Zahlen, kryptographische Tools

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2 Multiplikation msdptra_1 msdptrb_1 29 a_I + *a_l; b_1 + *b_l; Urn etwas Rechenzeit zu sparen, wird anstatt des oben geforderten Initialisierungsschritts das Partialprodukt (b n- 1bn- 2 ... bo)s-ao einer Schleife berechnet und in den Stellen Pn'Pn-l ,. ,Po gespeichert: carry = 0; av = a_l[l); for (bptr_1 = Isdptr_1 (b_l) , pptr_1 bptr_1 <= msdptrb_l; bptr_I++, pptr_I++) *p·ptr_1 *pptr_1 = = (USHORT) (USHORT) (carry = (ULONG) av * (ULONG) * bptr_1 + (ULONG) (USHORT) (carry» BITPERDGT)); (carry» BITPERDGT); Als nachstes folgt die geschachtelte Multiplikationsschleife, beginnend bei der Stelle a_l [2] von a_l: for (csptr_1 = p_1 + 2, aptr_l a_I + 2; aptr_1 <= msdptra_l; csptr_I++, aptr_I++) carry = 0; av = *aptr_l; for (bptr_1 = Isdptr_1 (b_l) , pptr_1 bptr_1 <= msdptrb_l; bptr_I++, pptr_I++) *pptr_1 = (USHORT) (carry = (ULONG) av * (ULONG) * bptr_1 + (ULONG) * pptr_1 + (ULONG) (USHORT) (carry» BITPERDGT)); *pptr_1 = (USHORT) (carry» BITPERDGT); Die groi3tmogliche Lange des Ergebnisses ist die Summe der Stellenzahlen von a_l und b_l.

Hierfiir wird noch einmal auf die Routine ftir kleine Divisoren der Funktion di v _1 () zuriickgegriffen, indem diese nahezu unverandert in eine eigene Funktion verpackt wird. Wir geben daher nur die Schnittstelle der Funktion an: Funktion: Division eines CLINT-Typs durch einen USHORT-Typ Syntax: in t udi v _1 (CLINT dv_1, USHORT uds, CLINT <1-1, CLINT r_1) ; Eingabe: dv_1 (Dividend), uds (Divisor) Ausgabe: <1-1 (Quotient), r_1 (Rest) Riickgabe: 0 falls alles O. K. E_DBZ bei Division durch 0 Es wurde bereits darauf hingewiesen, daB filr eine Berechnung der Quotient einer DivisioJl oftmals nicht ben6tigt wird und es nur auf den Divisionsrest ankommt.

Falls dies so ist, wird u ~ u' + b modulo BIl+l berechnet (Notation wie oben): if (borrow < BASE) carry = 0; for (bptr_l = lsdptr_l (b_l) , rptr_l bptr_l <= msdptrb_l; bptr_l++, rptr_l++) *rptr_l = (USHORT) *rptr_l += (USHORT) (*qptr_l)--; (carry = ((ULONG) (*rptr_l) + (ULONG) (*bptr_l) + (ULONG) (USHORT) (carry» BITPERDGT))); (carry» BITPERDGT); Weitersetzen der Zeiger auf die Stellen des Restes und des Quotienten und zurUck zum Beginn der Hauptschleife: msdptrr_l--; lsdptrr_l--; qptr_l--; 4. Die Grundrechenarten 48 Die Langen des Restes und des Quotienten werden bestimmt.

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Kryptographie in C und C++: Zahlentheoretische Grundlagen, Computer-Arithmetik mit großen Zahlen, kryptographische Tools by Michael Welschenbach


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