LectureNote15-ModularArithmetic-1

# LectureNote15-ModularArithmetic-1 - I NTRO TO N UMBER T...

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Unformatted text preview: I NTRO . TO N UMBER T HEORY P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University – 19 / 93 Modular Arithmetic P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University – 20 / 93 ● Modular Arithmetic is “clock” arithmetic ● Form: a = b mod n (read a congruence b mod n) ✦ says when divided by n, a and b have the same remainder ✦ 100 = 34 mod 11 ✦ –12 mod 7 = –5 mod 7 = 2 mod 7 = 9 mod 7 ● b is called the residue of a mod n ● Can do arithmetic with integers modulo n with all results between 0 and n–1 Some Properties P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University – 21 / 93 ● (a + b) mod n = ((a mod n) + (b mod n)) mod n ● ((a mod n) + (b mod n)) mod n = ((b mod n) + (a mod n)) mod n ● (a × b) mod n = ((a mod n) × (b mod n)) mod n...
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## This note was uploaded on 05/29/2010 for the course CS 556 taught by Professor Staff during the Spring '08 term at Colorado State.

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LectureNote15-ModularArithmetic-1 - I NTRO TO N UMBER T...

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