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 n1 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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LectureNote15-ModularArithmetic-1 - I NTRO . TO N UMBER T...

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