CIS3223 Homwork9 help PDF

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Homework 9 questions to review for the class....

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CIS 3223 Homework 3

Name:

Dr Anthony Hughes

Temple ID (last 4 digits:

1 (3 pts) Let a and b be a units modulo N , and z a zero divisor mod N . (a) Then modulo N , ab is a unit

a zero divisor

neither

(b) Then modulo N , az is a unit

a zero divisor

neither

2 (2 pts) Let N Ø 3 and gcd(17, N ) = 1. If 17N −1 ”© 1(mod N ), then N is not a prime. true

false

undecided

3 (2 pts) Convert (BAD)16 into a decimal integer.

4 (6 pts) Determine the following: (a)

231 (mod 17)

(b)

-55 (mod 17)

(c) φ(143)

(d)

2123 mod 55

5 (5 pts) Use the extended Euclidean algorithm (using matrices) to find integers s and t such that 72s + 11t = gcd(72, 11) (show all steps). a = 72, a

b = 11 b

q

r

Q

72

+11

=

If a and b are two n-bit numbers, what is a good bound for the number of iterations of the loop in the algorithm? O(log n) O(n) O(n log n) O(n2 ) 6 (3 pts). P38 1.2...