Exercise Set 5:
Public-key Cryptography Die-Hellman and RSA
Math 414, Winter 2010, University of Washington
Due Friday, February 12, 2010
1. You and Nikita wish to agree on a secret key using the Die-Hellman
key exchange. Nikita announces that p = 3793 an
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Exercise Set 2 Solutions:
More Prime Numbers
Math 414, Winter 2010, University of Washington
Due Friday (!), January 22, 2010
1. If f (x) and g (x) are (nonzero) functions, we write f (x) g (x) to mean
that limx f (x)/g (x) = 1. Prove that for any real nu
Exercise Set 1:
Prime Numbers
Math 414, Winter 2010, University of Washington
Due Wednesday, January 13, 2010
1. Compute gcd(2010, 1235) by hand.
Answer: 5
2. Use the prime sieve describe in the book to nd all primes up to 100.
Answer: [2, 3, 5, 7, 11, 13
Exercise Set 6:
Quadratic Reciprocity
Math 414, Winter 2010, University of Washington
Due Wednesday, February 17, 2010
This homework assignment is purposely short because you also will have
a take-home midterm this coming weekend.
1. Let p = 7 be an odd p
Exercise Set 4:
Applications of the Integers Modulo n
Math 414, Winter 2010, University of Washington
Due Friday, February 5, 2010
1. Let a, m, n be random integers with about 10000 digits each. How
long does it take Sage to compute am (mod n)? What if th
Exercise Set 3:
Integers Modulo n
Math 414, Winter 2010, University of Washington
Due Wednesday, January 27, 2010
1. Let n be a positive integer and let
P = cfw_a : 1 a n and gcd(a, n) = 1.
Is it necessarily the case that
a 1
(mod n)?
aP
Answer: Nope. E.g