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1. For 10,000 bit non-negative integers, give an estimate of the following.

1a) The maximum and minimum value of such a number.



1b) The running time of finding gcd's and modular inverses, in terms of the 
    number of arithmetic operations.



1c) The running time of factoring such a number using trial division, in terms 
    of the number of arithmetic operations.




1d) The running time of multiplying two such numbers using "grade school"
    multiply, in terms of the number of bit operations or machine 
    instructions.




1e) The running time of multiplying two such numbers using Karatsuba 
    multiplication, in terms of the number of bit operations or machine
    instructions.






2. Given the number n = 15, list the numbers which have multiplicative
   inverses mod n.





3. Let p and q be two large primes used to generate a key in the RSA algorithm.

3a) List how the following are determined based on p and q.
    n


    e


    d



3b) Given n and e, how would an adversary try to determine d?  And about how 
    long would this take, as a function of n?