1.  <b>k-server password manager</b>.
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a) I would like to store my password on a cloud server (online password manager).
But I don't wish to entrust any single server with my password.
Please devise a scheme such that I can store my password on 
k different servers, 
such that any coalition of k-1 servers learn nothing about my password.
However, I can recover my password by talking to all k servers. 
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b) In general, how can I split a secret amongst k servers, 
such that any coalition of t (t < k) servers 
cannot learn anything about my secret?
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(Assume the servers are honest-but-curious, i.e., they will store data honestly for me, and will not tamper
with the data. However, they may be curious to learn my password) 
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(Hint:  http://en.wikipedia.org/wiki/Shamir's_Secret_Sharing) 
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c) Let's do a concrete example of Shamir Secret Sharing. 
Although in practice, we should use finite field algebra, 
for simplicity, in this problem, we will use standard
integer rings. 

Suppose we have a 3-out-of-5 Shamir Secret Sharing scheme.
Reconstruct the secret from the following 3 shares:
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(1, 9)
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(2, 33) 
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(3, 77)