roles) || in_array('administrator', $user->roles) || in_array('admin',$user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>

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Problem

This exercise is about the RSA cryptosystem, named after its discoverers Ron Rivest, Adi Shamir, and Leonard Adleman.
Here's how it works: You need two prime numbers $p$ and $q$, compute their product $m = pq$, find a number $b$ that is relatively prime to $\phi(m) = (p-1)(q-1)$, and compute an inverse $c$ of $b$ modulo $\phi(m)$, i.e., $bc \equiv 1 \bmod \phi(m)$.
You keep all of this private except for the numbers $m$ and $b$ which you make public (in particular, your friends know $m$ and $b$). To send you a message $d$, your friend encodes it as
$e = d^b \bmod m \, .$
You can decode your friend's message by computing
$d = e^c \bmod m \, .$
Explain why this decoding works.
What makes this cryptosystem safe? How could you make it safer? What would one need to break it?

Details
Contributer: Matt
Authors
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References
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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