20140106

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RSA public key encryption

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1. Receiver
   1. Pick very large primes $p$ and $q$ and compute $n=pq$.
   2. Compute the least common multiple of $p-1$ and $q-1$; call it $m$.
   3. Pick $r$ relatively prime to $m$.
   4. Find $s$ such that $rs \text{ mod } m =1$.
   5. Publicly announce $n$ and $r$.
2. Sender
   1. Convert the message to strings of digits.
   2. Break up the message into uniform blocks of digits; call them $M_1$, $M_2$, $\ldots$, $M_k$.
   3. Calculate and send $R_i=M_i^k \text{ mod }n$.
3. Receiver
   1. For each received message $R_i$, calculate $R_i^s\text{ mod }n$.
   2. Convert the string of digits back to a string of characters.

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