The class is on an archeological expedition. Each person goes to a different part of a large country where 5 different dialects were spoken. Each person unearths an ancient clay tablet with numbers engraved on it which tell why this civilization thought their culture would last for centuries. Decipher the encoded message and send it to me via email along with the values of n and r.
I will give you the code for the first two statements. Christy will get the code for the third message from Greg, Greg will get the code for the fourth from Christina. And Christina will get the code for the fifth statement from Christy. You need to supply the person you are giving the code to with a value for n and r (as well as me).
So your email to me should contain three statements about
the civilization.
To translate to and from letters here is a handy table.
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Instructions:
| To decode a message: | To encode a message: |
| 1. Choose large primes p and q | 1. Translate letters to numbers denoted L. |
| 2. Calculate n = pq. Publish n, but keep p and q secret. | 2. Look up the values of r and n in the published directory. |
| 3. Calculate m where m = lcm ( p-1, q-1 ) | 3. Find c = Lr (mod n) |
| 4. Choose r so that the gcd (r, m) = 1. Publish r. | 4. Send values of c to the recipient who knows p and q. |
| 5. Find s such that rs = 1 (mod m). Keep s secret. | |
| 6. Receive each number denoted c | |
| 7. Find L = cs (mod n) | |
| 8. Translate to letters |
Here are the first two coded messages. Since
you are receivers and receivers know p and q, the value of m is given.
1. If n=667, r=9, m =616
529 149 1 288 149 169 149 1 340 149 660 362 418, 90 635 603
1 107 107 288 149 562 562 209 183 149.
529 149 288 149 562 169 149 340 603 635 362 288 90 149 209 107 653 512 635 288 562
1 90 13 418 635 183 149
107 635 13.
2. If n=589, r=7, m=540
215 377 377 1 514 312 377 1 582 514 312 161 166 582 582 180,
473 474 289 580 1 474 289 582 180 161 474 166 289 514, 21 377 121 377 514 1 128 582 377 38
1 174 481 121 474 1 289 174 38, 174 488 580 377 1 514.