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Any Cryptology/Cryptography experts here?

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Old 12-05-02, 11:26 AM Thread Starter   #1
Patrick G
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Any Cryptology/Cryptography experts here?


I just completed the following worksheet for class, but can someone check my work?

Suppose you want to receive private messages. To set up a public key system, you pick 2 primes p and q and set n=pq. Then you choose a positive integer e relatively prime with phi (n)=(p-1)(q-1). Suppose you choose p=101 and q=29, so n=2929 and phi(n)=2800.

Next you choose e=2291 which is relatively prime to phi(n)=2800. The pair (e,n)=(2291, 2929) is your enciphering key.

You now make public (only) your enciphering key. Of course, p and q need to be much larger in real life, so that n will be hard to factor.

Now suppose I have your enciphering key and decide to send you an encrypted message.

Given the value of n, the block size should be m=2 (2 letters per numerical block).

I use the key to encipher a message as follows.

First I translate to a numerical message.

i f t h i s i s m y m e s s a g e –
0805 1907 0818 0818 1224 1204 1818 0006 1426

Here we have used the translation table:

A b c d e f g and so on…. to z and then –
00 01 02 03 04 05 06 25 26

We added the symbol “-“ since all messages need to have length divisible by m (2 in this case) so we can add a “-“ to make an odd length even.

To encode the first block of message above, I raise 805 to the power e=2291 and take the result mod n=2929 obtaining 1372.

The first couple of blocks of the encrypted example message are 1372 937 2313

Ok, now I am sending you the following message using your enciphering key:

230 1989 362 653 516 1069 2373 571 724 1420



I figured out the above message, but now I am supposed to send back a message of my own using enciphering key: (e,n)=(7, 3131) using block length m=2.

Here’s what I came up with. Can anyone decode it to let me know I did it correctly:

2891 1202 2045 2069 1188 0072 2337 2863 0919 2891 2691 0102 0880 1581 2691 1931 0571
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Old 12-05-02, 11:49 AM   #2
Johnny Knoxville
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is this RSA chryptography?
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Old 12-05-02, 12:07 PM Thread Starter   #3
Patrick G
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Quote:
Originally posted by Johnny Knoxville
is this RSA chryptography?
Yes
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Old 12-05-02, 02:26 PM   #4
Johnny Knoxville
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I did this just last week, but differently, we found the inverse of E using a coprime formula and then used 2 other formulas to encode and decode the message, so i'm not sure
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