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3.6. KOBLITZ’S KID-RSA AND PUBLIC KEY CODES 45
in use today. We will study it in Chapter 12. The Kid-RSA is a Decimation
Cipher with a slightly complicated setup. It offers no actual security, hence it
is a “toy” system, but will allow us to introduce the concept of public keys.
Set-up of Kid-RSA:
1. Choose four integers, calling them a, b, A and B.
2. Compute AB − 1 and call it M.
3. Compute aM + A and bM + B and call them e and d, respectively.
4. Compute (ed − 1)/M and call it n.
Then e and d will serve as the enciphering and deciphering keys in a Decimation
Cipher modulo n.
A couple of examples will help clarify.
Examples:
(1) Suppose we choose a = 5, b = 7, A = 4 and B = 3. Then we compute the
other parameters:
M = AB − 1 = 11
e = aM + A = 59 and d = bM + B = 80, and
n = (ed − 1)/M = (59 · 80 − 1)/11 = 429.
Now we encipher numerical as usual:
plaintext n u m e r i c a l
plainnumbers 14 21 13 5 18 9 3 1 12
×59 826 1239 767 295 1062 531 177 59 708
%429 397 381 338 295 204 102 177 59 279
ciphertext 397 381 338 295 204 102 177 59 279
Because we are working modulo 429 we cannot at this point reduce modulo
26 to retrieve a ciphertext. Instead we simply use the reduced ciphernumbers
as our ciphertext. So numerical is enciphered to 397, 381, 338,
295, 204, 102, 177, 59, 279.
To decipher we multiply by d and reduce modulo 429:
ciphertext 397 381 338 295 204 102 177 59 279
×80 31760 30480 27040 23600 16320 8160 14160 4720 22320
%429 14 21 13 5 18 9 3 1 12
plaintext n u m e r i c a l
So we retrieve our plaintext numerical.