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44 CHAPTER 3. THE INTRODUCTION OF NUMBERS
Instead, we need to multiply by the inverse of 7, which from Figure 3.2 is
15.
ciphertext M K C C K F I
ciphernumbers 13 11 3 3 11 6 9
×15 195 165 45 45 165 90 135
%26 13 9 19 19 9 12 5
plaintext m i s s i l e
This works much better. The answer is missile.
(3) Decipher JCPCJS if the enciphering key was k = 9.
(4) Decipher RDYRSCSPQ if enciphering key was k = 19.
(5) Decipher AWVFWYKLC if the enciphering key was k = 11. 11
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄
3.5 Multiplication vs. Addition
We have seen that decimation ciphers cause letters which are adjacent in the
plaintext alphabet to be separated in the ciphertext alphabet. How much does
this improve security
Consider the following ciphertext that was enciphered with a decimation
cipher.
UQESF YFTGW SGPVS PPVQX QEDGR PMQFP YJSFG EORVQ DQBQF PVQWO
MRTQW PUOTT SPPOM QWOFE TIXQS FIMLQ DYJUY FXQDO FCW
It has the letter frequency table
0 1 1 4 4 9 4 0 2 2 0 1 4 0 6 9 13 3 6 5 3 4 5 3 4 0
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
There are no obvious places to fit the aei, no, rst and uvwxyz patterns. Nor,
for that matter, any non-obvious place! Clearly our efforts to construct and
understand the Decimation Ciphers have been fruitful – the techniques that
allow us to decrypt Caesar ciphers no longer suffice.
3.6 Koblitz’s Kid-RSA and Public Key Codes
To demonstrate the powers of the ideas we’ve studied in this chapter we are going
now to explain Neal Koblitz’s toy system, “Kid-RSA”. The RSA cryptosystem,
due to Rivest, Shamir, and Adelman, is one of the most important systems
11 (3) divide, (4) propagate, (5) subjugate.