Cryptology Through History and Inquiry

“There are extant likewise some letters from him to Cicero and others to his friends concerning his domestic affairs in which if there was occasion for secrecy he wrote in cyphers, that is he used the alphabet in such a manner that not a single ward could be made out. The way to decipher those epistles was to substitute the fourth for the first letter as d for a and so for the other letters respectively.” [15, p. 37]

“When he had occasion to write in cypher he put b for a, c for b [and] so forth and instead of z, aa.” [15, p. 134]

Schottus demonstrates, (though the calculation in his book be not exact) that a thousand million of men in as many years could not write down all those different transpositions of the alphabet, granting every one should complete forty pages a day, and every page contain forty several positions: For if one writer in one day write forty pages, everyone containing forty combinations, 40 multiplied by 40, gives 1,600, the number he completes in one day, which multiplied by 366, the number (and more) of days in a year; a writer in one year shall compass 585,600 distinct rows. Therefore in a thousand million of years he could write

\begin{equation*} 585,600,000,000,000, \end{equation*}

which being multiplied by 1,000,000,000, the number of writers supposed, the product will be

\begin{equation*} 585,600,000,000,000,000,000,000, \end{equation*}

which wants of the number of combinations no less than

\begin{equation*} 348,484,017,332,394,393,600,000. \end{equation*}

[4, pages 5-6]

"5. On the replacement of letters using the decimally-weighted numerical alphabet:

• By substituting decimal numerical alphabet for letters in four different ways: by writing the numbers in words as pronounced; or by finger-bending, using the fingers to communicate the message visually to a recipient; or by writing the numbers as numerals such as writing (mhmd: forty, eight, forty, four); or by giving the cryptogram a semblance of a page of a financial register.
• By recovering the cryptogram numeral into a number of letters - a method of encipherment which involves more sophistication. There are many combinations that can be used in this method; for example in (mhmd: jl, fb, jl, ca) or (kk, ga, kk, bb) . One can even form delusive words such as (mhmd: lead, cad, deal, baa), or substitute two words for a letter, e.g. (ali: \(\overline{dig\ fad}\text{,}\) \(\overline{cab\ ab}\)), in which case a line is to be drawn over two words to denote that they represent one letter.
• By multiplying the number representing the letter by two, and so write (mhmd: q, jf, q, h) and (ali: ob, jh), etc; or multiply it by three, thus writing (mhmd: sk, kd, sk, jb) and (ali: rc, kg). Numbers can also be multiplied by four or five." ¹ [12, vol. 3, pp. 69-70]

The examples here are very loosely based on the Arabic examples in the translation. The "mhmd" is Mohamed since Arabic is written without vowels, and for "ali" the a and l together are treated as a single letter.