The first two basic tools of cryptography are substitution and transposition, which are covered in chapters 5 through 8. The third fundamental element of cryptography is fractionation. This means breaking the normal units of language, letters, syllables and words into smaller units and operating on those units. The smaller units are commonly bits, decimal digits, hexadecimal digits, or digits in other number bases. This chapter covers fractionation using digits in bases 2, 3, 5, 6, and 16, plus some other forms of fractionation.
Possibly the oldest method for representing letters as smaller units is the Polybius Square, which we saw in section 4.4. Here each letter is represented by two base-5 digits, making 25 possible 2-digit combinations. (The Greeks did not have a representation for 0, so their digits started at 1.)
Here is the Polybius square from section 4.4. Each letter is represented by its coordinates in the square, that is, by its row and column numbers. For example, the letter P is on row 2 in column 5, so it is represented as 25. When needed for clarity this can also be written as 2,5.
