An unbreakable book cipher? In a recent press interview, a former terrorist of the 1970s described the cipher his group used to communicate. He claimed that method was unbreakable and I wonder if cryptographers today would agree. Here is how it functionned:


Take two identical books (same edition): one for the sender, one for the recipient.
Each sign - one could include spaces between words as signs - is encoded as follows: 



  (page number) (line number) (number of character on the line) (random
  number)



additions, subtractions, multiplications or divisions of certain agreed value in a certain order are then applied. For example, 357 could mean: 



  (page number*3) (line number -5) (character number +7)



This means that negative values can be created, especially if the
substraction value is in the double digits


A software script for such a cipher would be I think relatively easy to design. Also, the agreed values of the operations in step 2 can be changed anytime so the same base text can be reused.

Bottom line, it means for example a single 7-letter word would produce a string of 28 numbers, of various lenghts and some negative values or decimals or fractions perhaps - depending on what values are used for the operations.

what is your opinion on this method?
Book ciphers are well understood and this seems like a fairly minor variation. Following Kerchoff's Principle we separate the key being the book and the arithmetic operator and numbers and the rest. Picking a random number for fourth position makes no difference in this regard. But even if we let that be a secret to it makes little difference. Humans are lousy at picking random numbers and this will be apparent.

Multuplying by a constant is also a really bad idea. It will be very quickly apparent all numbers in a certain position are a multiple of constant and will be devided by it.

Subtracting or adding a number from row or character number will also be apparent after collecting sufficient data by observing the skewed range. such an addition will be slightly harder regarding page number due to higher cardinality of page numbers but won't necessarily be an issue see next.

Humans doing a poor job picking random numbers. Many people who use book ciphers flip forward a bit from where they are or start reading from the start of the page. This means rare letters will require on average more skipping forward leading to some leakage.

Also the book itself may be selected from a limited set of books can make the book itself guessable.  Given a large library of online books brute forcing such a cipher isn't all that difficult.

If you do not want to mark the book making it physically obvious it is a cipher key it is difficult to prevent repetitions when randomly selecting characters.

If the book is considered a secret not chosen from a limited selection available at your local book store for instance and the person using it picks a random starting point in the book for each letter and seeks the next matching one and marks off each used letter to prevent duplicates then it is a fairly secure cipher even without the additions described.

In reality most book ciphers have been and will be broken.