Straddling checkerboard
Encyclopedia
In cryptography
, a straddling checkerboard is a device for converting an alphabet
ic plaintext
into digits
whilst simultaneously achieving fractionation (a simple form of information diffusion) and data compression
relative to other schemes using digits. It also is known as a monôme-binôme cipher.
A straddling checkerboard is set up something like this:
The first row is populated with the ten digits, 0-9. They can be presented in order, as in the above table, or scrambled for additional security. The second row is typically set up with high-frequency letters (mnemonic ESTONIA-R), leaving two blank spots. It has no row label. The remaining rows are labeled with each digit that was not assigned a letter in the second row, and then filled out with the rest of the alphabet.
Much like the ordering of the digits in the top row, the alphabet can be presented in order (as it is here), or scrambled with a keyword or other technique. Since there are 30 slots in our grid, and we skipped two letters in the first row, there will be two spare cells in the other rows. We have filled these cells with a period '.', and a slash '/' to be used as a numeric escape character
(indicating that a numeral follows). It doesn't matter where these spares go, so long as the sender and receiver use the same system.
To encipher, a letter in the second row is simply replaced by the number labeling its column. Letters in the third and fourth rows are replaced by a two-digit number representing their row and column numbers. Mapping one-digit numbers to common letters reduces the length of the ciphertext, while also concealing the identities of the two-digit numbers by reducing the frequency of their first digits. Here is an example:
The resulting message, 3113212731223655, may be sent directly (if the table is scrambled), but is usually processed through a second cipher stage, such as transposition
or substitution
. As a simple example, we will add a secret key number (say, 0452) using modular (non-carrying) arithmetic
:
Optionally, we could then use the same straddling checkerboard to convert the ciphertext
back into letters:
Deciphering is simply the reverse of these processes. Although the size of groups can vary, deciphering is unambiguous because whenever the next element to be deciphered starts with a 2 or a 6, it is a pair; otherwise, it is a singleton.
Ciphers that use a straddling checkerboard include the VIC cipher
and SECOM.
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
, a straddling checkerboard is a device for converting an alphabet
Alphabet
An alphabet is a standard set of letters—basic written symbols or graphemes—each of which represents a phoneme in a spoken language, either as it exists now or as it was in the past. There are other systems, such as logographies, in which each character represents a word, morpheme, or semantic...
ic plaintext
Plaintext
In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....
into digits
Numerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...
whilst simultaneously achieving fractionation (a simple form of information diffusion) and data compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
relative to other schemes using digits. It also is known as a monôme-binôme cipher.
A straddling checkerboard is set up something like this:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| E | T | A | O | N | R | I | S | |||
| 2 | B | C | D | F | G | H | J | K | L | M |
| 6 | P | Q | / | U | V | W | X | Y | Z | . |
The first row is populated with the ten digits, 0-9. They can be presented in order, as in the above table, or scrambled for additional security. The second row is typically set up with high-frequency letters (mnemonic ESTONIA-R), leaving two blank spots. It has no row label. The remaining rows are labeled with each digit that was not assigned a letter in the second row, and then filled out with the rest of the alphabet.
Much like the ordering of the digits in the top row, the alphabet can be presented in order (as it is here), or scrambled with a keyword or other technique. Since there are 30 slots in our grid, and we skipped two letters in the first row, there will be two spare cells in the other rows. We have filled these cells with a period '.', and a slash '/' to be used as a numeric escape character
Escape character
In computing and telecommunication, an escape character is a character which invokes an alternative interpretation on subsequent characters in a character sequence. An escape character is a particular case of metacharacters...
(indicating that a numeral follows). It doesn't matter where these spares go, so long as the sender and receiver use the same system.
To encipher, a letter in the second row is simply replaced by the number labeling its column. Letters in the third and fourth rows are replaced by a two-digit number representing their row and column numbers. Mapping one-digit numbers to common letters reduces the length of the ciphertext, while also concealing the identities of the two-digit numbers by reducing the frequency of their first digits. Here is an example:
| A | T | T | A | C | K | A | T | D | A | W | N |
| 3 | 1 | 1 | 3 | 21 | 27 | 3 | 1 | 22 | 3 | 65 | 5 |
The resulting message, 3113212731223655, may be sent directly (if the table is scrambled), but is usually processed through a second cipher stage, such as transposition
Transposition cipher
In cryptography, a transposition cipher is a method of encryption by which the positions held by units of plaintext are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed...
or substitution
Substitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
. As a simple example, we will add a secret key number (say, 0452) using modular (non-carrying) arithmetic
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....
:
| 3 | 1 | 1 | 3 | 2 | 1 | 2 | 7 | 3 | 1 | 2 | 2 | 3 | 6 | 5 | 5 | |
| + | 0 | 4 | 5 | 2 | 0 | 4 | 5 | 2 | 0 | 4 | 5 | 2 | 0 | 4 | 5 | 2 |
| = | 3 | 5 | 6 | 5 | 2 | 5 | 7 | 9 | 3 | 5 | 7 | 4 | 3 | 0 | 0 | 7 |
Optionally, we could then use the same straddling checkerboard to convert the ciphertext
Ciphertext
In cryptography, ciphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher...
back into letters:
| 3 | 5 | 65 | 25 | 7 | 9 | 3 | 5 | 7 | 4 | 3 | 0 | 0 | 7 |
| A | N | W | H | R | S | A | N | R | O | A | E | E | R |
Deciphering is simply the reverse of these processes. Although the size of groups can vary, deciphering is unambiguous because whenever the next element to be deciphered starts with a 2 or a 6, it is a pair; otherwise, it is a singleton.
Ciphers that use a straddling checkerboard include the VIC cipher
VIC cipher
The VIC cipher was a pencil and paper cipher used by the Soviet spy Reino Häyhänen, codenamed "VICTOR".It was arguably the most complex hand-operated cipher ever seen, when it was first discovered...
and SECOM.