Crypto-Number-Sheet-bar

The crypto number table is a simple, yet far from trivial cipher. Can you break a cryptogram I have created with this method?

Designing a purely manual cipher (i.e., one that can be computed by hand) has proven a difficult problem. Most designs are either too complicated for practical use or insecure (some are even both). Almost all manual ciphers that were developed in the pre-computer era can be broken today with a computer. Although manual encryption algorithms have lost importance with the advent of cheap computers, they are still an active field of research.

 

The crypto number table

On the website of crypto collector Nick Gessler, …

Nick-Gessler

… who is a professor emeritus at Duke University, I found a very simple manual cipher that looks quite interesting. It is referred to as crypto number table.

Number-Table

It is obvious how this method works. The table contains 100 entries, each one consisting of a letter, a digit, a letter pair (bigram) or a letter triple (trigram). The bigrams and trigrams represent the most frequent ones in the English language. For encryption, each entry is encoded by its line and column number.

For instance, the cleartext TO BE OR NOT TO BE, when written as TO BE OR N O T TO BE, is encrypted as follows:

TO BE OR N  O  T  TO BE
02 24 77 60 63 93 02 24

It is clear that the table can be easily varied by permuting the numbers indicating the line and the column. Here is an example:

Crypto-Number-Table-Varied

In this case, TO BE OR NOT TO BE encrypts to 88 99 17 66 19 21 88 99.

There are, of course, other ways to change the table, but we only consider line and column number permutations. This means that the key can be provided as two numbers, say 7341589260 and 6048321957. Instead of two numbers, two keywords can be used.

A spy using a crypto number table only needs a sheet of paper with the table written on it (as an alternative, he can memorize the table) and two passwords. This looks like a handy, inconspicuous cipher.

I wonder who created the crypto number table and if it was ever used in practice. Nick’s web page doesn’t provide any information. Perhaps, a reader knows the answer. Otherwise, I will ask Nick when I meet him at a conference next time.

Is the crypto number table a secure cipher? I am sure that it can be broken today with Hill Climbing or some other algorithm. Without computer support, it is certainly a lot more difficult.

 

A challenge

Here is a text I have encrypted with the crypto number table above (with permuted line and column numbers)

93 83 03 91 84 92 05 91 83 71 08 51 58 80 83 43 88 66 57 97 55
02 54 00 66 12 10 49 35 65 33 50 07 83 33 84 20 88 10 59 65 65 59 70 92 10 59 59 91 54 83 97 02 52 97
97 07 71 12 16 92 10 57 05 91 83 10 90 83 28 52 91 88 69 49 65 59 64 90 91 83 69 37
00 12 16 91 85 70 81 69 81 50 12 92 70 81 60 10 90 21 59 59 64 90 02 74 52
70 49 65 65 01 83 25 16 83 54 60 74 12 07 71 53 40 92 25 36 13 55 77 16 49 25 16 44 82
62 81 65 16 84 40 92 01 80 70 81 65 55 92 16 84 29 16 40 33 92
29 66 25 16 74 52 70 49 65 65 10 40 31 28 59 72 24 51 83 40 47 10 71 03 92 03
40 93 03 71 25 73 50 02

Can you break this challenge?


Further reading: The low-tech cipher LC4

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Kommentare (13)

  1. #1 Thomas
    1. September 2018

    Klaus:
    This Syllabary cipher was introduced by G-MAN (Robert J Friedman) in the May-June 2012 issue of the Cryptogram magazin, https://sites.google.com/site/bionspot/the-syllabary-cipher

  2. #2 Thomas
    1. September 2018

    Here is a encipher/decipher worksheet (for trial and error): http://bionsgadgets.appspot.com/gadget_forms/syllabary_worksheet.html

  3. #3 Klaus Schmeh
    1. September 2018

    @Thomas: Thanks!

  4. #4 Thomas
    1. September 2018
  5. #5 Thomas
    1. September 2018

    @Klaus

    Are there word spaces in your number cipher? (The are changing distances between consecutive numbers.)

  6. #6 Klaus Schmeh
    1. September 2018

    @Thomas: The distances between the numbers are not relevant. I have corrected this. All distances should be equal now.

  7. #7 Thomas
    1. September 2018

    Some statistics:

    192 numbers in total, 60 different (of 100) numbers used.

    Most frequent numbers:
    83 (11 times)
    65 (10 times)
    16 (9 times)
    92 (9 times)
    10 (8 times)
    59 (8 times)
    91 (7 times).

    double numbers:
    6565 (3 times)
    5959 (2 times)

    patterns:
    74 52 70 49 65 65 (repeated in lines 6 and 8)
    59 65 65 59 70 92 10 59 59 (line 2)

  8. #8 Narga
    1. September 2018

    I quickly wrote a hill climber. It found this:

    START AT THE RESTAURANT NEAR A81 NORTH OF SPRINGFiELD ON ROAD AT 31 FOLLOW THE FOOTPATH SOUTH THROUGH THE FORREST AFTER ABOUT 1
    KiLOMETER TAKE ARIGHT AND WALK ALONG THE WALL AFTER 2OO METERS YOU WiLL REACH A PLAYGROUND IN THE CENTER OF WEHiCH IS A SMALL HAT IN THE REAR WALL OF THE HAT BEHIND THE BENCH YOU WiLL FIND A BOX CONTAINING FURTHER INSTRUCTIONS

  9. #9 Klaus Schmeh
    1. September 2018

    @Narga: Congratulations, this is correct.

  10. #10 Thomas
    1. September 2018

    @Narga
    Good job, congratulations!

  11. #11 Klaus Schmeh
    4. September 2018

    Bart Wenmeckers via Facebook:
    This is definately solvable by hill climbing if the ngram table is know. Ie solve for the keys. But if nothing was known it would be very difficult to solve

  12. #12 Klaus Schmeh
    10. September 2018

    Bart Wenmeckers via Facebook:
    I finally got some time tonight and got this to solve.

    The variable length and high frequency tri-grams in the key table required a slight mod to my scoring / fitness tester module.

    If any one wants to try this in their hill climber i am willing to share my C coder for the init, tweak and decoder for this. Just PM me.

  13. #13 Nils
    13. September 2018

    This method has a very small keyspace, when we know the table and only the X-Y-coordinates are transposed, i.e. are the key.

    The keyspace is, therefore, 10! for X and 10! for Y.
    This is 3,628,800 ^ 2 = 13,168,189,440,000 ~> 43,58.
    Roughly we have to search through 44 bits.

    This can be even attacked by a brute-force attack :-)