A New Type of Additon

[Gregory Matthews]

During the cold war, Soviet agents encrypted messages in a multi-step process which included adding two lines of number using a specialized type of addition.  I will give an example in which lines 1 & 2 are added together to yield the result in line 3.

1)   45368--81792--67153

2)   25842--53491--71234

3)   60100--34183--38387

Tell me what type of addition is represented above.

NOTE:  In the above, I have three groups of numbers what are not related to any other group.

NOTE:  The above is just one step in a multi-step process of encryption.  The end result consisted of five numbers groups, each of which represented a word.

The basis for the above comes from an article which tells the story of a group of women who broke the Soviet code.

See:

Liza Munday, "Code Name: Venona,"  The Smithsonian, September 2018, pages 30-39.

4)   20526--38301--96929

As an additional clue, line 2 substracted from line 1 yields line 4.

 

[Gregory Matthews]

The answer is:

Nothing is carried over.

 

E.G.  9 + 9 is give the answer of 8, not 18.  In the subtraction example,  3 - 8 is considered to be 13 - 8 with the answer being 5.  In neither case is the "1`" carried over.

The complexity of this process is illustrated by the fact that it required six (6) different steps to encode the message and the same to decode it.  

When the women began the task in early 40s, computers were not available, in any modern sense, and the process was largely discovered by human brain power.  [NOTE:  IBM punch-card machines did provide some early help in identifying similar code numbers in different messages.]

  This program ended in 1980.

During the almost 40 years that this program existed, only a few thousand messages were decoded and those were generally only partially decoded, probably less than 4,000.  Yet, in the early days, during WWII, some 2,500 messages in an average week were    brought to the group for possible decoding.

Despite the limited number of messages decoded, only in part, the U.S. gained important knowledge from the work of those women.  Julius and Ethel Rosenberg, are two who were implicated, along with others.

 

 

 

[Gregory Matthews]

The complexity of the process is illustrated by the following which was directly taken from page 33 of the referenced article.

1)   7934--2157--1139--3872--2166     An alphabetic message is converted to a numbered message.  E.G.  Pilot delivered report about rockets.

2)   79342--15711-39387--2266           This is a conversion into 5-number groups from 4 number groups.

3)   26473--79342--15711--39387--22166    In this step a 5-number group is added to the beginning of one 2.

4)   56328--29731--35682--23798   This is a group of numbers that is added to line 1.

        25660--34442--64969--45854   This is the result of that addition.

5)   UETWZ--UREEO--ZTTTU--ETPEP--TRART   In this step, the set of numbers from line 4 is converted to alphabetic letters..

6)   One 5-letter group and one 5-number group is given to the message which is went to Moscow.  These two groups identify the date the message is sent and provide information needed to decode the message.

7) Moscow receives the message and decodes it into a readable message.   Decoding the message requires a reversal of the steps taken to encode it.  E.G.  Pilot delivered report about rockets.

Any of you want to take up coding and decoding as a hobby?  That hobby exists    today.

By the way, in the beginning of this project, the women were paid $1,800 per year, plus additional pay for Saturday work.   this was twice what one of them had been paid as a teacher.