Dorabella & D'Agapeyeff Ciphers - Solutions

Message Setting and Key Phrase

 

The Dorabella cipher matches (in part) a system described by Helen Fouché Gaines (HFG) - ‘Polyalphabetical Encipherment Applied By Groups’. In the case of Dorabella, the group length is variable but limited to the values 1, 2, or 8 (hereafter referred to as 1s, 2s, 8s). The Running Key segments and the Key Phrase (in 2 parts, CV2 and CV5) are described as Secondary Keys (again, using HFG terminology). In short, these are the variables one would expect to change for each new message to be sent (unlike the Primary Keys CV1/CV6 and CV3/CV4, which would probably be reused over a period of time). To understand how the Key is applied, it’s probably best if we put ourselves in the position of the Intended Recipient (IR) of the message. Let's have a look at the information that needs to be conveyed to the IR, who will be in possession of:

 

The Cipher text (the 87 hoop characters)

The 2 Vigenère tables (Table 1 and Table 2, constructed from the Primary keys)

The Running Key (the 2 segments of running key text used to encipher the message and which will be used to decipher)

The rules governing the running key usage, which appear to be:

• the running key is controlled by a key phrase which will be recognizable to the IR

• the 1st n chars of the Plaintext are also the start of the key phrase and tell the IR how many 8s and 2s (and hence 1s) are used in Part 1

• the 1st n chars of the Plaintext also mark the start letter of each 8 or 2 - the 8s in order L to R followed by the 2s in order L to R (with a rewind being permitted between 8s and 2s) – ie – the start of the key phrase is concealed in the Plain, not once but twice – first, as the indicator at the start of the Plain (as consecutive letters); and again but spread throughout the Plain (bar the 1st letter, which is also the start of the 1st of the 8s)

• the number of 8s and 2s will be equal or differ by a maximum of 1 (apparently)

• any 2s in Part 2 will be spelled out in full in the Plain, marking the end of the key phrase

 

Cipher (Z), Key (K) and Plain (P) chars are referenced in this section, their message positions being given as Z7, K47, P65 etc.

 

The Running Key comprises a total of 48 characters, in 2 sections - RK2 (message part 1)=22 chars and RK5 (message part 2)=26 chars. The IR doesn’t know how many 8s and 2s (and hence 1s) are to be used, nor where the message splits - but can easily work it out, as follows:

 

Knowing that the Key text must expand to match the length of the cipher and plain, the Expansion=87 – (22+26)=39

If any Key letter ‘Kn’ is to be used as an ‘8’, this will expand the Key length by 7 characters; likewise, any 'Kn' as a ‘2’ will mean an expansion of 1.

 

So, ((nr_of_eights) * 7) + ((nr_of_twos) * 1)  =39 and (nr_of_eights) – (nr_of_twos)=(-1 ≤ 0 ≤ 1)

    which gives 5*7 and 4*1, split as 3,2 (three 8s, two 2s) and 2,2 (two 8s, two 2s) - but the IR doesn’t yet know which way round)

 

The encipherer only needs to communicate to the IR (in possession of the Cipher and Keytext but not the Plaintext) the starting letters of the 8s and 2s (in that order) for the 1st part of the message. This is the Message Indicator. Everything can be worked out from this information.