# Polyalphabetic Cipher Exercise by Royalist Minister Edward Nicholas

## Variant Vigenere Cipher (Beaufort Cipher)

Egerton MS 2550 includes many cipher keys related to Edward Nicholas, secretary of state for Charles I and Charles II. Among them, Eg. MS 2550 f.39 shows experimenting with a polyalphabetic cipher, i.e., a variant of the Vigenere cipher also known as the Beaufort cipher. A printed Vigenere table (with a 24-letter alphabet without J and U) is in f.86.

### Vigenere (C=P+K)

At the top of f.39 is written the following:

robe rt usrobertu sro
This is midsummer day
mxly bn hywhqrezf xsn
bsfn

The first line repeats the keyword ROBERTUS. The second line is the plaintext.

The third line is a ciphertext obtained through the ordinary Vigenere cipher scheme: C=P+K, where C is ciphertext, P is plaintext, and K is the keyword. In non-mathematical terms, this corresponds to finding a column headed by a plaintext letter (e.g., "T") on the top row, finding a row headed by a keyword letter (e.g., "R"), and identifying a cipher letter (e.g., "M") at the intersection of the row and the column. (There seem to be enciphering errors for the plaintext I and R in MIDSOMMER. The first can be explained if the enciphering was based on the spelling "mEdsommer.")

### C=P-K

The fourth line is (the beginning of) another ciphertext obtained through C=P-K. (The third character "f" seems to be an error for "g.")

But these two ciphertexts are struck out.

### Beaufort (C=K-P)

In the middle of the sheet is written the following:

robe rt usrobertu sro
This is midsummer day
xfrl ha hinumreoc oqp

This ciphertext can be obtained by another variant of the Vigenere cipher: C=K-P. Compared with the common Vigenere cipher: C=P+K, this switches the roles of ciphertext and key. So, in non-mathematical terms, this corresponds to finding a column headed by a plaintext letter (e.g., "T") on the top row, finding a cell matching the key letter ("R") in that column, and reading off the leftmost letter ("X") of the row to which the cell belongs. This corresponds to what is called the Beaufort cipher. (Alternatively, since this changes the sign of P, we may regard it as the Vigenere cipher with a reversed alphabet.)

This appears to be the adopted scheme. The next example can be explained with the same scheme.

rob ertu srob ertusro
God saue King Charles
kzx lqyp hhat biscgmu

This is accompanied by an explanatory note to the effect that "G" is enciphered by the key "R" as "K" and deciphering "K" by "R" gives "G".

One more example is given in the same scheme.

robe rtus rob ertu
when will you come
ufwq ukig szf bcgp

### Assessment

It is apparent that portions of f.39 were written at different times. I think at least the main part of the above was written by Nicholas (A specimen of Nicholas' original letter is found in Add MS 18982, f.48 (BL. I hope someone can verify the handwriting.). F.39 is endorsed "New cipher", and this appears to correspond to the entry "7 New Cypher enclosing expenditure" on the "List of Ciphers from West Horseley" (f.26) (Nicholas spent his last years in the manor of West Horsley in Surrey. The reciprocal cipher described in the next section may correspond to "8 My Cypher with the application Lord Jermyn sent by S.Y.C[S.F.C.?]" in the list, which, however, is an inference solely based on the ordering of items, which is not always regular.). It is yet to be found out how and when Nicholas learned of polyalphabetic ciphers.

On the other hand, the printed Vigenere table on f.86 may have been an insertion at a later period.

Another polyalphabetic table (not Vigenere) possibly from the same period is described in another article.

## Reciprocal Substitution Cipher (Pairing-based Cipher)

In the bottom half of f.39, another scheme (not polyalphabetic) is demonstrated.

bouchardinef
gklmpqstwxyz
Write these le[tter]s one for another[,] as g for b and b for g, &[?] for nulls[,] make figures or suuni[?] & capitall le[tter]s, & words as and[,] the[,] w^th[,] w^ch.
Example
gy RE wxkmyxd 3. qr tklyr
be    inocent    as doves
& the better to obscure[?] this[,] write your[?] letter[?] in french, or Spanishe & that w^ch is in this cipher with in Englishe.

This presents the 24 letters of the alphabet in two rows. It starts with a keyword "Bouchardine", followed by the letters not occurring in the keyword in the regular alphabetical order up to "wxyz."

The two rows make 12 pairs of letters, and the letters of each pair is enciphered into each other. For example, "B" is enciphered as "G" and "G" is enciphered as "B". It is prescribed that figures and capital letters are nulls.

And in order to better confuse codebreakers, it is advised to write the cleartext in French or Spanish, and use English for enciphered text.

## References

CrypTool-Online (Vigenere, Beaufort) ... On this site, you can adapt the alphabet to the 24-letter alphabet without J and U. In order to try different schemes such as C=P+K, C=P-K, C=K-P, I used Microsoft Excel (private filename: EgertonMS2550.xlsx).

Inventory of Egerton MS 2550 (CSV) (This may include many transcription errors.)

### DECRYPT Project

Egerton MS f.39 is no.3077 of the DECODE Database maintained by the DECRYPT Project. The "list" at f.26 is no.3067. The Vigenere table at f.86 is no.3105.

Megyesi Beáta, Esslinger Bernhard, Fornés Alicia, Kopal Nils, Láng Benedek, Lasry George, Leeuw Karl de, Pettersson Eva, Wacker Arno, Waldispühl Michelle. Decryption of historical manuscripts: the DECRYPT project. CRYPTOLOGIA 44 : 6 pp. 545-559. , 15 p. (2020) [link]

Megyesi, B., Blomqvist, N., and Pettersson, E. (2019) The DECODE Database: Collection of Historical Ciphers and Keys. In Proceedings of the 2nd International Conference on Historical Cryptology. HistoCrypt 2019, June 23-25, 2019, Mons, Belgium. NEALT Proceedings Series 37, Linköping Electronic Press. [pdf]