William Blencowe's "Safest and Most Expeditious" Cipher

William Blencowe was a grandson of the celebrated mathematician and codebreaker, John Wallis (see another article), who taught his skill of deciphering to his grandson. Upon Wallis' death, Blencowe became the first official decipherer of England, and was guaranteed a fixed annual income.

The papers related to Blencowe in Lambeth Palace Library, Gibson Papers M930 (TNA catalogue, Library catalogue) include:

225 Description of a system of cypher entitled 'A method of writing that I count the safest and most expeditious that was euer yet practised when well understood', c.1700. Perhaps by William Blencowe. 5 ff.

The "safest and most expeditious" scheme is a columnar transposition cipher, with the key (the order of columns) hidden by a substitution cipher. An additional twist is in that units of transposition can be bigrams such as fo, la, to, ar, nd, ng, th, tw, and th as well as single letters. In principle, the plaintext can be split into any units. Although the bigrams may mislead codebreakers at first, once transposition is suspected, they would help rather than hinder codebreaking.

Scheme

1. Enciphering the Key

The key (the order of columns), e.g.,

15 12 10 6 1 14 3 8 5 2 7 9 13 4 11 16

is enciphered as

p  m  k f a  o c h e b g i  n d  l  q

with a substitution cipher:

a b c d e f g h i  k  l  m  n  o  p  q  r  s  t  u  w  x  y  z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Nulls may be added at the beginning and the end.

2. Filling a Grid

The plaintext, broken into single letters or bigrams in any way, is written in a grid, from top to bottom and from left to right, as usual. Some columns are reserved and filled with null characters (or bigrams).

A comma is appended to the last letter (or bigram) of a word. This is to help the recipient.

3. Columnar Transposition

Letters/bigrams are transcribed columnwise, from bottom upwards, according to the ordering specified by the key.

The number of lines, which is necessary for the recipient, is written at the bottom. In the example given, "13" is indicated by "(4.1.3.37.)", in which only the middle figures "1" and "3" are significant.

The recipient prepares a grid with a number of lines specified in the ciphertext, and numbers the columns according to the key. The letters/bigrams of the ciphertext is transcribed in the order of columns specified by the key, from bottom upwards.

Dating

The plaintext used as an example is about expected counterattack of James II by landing in Scotland. The situation reminds one of battles during the Nine Years War such as the Battle of the Boyne (1690) and the Battle of La Hogue (1692). Even in 1692, Blencowe was yet only nine years old, but of course, even if this counterattack had been really expected at the time, it would not exclude the possibility that the document was made in later years.

Transcription

A method of writing that I count the safest and most expeditious that was euer yet practiced when well understood.

Theorem

The writing in 34 Columns as within lin[?](16) affords more variety of positions then the number of sands that would make a globe of ten times a greater Diameter then that of our Earth & sea

vid. Tacquel[?]

(1)

Let two men Correspond, and agree to write one to another in 16 Columnes as on the other leaf. and in this order viz 15.12.10.6.1.14.3.8.5.2.7.9.13.4.11.16. And this their key they must place on the top, or at the head of a ruled paper & it will bee convenient to write them in red Ink for distinction. And let them agree that the 3 columnes (15) (8) & (16) bee nulls, & filld up before they begin to write to prevent mistakes.

And let the number of lines whateuer it bee (as they haue occasion) bee markt at the head, or, else at the lower end of the letter. being ye middle figures for ex. if the number of lines exceed not 9, let it bee the two middle figures, that signify.

So then let the number of lines bee (13) & thus express (4.1.3.37.) And one of them writes to his correspondent as on the other side beginning at the lower end of the columnes, & so write upwards.

And they may eith[?] haue printed papers ready ruled, or else they may draw lines by the help of a ruled paper underneath as I haue don, & when they haue read their letters, burn them & to[?] keep no thing ....

(2)

But there are thousand other ways of disguising the key of the cypher. so as if any one take up or find the paper where they are, they can neuer find what it is. which will depend upon euery mans particular fancy.

For example When they haue made an Alphabet of the 24 letters thus

a|b|c|d|e|f|g|h|i| k| l| m| n| o|&

1|2|3|4|5|6|7|8|9|10|11|12|13|14|

p| q| r| s| t| u| w| x| y| z|

15|16|17|18|19|20|21|22|23|24|

Then take the letters answering to the particular numbers of the Key, and keep them apart[?], & when you haue occasion, make a new Alphabet, & you will find by them the numbers, p for (15) m for (12) &c.

p m k f a o c h e b g i n d l q

And if you will bee more secure you may putt 3 (or 4) nulls before and as many at the end, suppose 3. Then

s f m p m k f a o c h e b g i n d l q h p d

And thus I think it impossible to divine that these letters signify the order of Columnes by their respective numbers.

(3)

[The plaintext reads: Sir, I can assure you that King James is got into Scotland with an Army of twenty thousand Irish & there ar twenty thousand Highlanders who ar al papists joyned with him. And they intend to march towards Edenborough the fourteenth of the next month. And they hope in ye meantime that ye French wil be able to land an Army in ye north.]

Hauing filld the Cypher hee dictates to his clerk or secretary, as follows who can neuer know what hee writes. And makes him write just[?] two columnes in a line

One thing is likewise to bee observed that a comma bee at the end of euery word as you write. And the Clerk must otherwise make a prick at euery Letter & begin to write at the bottom & so upwards.

a.c.e.o.t.ds,th.al,th.an,th,es,an,my,be,m.n.t.o.nd,jo.H.sh,y,in.y.

A.w.n,th,e.de.in.pi.sa.I.A.g.su.r.to,ye,ho.e,th.c.wth,de.re,en.t.at,

r.il,ti.A.n.nb.te.sts,nd,ri.rm.ot,re,d,n.m.m.r.ar,nd,ar,ty,us.i.m.c

in,a.e,d,h,ro.to,y.ig.&,of,to,ou,a.b.d.g.f.p,no,n.is,d,a.p,k.

ye,b.th.th.of,u.m.n.hl.th.t.S.t.n.e.ye,xt,u.w.A.ho,en.o.w.Ja.I

th,l.F.pe,n.e,h,hi.rs,ar,ty,la.ki.a.r.in,e.fo.to.m,w.tw.th.nd,ng,Sr,

no.le,at,ey,th.gh,ar.ed,an.e.w.co.h.n,h,a.n.e.E.ey,pa.ou.d,an,is,as.

r.p.m,g.f.c,a.n.do,ll,b.m,d.g.b.d.m,p.q.b,s.r,d.c,a.n

(4.1.3.37.)

[(4) is missing in my copy.]

(5)

His Correspondent who receiues this Letter, finding at the bottom 4.1.3.37. knows that its written in 13 Lines. And by his key knows the order of Columnes. And therefore draws his Lines, as beneath, and marks the Columne with red Ink, and then begins with the first & 2d Columne to inscribe, till hee has filld the Figure, onely where there is a prick, hee need make nothing, bec: the Letter is confined in a square, and the Commas will help him to read it the easier, because they terminat each word. And the 15th 8th & 16th Columnes hee needs not inscribe, being nulls.

And when hee has filld all the columnes hee may read the Letter with pleasure.

Here the Clerk may dictat, & the Correspond^s inscribe, and when hee has filld it, it will bee pleasant to find it right.