A New Method of CRYPTOGRAPHY, Humbly presented to The Most SERENE MAJESTY OF CHARLES the II. By SAMVEL MORLAND Knight and Baronet, and one of the Gentlemen of His MAJESTIE'S Privy Chamber in Ordinary. 1666. THE two Correspondents having provided themselves with a sufficient number of printed Papers delineated and shadowed conveniently for the purpose: 1. They must first of all by a mutual consent, complete their Numerical Alphabet and Clavis Vniversalis, in like manner as is done Page 5. placing in the Numerical Alphabet what Letters they please, (some Capital, others small) from an Unite to 34. and transposing the Numbers contained in each Marginal Number of the Clavis Universalis, in any broken Order whatsoever, each of them reserving a Copy. 2. They must agree in what kind of Figure to write to each other; For by those few Schemes, Page 2, & 3. it is evident, that the various Figures, in which any Writing of a considerable length may be inscribed, are very numerous. 3. They are to resolve what Number of Nulls they will either prefix, adjoin, or intermingle with that Writing; and where those Nulls shall be placed. 4. It is necessary to be concluded, whether they will transcribe what they intent to Conceal, in Upright Columns, or else by way of diagonals, or otherwise? as likewise whether the Transcription shall be ascending, descending, Alternate, or Retrograde? An Example or two will clear all Doubts. Let A. and B. be Two Correspondents: 1. Let their Numerical Alphabet, and Clavis Universalis, be the same with that Pag. 5. 2. Let it be agreed between them, to write to each other in a Parallelogram, such as is Pag. 2. Fig. I. 3. Let the Number of Nulls before the Writing be evermore 3, and after the Writing 4. 4. Let the way of Transcription be in Upright Columns, and descending. This done, A. writes to B. the following words: viz. This Way of Writing is of all other the most facile and expeditious, as well to unlock, as to conceal. The Method of Hiding. That is to say, First, He inscribes it in one of the printed Papers delineated and ready for the purpose, as Page 2. Fig. I. only every other Word (or thereabouts) he gins with a Capital Letter, for the ease of B. in Discovering. 2. Then he finds by the small Figures over the Parallelogram, that his Writing has advanced 9 Columns. 3. Therefore he seeks for 9 in the Margin of the Clavis Vniversalis, and in the same Row finds (6, 5, 9, 1, 4, 7, 2, 8, 3.) which he places in the void Squares over the said 9 Columns. 4. This done, he takes the Paper in which he intends to write, and according to the Agreement aforesaid, prefix 3 Nulls, viz. (s t l) After that, to let his Correspondent know, that there are just 9 Columns in the Writing, he puts down (N) which by the Numerical Alphabet signifies 9 and next to that, another (N) to signify that there are just 9 Lines; As likewise the following Letter (d) to notify, that there are 2 Nulls to complete the Figure; and the next Letter to that, viz. (n) that there are 4 Nulls at the latter end. 5. Lastly, He transcribes all the Columns, beginning first with that which is (1,) and to that adjoins the Column over which is (2,) and so to the end; to which he adds 4 Nulls, and sends the Writing to B. thus: s t l N N, d n s t l e l i e c c y g t t s d oh t s l f s e F x s, U oh d W i l M a t l k, c h r f T c e s l oh T W O r a p A n c a n o o n i l A a oh i h t E u oh t p i i a h i d w oh n f o a k. The Method of Discovering. When B. receives this Writing, First of all (according to the aforesaid private Agreement) he cancels 3 Letters at the beginning, and 6 at the latter end, for Nulls; then he finds by the 4th and 5th Letters, viz. (N) and (N) that the Writing is composed of 9 Columns, and does contain 9 horizontal Lines. Therefore he immediately repairs to his Clavis Universalis, and out of that, over the head of 9 Columns of one of his printed Papers (delineated and shadowed for the purpose) he transcribes the following Numbers, viz. (6, 5, 9, 1, 4, 7, 2, 8, 3.) and then, having divided the Writing by a Prick, Line, or any other Mark of Distinction between each 9 Letters, as is hereafter done, he inscribes the first 9 Letters in that Column over which is the Figure (1) and the next 9 Letters in that Column over which is the Figure (2) and so on, till all the Columns be filled and completed; (where is to be noted by the way, that He who writes, if he has written all his mind, and there yet remain any odd blank Squares, he fills them, and those Letters (such as are (p d) in the Example) are always to be Nulls of course.) Which done, the Writing discovers itself to be the very same with that Pag. 2. Fig. I. To which there are also adjoined divers other different Figures, containing the same form of words. *** N N] s t l e l i e c e] y g t s d oh t s l] f s e F x s, V oh d] W i l M a t l k, c] h r f T c e s L oh] T W O r a p A n c] a n o o n i l A a] o i h t E U oh t p] i i a h i d w ● n **** tables of cryptographical transcription Fig. I. 1 2 3 4 5 6 7 8 9 6 5 9 1 4 7 2 8 3 1 T h i s W a y o f 2 W r i t i n g i s 3 O f a l l oh t h e 4 r T h e M oh s t F 5 a c i l a n d E x 6 p e d i t i o u s 7 A s w e l l t o U 8 n l o c k A s t oh 9 c oh n c e a l p d Fig. II. 12 7 8 1 6 2 10 5 9 4 12 11 3 12 T h i s W a y o f W r i t i n g i s O f a l l oh t h e r T h e M oh s t F a c i l & E x p e d i t i o u s A s w e l l t o U n l o c k a s t oh C o n c e a l e Fig. III. 12 7 8 1 6 2 10 5 9 4 12 11 3 12 T h i s W a y o f W r i t i n g i s O f a l l oh t h e r T h e M oh s t F a c i l & E x p e d i t i o u s A s w e l l t o U n l o c k a s t oh C o n c e a l e Fig. IU. 17 11 12 5 1 10 2 8 12 9 13 3 7 17 4 15 6 1 9 T h i s W a y o f W r i t i n g i s O f a l l oh t h e r T h e M oh s t F a c i l & E x p e d i t i o u s A s w e l l t o U n l o c k a s t oh C o n c e a l e p d e Fig. V. 17 1 12 5 1 10 2 8 14 9 13 3 7 17 4 15 6 16 9 T h i s W a y O f W r i t i n g i s O f A l l oh t h e r t h e M o s t F a c i l & E x p e d i t i o u s A s w e l l t o U n l o c k A s t oh c oh n c e a l e p d e Fig. VI 18 13 4 3 12 2 14 15 1 11 10 5 16 6 9 7 8 18 1 9 ● h ● s ● a ● O ● W ● i ● i ● g ● s O ● A ● l ● t ● e ● t ● e ● o ● ● F ● c ● l ● n ● E ● p ● d i ● i ● u ● A ● w ● l ● ● o ● n ● o ● k ● s t ● C ● n ● e ● ● e ● n ● L e ● t ● ● s Fig. VII. 18 13 4 3 12 2 14 15 1 11 10 5 16 6 9 17 8 18 17 9 ● h ● s ● a ● O ● W ● i ● i ● g ● s ● f ● l ● o ● h ● r ● h ● M ● s ● F ● c ● l ● n ● E ● p ● d ● t ● o ● s ● s ● e ● l ● o ● n ● o ● k ● s ● o ● o ● c ● a ● e ● n ● S ● c ● e ● s Fig. VIII. 15 3 10 5 1 8 2 4 9 12 11 7 13 6 10 ● h ● s ● a ● ● f ● r ● t ● ● g ● s ● f ● ● l ● t ● e ● t ● e ● o ● t ● a ● i ● a ● d ● x ● e ● i ● i ● u ● A ● w ● l ● t ● U ● ● o ● k ● s ● o ● o ● c ● ● l ● n ● S ● c ● e ● W ● ● t ● o ● v ● r ● d ● x ● Fig. IX. 15 13 4 3 12 2 14 15 1 11 10 5 8 6 9 7 8 T h i ● ● ● ● ● ● ● ● ● ● ● ● s W a ● ● ● ● ● ● ● ● ● ● ● ● y oh f W r i ● ● ● ● ● ● ● ● ● t i n g i s ● ● ● ● ● ● ● ● ● o f A l l oh t h e ● ● ● ● ● ● r T h e M oh s t F ● ● ● ● ● ● a c i l A n d E x p e d ● ● ● i t i o u s A s w e l l ● ● ● Of all the foregoing Methods, this last is the most intricate, and for aught I know, the most useful and (sure I am) applicable to any Figure whatsoever. Scriptio Cryptographica. State cauti, cras horâ decimâ noctis venient h●stes, ut invadant Urbem diagram of cryptographical pentagons Pentagonum Centrale Pentagonum Simplex diagram of cryptographical hexagons Hexagonum Centrale Hexagonum Simplex diagram of cryptographical heptagons Heptagoni Centralis Heptagonum Simplex Various Methods of Transcribing the Words contained in Fig. I. Pag. 2. The First Method reads and transcribes the Writing (as before, Pag. 1.) in Upright Columns, and descending according to the Numerical Alphabet, and the Clavis Vniversalis. s t l e l i e c c y g t s d oh t s l f s e F x s U oh d W i l M a t l k e h r f T c e s l oh T W O r a p A n c a n o o n i l A a oh i h t E u oh t p i i a h i d w o n The 2d Method reads and transcribes it in Upright Columns, ascending. c c e i l e l t s l s t oh d s t g y d o U s x F e s f e k l t a M l i W o l s e c T f r h c n A p a r O W T a A l i n o o n a p t u E t h i o n o w d i h a i i. The 3d Method reads and transcribes it in Upright Columns, descending and ascending, alternately. c t l e l i e c c l s t oh d s t g y f s e F x s U oh d e k l t a M l i W h r f T c e s l oh c n A p a r O W T a n o o n i l A a p t o u E t h i oh i i a h i d w oh n. The 4th Method reads and transcribes it in Upright Columns, ascending and descending alternately. c c e i l e l t s y g t s d oh t s l d o U s x F e s f W i l M a t l k e oh l s e c T f r h T W O r a p A n c a A l i n o o n a o i h t E u oh t p n oh w d i h a i i. The 5th Method reads and transcribes it in Upright Columns, and descending, (and that in their natural Order, as likewise do all the following Methods!) not respecting the Numerical Alphabet, or Clavis Vniversalis. T W O r a p A n c h r f T c e s l oh i i a h i d w oh n s t l e l i e c c W i l M a t l k e a n o o n i l A a y g t s d oh t s l oh i h t E u oh t p f s c F x s U o d. The 6th Method reads and transcribes it in Upright Columns, ascending. c n A p a r O W T oh l s e c T f r h n oh w d i h a i i c c e i l e l t s e k l t a M l i W a A l i n o o n a l s t oh d s t g y p t o u E t h i oh d o U s x F e s f. The 7th Method reads and transcribes Fig. I. in Diagonal Lines, and descending, beginning with the first Letter [T] in the Dexter Point. T h W i r O s i f r W t a T a a i l h c p y n i e i e A oh g oh M l d s n f i t o a i w l c s h s n t e o o e t d i l c n F E oh l k c x u t A e s oh s a U t l oh p d. The 8th Method reads and transcribes Fig. I. in Diagonal Lines, and ascending, beginning with the the same Letter [T] in the Dexter Point of the Figure. T W h O r i r f i s a T a t W p c h l i a A e i e l n y n s d l M oh g oh c i w i a oh t i f oh oh e t n s h s n c l i d t e c k l oh E F e A t u x a s oh s l t U p oh d. The 9th Method reads and transcribes Fig. I. in Diagonal Lines descending, and ascending alternately, from the same Letter [T.] T h W O r i s i f r a T a t W a i l h c p A e i e l n y o g oh M l d s n c l w i a oh t i f s h s n t e o o n c l i d t e F E oh l k c e A t u x s oh s a l t U oh p d. The 10th Method reads and transcribes Fig. I. in Diagonal Lines, ascending and descending alternately, from the same Letter [T.] T W h i r O r f i s W t a T a p c h l i a y n l e i e A n s d l M oh g oh f i t oh a i w l c oh oh e t n s h s e t d i l c n c k l oh E F x u t A e a s o s U t l p oh d. By these few Methods of transcribing this first Figure, the Ingenious and learned Reader will easily perceive, that it may yet be read and transcribed in a very great number of other different ways and Methods, and that without altering the Transpositions of the 9 Columns. Now, if this first Figure afford such variety of Transcriptions without new Transpositions, the other different Figures afford each of them as many more; And by the Clavis Universalis, Pag. 5. composed from the Table of Permutation, Pag. 7. it is evident, that every such Figure containing but 9 Columns, admits of no less than Three Hundred Sixty two Thousand, eight Hundred and eighty different Transpositions; And others of them, as Fig. VI and VII. containing 18 Columns, admit of Six Thousand four Hundred and two Millions of Millions, of different Transpositions; More by Three Hundred seventy three Thousand, seven Hundred and five Millions; More by Seven Hundred twenty and eight Thousand; And there being in the Writing 81 Letters, they make an Oblong containing 27 Columns and three Lines; And consequently such a Figure will admit of 10888869450418352160768000000 distinct Transpositions. But forasmuch as Examples edify the Reader much better than bare Words, I have in the 6th Page inserted a longer Writing than the former, in a plain Parallelogram, consisting of 34 Upright Columns, and containing 20 Lines, excepting only 2 Nulls at the latter end to complete the Figure. The Words of the Writing are in French, viz. Entre les plus belles & admirables Inventions qu' ait jamais produit l'esprit de l'homme, sans doute que celle des Chyffres n'y tient pas le dernier lien, puisque par son moyen nous travestissons nos pensées, & les desguisons en sort, qu'elles passent inconnuës dans les Pays Ennemis, & sont quelque fois mieux venuës, en Pays de cognoissance, & plus cherement accueillés de nos Amis, habillés à l'estrangere, & dans ce desguisement, que si elles y paroissoiens sans Voile, & à la descowerte. Et veritablement c'est une raison qui la doit faire beaucoup estimer, comme sçauent assez tous ceux qui font profession de gowerner en la Politic, où commander en la Militaire, lesquels seroient en dainger de voir souuent leurs desseins trahis par l'infidelité d'un Messager, & leurs pensées descouuertes par la surprise de leurs Ennemis. tables of cryptographical numerical alphabet The Numerical Alphabet. A B C D E F G H K L M N R S T V W X a b c d e f g h i k m n o p q r 14 28 15 8 34 16 6 27 7 17 5 9 13 29 10 30 1 25 12 18 26 2 24 11 19 22 3 20 31 4 32 21 23 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 W d i n M G K D N T f a R A C F L b g k p h q e X c H B S V m oh r E table of cryptographical key, the clavis universalis CLAVIS UNIVERSALIS. 1 1 2 ● ● 3 1 3 2 4 ● ● ● ● 5 2 5 1 4 3 6 ● ● ● ● ● ● 7 3 7 1 5 2 4 6 8 ● ● ● ● ● ● ● ● 9 6 5 9 1 4 7 2 8 3 10 ● ● ● ● ● ● ● ● ● ● 11 6 1 11 10 3 5 7 2 4 9 8 12 ● ● ● ● ● ● ● ● ● ● ● ● 13 3 10 5 1 8 2 4 9 12 11 7 13 6 14 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 15 8 10 9 1 13 2 12 7 15 11 5 14 6 3 4 16 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 17 11 12 5 1 10 2 8 14 9 13 3 7 17 4 15 6 16 18 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 19 10 1 17 9 7 16 3 11 5 18 15 12 8 2 19 13 14 4 6 20 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 21 9 8 10 6 7 12 5 11 1 18 17 2 21 3 4 16 20 15 14 19 13 22 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 23 18 10 8 6 4 2 11 16 19 17 1 22 5 12 20 13 3 21 7 14 23 15 9 24 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 25 5 25 16 23 1 6 15 14 22 13 4 24 2 7 12 20 3 11 17 21 19 9 10 18 8 26 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 27 27 12 25 11 24 1 5 13 2 23 15 22 14 21 6 10 3 20 4 26 9 7 19 17 8 16 18 28 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 29 17 28 19 18 2 1 27 20 7 8 21 16 3 5 4 15 14 22 6 29 23 11 9 10 24 12 25 26 13 30 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 31 27 26 11 1 10 25 2 9 24 21 22 3 8 23 20 4 12 19 13 5 18 14 6 7 28 17 29 15 16 31 30 32 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 33 3 14 13 16 8 23 9 15 22 1 7 12 24 6 26 2 11 25 21 17 28 4 10 18 27 5 20 30 32 29 19 31 33 34 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Thus is written, what is to be hidden. table of cryptographical transcription 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 6 11 30 17 29 18 3 12 28 39 31 27 2 13 20 32 7 26 14 10 5 25 21 33 1 9 23 15 34 22 4 16 24 8 1 E ● t ● e ● e ● P ● u ● B ● l ● e ● & ● d ● ● ● a ● l ● s ● n ● e ● 1 2 t ● o ● s, ● u ' ● ● ● j ● m ● i ● p ● o ● u ● t ● E ● p ● i ● d ● l' ● 2 3 o ● m ● S ● n ● d ● u ● e ● u ● c ● l ● e ● e ● C ● y ● r ● s ● y ● 3 4 i ● n ● p ● s ● e ● e ● n ● e ● l ● e ● p ● i ● q ● e ● a ● s ● n ● 4 5 o ● e ● n ● u ● T ● a ● e ● t ● s ● o ● s ● ● ● p ● n ● é ● s, ● l ● 5 6 s ● e ● g ● i ● o ● s ● n ● o ● t ● q ● e ● l ● s ● a ● s ● n ● I ● 6 7 c ● n ● u ● s ● a ● ● ● e ● P ● y ● E ● n ● m ● s, ● s ● n ● q ● e ● 7 8 q ● e ● f ● i ● m ● e ● x ● e ● ● ● s ● n ● a ● s ● e ● o ● n ● i ● 8 9 s ● n ● e, ● p ● u ● ● ● e ● ● ● e ● t ● ● ● ● ● i ● l ● e ● d ● N ● 9 10 s ● m ● s, ● a ● i ● l ● e ● a ● e ● t ● a ● g ● r ● & ● a ● s ● e ● 10 11 e ● u ● s ● m ● n ● q ● e ● ● ● l ● e ● y ● a ● o ● s ● o ● e ● t ● 11 12 a ● s ● o ● l ● & ● l ● D ● s ● o ● v ● r ● ● ● t ● e ● i ● a ● l ● 12 13 m ● n ● C ● s ● V ● ● ● a ● s ● n ● u ● L ● ● o i ● f ● i ● e ● e ● 13 14 u ● o ● p ● s ● i ● e ● c ● m ● e ● ç ● u ● r ● A ● s ● z ● o ● s ● 14 15 e ● x ● u ● f ● n ● P ● o ● e ● s ● o ● d ● ● ● u ● e ● n ● r ● n ● 15 16 a ● o ● i ● i ● u ● O ● ● ● m ● a ● d ● r ● n ● ● ● i ● i ● a ● r ● 16 17 L ● s ● u ● l ● S ● r ● i ● n ● e ● D ● ● ● g ● r ● e ● o ● r ● o ● 17 18 u ● n ● l ● u ● s ● e ● s ● i ● s ● r ● h ● s ● a ● l' ● n ● i ● e ● 18 19 i ● é ● U ● M ● s ● a ● e ● & ● e ● r ● P ● n ● é ● s ● e ● c ● u ● 19 20 e ● t ● s ● a ● l ● s ● r ● r ● s ● D ● L ● u ● s ● n ● e ● ï ● d ● 20 Thus, by a bare Transposition (together with a few Nulls,) is hidden, what is above written. a E C q p s s, s i r oh t i A u a r a é s B m e n e n e x e e e D a c oh c i s e r e u ' n s u i s i p a ml s s f i l u M a A s p W X n p E k i n d s s s, n q n d s e a ● o r a r i c i d u e P s e n n c a y r L u d r i h P L E t oh i oh s c q s s e a m u e a L u i e e e p c l s t y u e e l o n e s a e s e s n h T M e n l s oh D S e a C l e, u l u s b s h u e P & d l e i V t s u M D r e E a d l u, n u ' u E A r s e i a n e a a s e n i m e y D o u a A g n e c u P e e t r s a s l s s d s l ● e e t t o q s r e r e a Q i s s s V r s s e i oh f oh e e r, p & oh l e o q E s t t e u u ç oh d D r r D e r ff p s s oh C i d s r a e r l v i D n v e n' o & t u o e c n b B u E i S d oh s r n e, t n s n s c i i V t u ' Q l q t d' e l q a a o u ë o & h e i' e e i t e e n p l t oh D r n n i s l t, à n m t e, e D s a l i u e t oh P e e à i s s m e m n i & r i t e i oh l m a u g a e D n G n g s n u I t e r e e t g s n i t r T e t i f s m l p y e n a s e l & s e f s e i e l' s n e l' y n l I e i N e t l e s n r oh e u d m i d u N l e p c n P t a e e e n i e e s r e i s e, s ë n s l u Q S i n n t u e s a t r u e l u h é u a R r, r ù o s g u P i d e T oh a m u i n & V i n u S s s l e s, S p n g u f e, s, s oh C p u i u l U s t oh m n e e n e n m u s n o x o s n é t u j u e a s s e c l q l e e P O r e a s l s e r i r a n m l' E c oh m s m t n l i r l' s s s e i y e e r E oh t oh L e P s r s i r a é s n o e a oh i i z n i oh n e e p f g. Thus, by the help of the Clavis Universalis, and Numerical Alphabet, a bare Transcription discovers what was hidden. table of cryptographical transcription 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 6 11 30 17 29 18 3 12 28 19 31 27 2 13 20 32 7 26 14 10 5 25 21 33 1 9 23 15 34 22 4 16 24 8 1 E ● t ● e ● e ● P ● u ● B ● l ● e ● & ● d ● i ● a ● l ● s ● n ● e ● 1 2 ● ● o ● s, ● u ' ● i ● j ● m ● i ● p ● o ● u ● t ● E ● p ● i ● d ● l' ● 2 3 o ● m ● S ● n ● d ● u ● e ● u ● c ● l ● e ● e ● C ● y ● r ● s ● y ● 3 4 i ● n ● p ● s ● e ● e ● n ● e ● l ● e ● P ● i ● q ● e ● a ● s ● n ● 4 5 o ● e ● N ● u ● T ● a ● e ● t ● s ● o ● s ● o ● p ● n ● é ● s, ● l ● 5 6 s ● e ● g ● i ● o ● s ● n ● o ● t ● q ● e ● l ● s ● a ● s ● n ● I ● 6 7 c ● n ● u ● s ● a ● s ● e ● P ● y ● E ● n ● m ● s, ● s ● n ● q ● e ● 7 8 q ● e ● f ● i ● m ● e ● x ● e ● u ● s ● n ● a ● s ● e ● n ● n ● i ● 8 9 S ● n ● e, ● p ● u ● c ● e ● e ● e ● t ● c ● u ● i ● l ● e ● d ● N ● 9 10 s ● m ● s, ● a ● i ● l ● e ● à ● e ● t ● a ● g ● r ● & ● a ● s ● e ● 10 11 e ● u ● s ● m ● n ● q ● e ● i ● l ● e ● y ● a ● o ● s ● o ● e ● t ● 11 12 a ● s ● o ● l ● & ● l ● D ● s ● o ● u ● r ● e ● t ● e ● i ● a ● l ● 12 13 m ● n ● C ● s ● V ● e ● a ● s ● n ● u ● L ● D ● i ● f ● i ● e ● e ● 13 14 u ● o ● p ● s ● i ● e ● c ● m ● e ● ç ● u ● n ● A ● s ● z ● o ● s ● 14 15 e ● x ● u ● f ● n ● P ● o ● e ● s ● o ● d ● G ● u ● e ● n ● r ● n ● 15 16 a ● o ● i ● ● ● u ● O ● c ● m ● a ● d ● r ● n ● a ● i ● i ● a ● r ● 16 17 L ● s ● u ● l ● S ● r ● i ● n ● e ● D ● i ● g ● r ● e ● o ● r ● o ● 17 18 u ● n ● l ● u ● s ● e ● s ● i ● s ● r ● h ● s ● a ● l' ● n ● i ● e ● 18 19 i ● é ● U ● M ● s ● a ● e ● & ● e ● r ● P ● n ● é ● s ● e ● c ● u ● 19 20 e ● t ● s ● a ● l ● ● ● r ● r ● s ● D ● L ● u ● s ● u ● e ● ï ● d ● 20 I Am not ignorant that there are some Virtuosos of this Saeculum, who vainly persuade others, and (I believe!) deceive themselves, by pretending that they are able, by I know not what Analytick Art, to unfold all Mysteries of this nature whatsoever, and that no Secret can be made so to wander in any Paper- Labyrinth, But they will find an Ariadnian Clue to trace it in, and fetch it out. I must confess, as to the ordinary Methods of Cryptography, (vulgarly termed Writing in cipher) where they are weakly contrived, or carelessly written, it's very possible, with much pains and industry, to gather the Contents; (I have often done it myself, and seen it done by others!) But where a cipher is dexterously composed, and made use of warily, There let any such Pretender show his ability in making the least discovery,— & erit mihi Magnus Apollo!) In the mean time, if he please, he may contemplate the following Reflections upon the foregoing Method. 1. The foregoing Method is comparatively with others, wonderfully facile and practicable, forasmuch as it requires very little more pains than a double Transcription of the Letter to be written, (which is no more than what all Statesmen do, whether they writ in cipher or no!) And to uncypher or open, one single Transcription does the Business. 2. Let him consider in how many Parallellograms, Triangles, and other mixed Figures, any Writing may be inscribed. 3. The various ways, wind, and turn by which any Writing may be transcribed out of any such Figures. 4. The many places each Line affords for inscribing Nulls, besides the beginning, and latter end; as likewise whole Columns, which may, by a private accord, be reserved. 5. Into how many Millions of Millions, of Millions, of Millions, of Millions, of Millions, of distinct Orders, both the Numerical Alphabet, and Marginal Numbers of the Classis Universalis, may be transposed, as in the following Table; for an Explanation whereof, I refer the Reader to Clavius, Kircherus, and others. tables of various cryptographical permutations A Table of the various Permutations, or Transpositions of 34 different Letters, Numbers, or Things. I 1 TWO 2 III 6 IV 24 V 120 VI 720 VII 5040 VIII 40320 IX 362880 X 3628800 XI 39916800 XII 479001600 XIII 6227020800 XIV 87178291200 XV 1307674368000 XVI 20922789888000 XVII 355687428096000 XVIII 6402373705728000 XIX 121645100408832000 XX 2432902008176640000 XXI 51090942171709440000 XXII 1124000727777607680000 XXIII 25852016738884976640000 XXIV 620448401733239439360000 XXV 15511210043330985984000000 XXVI 403291461126605635584000000 XXVII 10888869450418352160768000000 XXVIII 304888344611713860501504000000 XXIX 8841761993739701954543616000000 XXX 265252859812191058636308480000000 XXXI 8222838654177922817725562880000000 XXXII 263130836933692530167218012160000000 XXXIII 8684967618811853495518194401280000000 XXXIV 295288899039603018847618609643520000000 Learned Tacquet in his Arithmetic, lib. 5. c. 8. affirms, That the Permutations of 24 Letters are so numerous, that a Thousand Millions of able Clerks, in a Thousand Millions of Years, (and that neither sparing Dominicals or Festivals) were not able to transcribe them! And Guldinus asserts, That the Books which might be compiled of the variety of 23 Letters only (accounting 500 Pages, or 1000 Faces to each Volume, and 100 Lines to each Face, and 60 Letters to each Line, and not any two Words in any of those Volumes the same!) would do more than twice cover the whole Superficies of the Earth and Sea. Nay further, he seems to be of opinion, That the Paper of those Volumes, laid singly Sheet by Sheet, would cover the very Firmament. Now, if the Transpositions of 24 Letters be so numerous, what are those of 34 (which are yet of greatest use in this Method)? The last Sum of the foregoing Table is a Number consisting of 39 Places, and that for the bare Transpositions of 34 Letters or Numbers: But when each of those shall come to be altered, intermingled with, and transformed by all the various Figures of Inscription, Methods of Transcription, and Nulls; I am bold to assert, that the Sum. Tot. would be greater than that of Archimedes in his ΨΑΜΜΙΤΗΣ, whereby he would express the Number of Sands, which would do more than fill the cavity of a Sphere equal to the Orb of the Fixed Stars, according to the dimensions of the Celestial Bodies determined by Aristarchus Samius. To apply this more closely to the purpose, suppose the Writing, as it lays hid Page 6. were given to the ablest Cryptograph-Analyst in the World, to open, or Uncypher; and grant that he knew, that it was written according to some of the Rules of the foregoing Method. 1. It is impossible for him to divine the Number of Nulls, or where they are placed. 2. It's as impossible (without being privy to the Numerical Alphabet) to know certainly how many Columns, or how many Lines this Writing consists of, or where those Indicial Letters are placed. 3. Admit he should (which is never to be imagined!) accidentally guests at the Number of Columns, Lines, Nulls, and Indicial Letters; yet still he is to seek in what Figure it is inscribed, that is to say, whether in a Parallelogram, Triangle, Trapezium, Rhomboides, Polygon Simple, Polygon Central, or some other mixed Figure, or Figures? 4. Put case he knew that it was (as it is) in a Parallelogram; He is but little nearer his ends than before, unless he knew whether the Transcription were in Upright Columns, or diagonals? And that Descending, Ascending, or Retrograde? Or whether in Circular, Serpentine, or Horizontal Lines? 5. But imagine he had all these: As likewise that he knew in what Language it were written, (for that also is no small Difficulty!) He has yet another Task, which is, to find out the true Transpositions of these 34 Columns, by often trying, and comparing Columns with Columns; where there are no less than 295288899039603018847618609643519999999 false ways, and but only one, which is exactly true. Now how any Mortal should hope in all his life time, (were he sure to live Quadrillions of Trillions, of Billions of Methusalem's years!) to hit upon so many Heterogeneous Quasita mentioned in the Premises, for which he has in a manner no Data, it cannot enter into my Understanding. And I leave the Ingenious Reader to Judge, whether the rolling of Sicyphus his Stone up the Hill, be not a Labour as likely to succeed as His? But if all this will not satisfy, Then let such a Pretender give me leave to lead him yet a Step further, where he will quickly see, what false footing all his Zetetick and Analytick devices are like to find upon these Steganographical Quicksands: And that it will be as easy for him to discover the way of an Eagle in the Air, and to mark out precisely, where that subtle Element has been divided and closed up again; as to trace a Secret through all the turn, wind, and dark Passages of so many Cryptographical Maeanders, Unless he work (and that most profoundly!) by the Black Art, or else an Angel from Heaven, in kindness, reveal it to him. CRYPTOGRAPHIA CRYPTOGRAPHICA duplex, triplex, quadruplex, etc. in infinitum. LET the Correspondents A. and B. mutually agree, in all Matters of great importance, to write to each other by a Cryptographia Cryptographica Quadrupla, for which they have some private Mark. And suppose A. desire to send B. the following Intelligence: Sir, Look to yourself; for this Night your Person is to be seized, And the Castle to be delivered up to the Enemy by your own Soldiers. 1. It is accorded between them, that whatsoever they writ, must be inscribed in 4 distinct Figures: the first whereof is to be a Rectangle Parallelogram, as Pag. 9 Fig. 1. The 2d Figure a Rhomboides, as Pag. 9 Fig. 2. The 3d a Rectangle Triangle, as Pag. 10. Fig. 3. And the 4th a Trapezium, as Pag. 10. Fig. 4. 2. These 4 Figures are to be inscribed, and read as follows: The First Figure is to be inscribed in Horizontal Lines, and to be read in Upright Columns, and descending (according to the foregoing Precept) by the Numerical Alphabet, and Clavis Universalis. The Second Figure is likewise to be inscribed in Horizontal Lines, and to be read in Upright Columns; that is to say, The first Upright Column of the First Figure, makes the first Horizontal Line of the Second Figure. And so the second Upright Column of the First Figure, makes the second Horizontal Line of the Second Figure; And so all the Columns of the First Figure is to be inscribed into the Second Figure one after the other in their Order. The Third Figure is to be inscribed in Horizontal Lines, that is, The first Upright Column of the Second Figure makes as many, or as few Horizontal Lines of the Third Figure, as it falls out to be longer or shorter, (beginning with the Vertex or Rectangle of the Third Figure.) Thus of (o r n u s e e) the first Letter (o) makes the first Horizontal Line of the Third Figure; and (r n u) make the second; and (see) make a part of the Third, which (i r) the two first Letters of the second Upright Column of the Second Figure make good; And the following Letters (s C D e o o s) make the fourth Horizontal Line; And so on, till the Third Figure be fully completed. But now the Third Figure is to be read, (not in Upright Columns, but) in Diagonal Lines, according to the following Method, That is to say, Beginning with the Diagonal Line (r b e t t n y, etc.) from Numb. (1) under the Hypotenuse of the Figure; And so ascending to the Letter (o) at the Vertex, and from thence descending to (a) which answers to Numb. (2); Then again beginning with the Letters (n n e e t y, etc.) of the Diagonal Line answering to Numb. (3) and ascending to (n) in the Angle, and from thence descending to the Letter (i) which answers to Numb. (4). Then repeating the same Thing from Numb. (5) to Numb. (6), Then from Numb. (7) to Numb. (8); And so on, till the Figure be as it were wound off to nothing. The Fourth and last Figure is to be inscribed in Alternate Diagonals, Thus, namely of the Letters [r b e u t n y s s r oh] of the first Diagonal Line of the third Figure, A. places the first Letter [r] in the Dexter Point of the fourth Figure. Then, leaving the two next Squares void, he fills the third Diagonal with the 3 next Letters [b e u] After which he leaves another Diagonal void, and the fourth Diagonal he fills with the Letters [t n u s s] And so he proceeds, till the whole Writing be inscribed. This done, A. might fill the void Diagonals with Nulls; But supposing him to be in the Enemy's Country, and fearing his Letter may fall into their hands, and he be constrained to open the Writing, he fills the void Diagonals with another Discourse altogether different from the former, viz. Dear Cousin, I do not a little wonder at your long silence, and am exceeding fearful, that some accident has befallen you since your arrival. After which Writing he puts six Nulls [p l s a d d] to fill up all. But of this more at large in the Method of Opening, or Discovering the forementioned Intelligence. 3. This fourth Figure is to be read in Upright Columns, according to the foregoing Method, by the Numerical Alphabet, and Clavis Vniversalis, and so transcribed fairly, as it ought to be sent to B. leaving only room for 13 Letters at the beginning of the second Line. 4. Of the 13 Letters at the beginning of the 2d Line (which are to serve for Indices, or Exponents!) the first three serve to expound the first Inscription or Figure, the three next, the second Figure; the three following serve for the third Figure, and the last three for the fourth: That is to say, The first Letter [T] gives B. to understand, that the first Figure consists of 10 Columns; The next Letter [f], that there are in it just 11 Lines; The third Letter [d], that there are two Nulls to complete the Figure. The fourth, fifth, and sixth Letters [k T s] let B. know, that the second Figure has 20 Columns, 10 Lines, and no Nulls to complete it. For [s] and all other Letters that are not found in the Numerical Alphabet, may be used at pleasure, to signify Negatives; as here [s] signifies that there are no Nulls to complete the second Figure. The seventh, eighth, and ninth signify, that the Base of the third Figure contains 21 Places, the Lines thereof are eleven, and the Nulls to lengthen out the last Line eleven, viz. [s p k m d a s w x n a.] The tenth, eleventh, and twelfth denote, that the Columns of the fourth Figure are 27, the Lines 11, and the Nulls 3. viz. [n f n.] And the thirteenth and last Letter [G] serves to inform B. that there are 6 Nulls at the latter end of the Writing, as A. sends it to him. All which may be seen by the respective Figures, in which are the 4 Transcriptions. tables of cryptographical transcription Fig. I. The First Inscription. 3 7 1 10 6 2 8 9 4 5 11 S i r l oh oh k t oh y o u r S e l f F oh r t h i s n i g h t y o u r P e r s oh n i s t oh b e e s e i z e d A n d t h e C a s t l e t oh b e e D e l i u e r e d u p t oh t h e E n e m y b y y o u r oh w n S o u l d i e r s d e 10 Fig. II. The Second Inscription. 7 11 15 4 17 12 1 6 16 5 20 2 13 10 18 19 9 14 3 8 10 r ● i ● o ● l ● t ● l ● l ● r ● t ● r ● r ● S ● t ● s ● s ● t ● o ● o ● n ● C ● u ● n ● y ● y ● z ● D ● y ● e ● e ● e ● d ● e ● u ● i ● h ● t ● t ● o ● u ● f ● s ● h ● e ● o ● t ● h ● e ● e ● e ● s ● S ● p ● n ● u ● o ● 20 Fig. III. The Third Inscription. 11 o ● n u ● e e i r s C D e oh oh s ● e ● f h p r l t ● z d t e e ● s oh y e ● h e u l l ● E b d oh t s ● y u u t S y e h s e n r e e e p e y r t r oh k F s oh oh t i e d ● d h o u g oh b A oh e m S i l r t n e r i oh i a t l n w d s p k m d a s w x n a 1 4 5 8 9 12 13 16 17 20 21 19 18 15 14 11 10 7 6 3 2 21 Fig. IV. The Fourth Inscription. 11 17 8 16 22 2 12 27 1 21 26 7 13 15 6 18 5 20 14 23 4 25 10 19 24 3 9 11 r D ● a ● s r n s l t y y ● D c r f y A b B ● S s r A e e r n i o o e e y o p n e e t u o c e e S i S i k ● C y n ● t d W l u d c oh e n l i c oh f ● n d v ● o s I r a e oh oh r i e ● d d l ● i l a g c m a k s d s l a n i L oh A ● i s T ● d s l ● e m l p o t i n d n o h n o n p h ● e a l l y F l oh e t n e e n e d r g e a ● n i e o o ● o d t e r C g u a i F f t T t o n r u o o s e A e s e m t e r s ● H s y ● r b a ● t z i d E x a u oh h a E oh i A n a f h l i x w r u m oh s e u h r w n ● 27 The Writing, as it is sent to B. s e l r o n r F t oh oh s oh t e n n n u m x r r k b e t c m l d r u i i s l o u b a n D e n l u e i n y A w y p c r i p a l H E u b r y I s T f d k T s p f f H f n G i n r e i i A l i d a p r e u o s oh e t e t h r oh d oh i oh e a t a u y n o d s h t t s oh h y c oh a t y e o n e e d T r n o y i r a n n r l n e C s d x D e C s d t t e A z l c t l a d a e r r n n S S v k f oh c l l l oh oh a f l y u i A o g f s h s t i u a a d e g e E W A e f g e F oh s s i e B S n m l oh t oh d e o n e t e a e n e W oh L h d i e u m s p w oh n k. The Method of Discovering what is before, by a Quadruple Inscription, hidden. 1. WHen B. receives the Writing, The first thing he does, is to draw a Line under, or to put some other Mark of distinction upon the 13 first Letters of the 2d Line of the said Writing, which he knows to be Indices of the 4 Figures. 2. That done, by the 10th and 11th of those Letters, [H f] he marks with pricks, as here underneath is expressed, the first Figure of Transcription, (which by the forementioned Accord, he knows to be a Trapezium!) And then transcribes the Writing into that Figure, till it be completed; as it is, Pag. 10. Fig. 4. omitting only a certain Number of Nulls, which are easily known by the 13th and last of those Indices, viz. [G] 3. In the next place, he dashes out all the alternate Diagonal Lines of that Figure, commencing from the Letter [r] in the Dexter Point of the Figure exclusiuè, which by the same private Agreement were destined for Nulls, (or at least for Disguises) And then transcribes the remainder into a Rectangle-Triangle, of whose Height and Hypotenuse, the 7th and 8th Letters of the 2d Line of the Writing, are sufficient Indices, only a certain Number of Nulls, denoted by the 12th Index, viz. [n] are omitted. In the 4th place, having, by the 4th and 5th Indices, with points or pricks, determined by limits, the 3d Figure of Transcription (which he knows is a Rhomboides) he fills and completes it out of the Rectangle-Triangle, omitting only so many Letters for Nulls, as [f] the 9th Letter of that 2d Line, indigates. Lastly, By the first, 2d, 3d, and 6th Letters, he determines and fills the 4th and last Figure of Transcription, (which was the first Figure of Inscription) and consequently he has before his eyes what he sought for, which I do not believe the Understanding of any Mortal man were, by any other means than by being privy to the forementioned Accord, ever able to discover. I have here underneath inserted the Scheme of that first Figure of Transcription, (or 4th Figure of Inscription,) that so by it, the Reader may plainly discern the manner of performing all the rest. table of cryptographical transcription Fig. I. The First Transcription. 11 17 8 16 22 2 12 27 1 21 26 7 13 15 6 18 5 20 14 23 4 25 10 19 24 3 9 11 ● ● ● s ● ● ● y ● ● ● ● ● ● ● r ● e r o e ● e ● u ● e i ● u y t l ● c ● i ● ● ● ● o I e r ● r ● l i ● c ● a s s n o i ● ● ● ● p o i n n ● e l l e n n r a i o ● d t r u F l n u · e e m ● H y ● · t i x o E A ● · h · i · · r · · o · · u · · w · n 27 But forasmuch as those who writ much in a Crytographical Method, have oft times occasion to hid a Word, or short Sentence, and not a whole Page, or Letter, I have thought it convenient (besides those Printed Papers which I have provided of all sorts) to publish the Description and Use of a small portable, and low-prized Machina, very useful for that purpose. A Description of the MACHINA CYCLOLOGICA CRYPTOGRAPHICA. THe lower part of the Instrument consists of two Circular Plates, the one turning round on a Centre within the other, And in that which turns there are 25 small holes or Foramina at an equal distance. And both above, and beneath those 25 foramina, there are 25 Letters, as Pag. 12. Fig. I. The upper part or lid is a Circular Plate, the inner part whereof is curt away, and upon the inner Limb thereof 25 Letters graved, and in it a small hole or window. And those 25 Letters in any broken Method whatsoever, (vid. Fig. TWO, III, IV, & V.) only the two Correspondents must have each of the same Alphabet, in the very same Order, Letter for Letter: For Example, let their Alphabet be this, viz. h q f r e i s d k s v l c t m y b x n w o z g a p. The Use of this Machina. Let the Correspondents A. and B. agree, 1. That one of those 25 Letters shall be their Key, suppose (m). 2. That a certain number of Nulls (suppose 3) shall be placed between the 3d and 4th Letter of the Writing, and another number of Nulls (viz. 4.) at the latter end. Then, let A. write to B. these words: Your Brother betrays you. The Method of Hiding. First, A. with the Digital Index (which is to be put on the third Finger of the Right hand, that so he may not be constrained to lay down his Pen, at every motion, vid. Fig. VI) turns the Letter (m) which is the Key, under the Window. 2. He puts the small end of the Digital Index into the foramen or hole under the Window, and turns about the movable Plate, till the small end of the Index stand over against the first Letter of what he is to hid, and the Letter that appears through the Window is (b), which he sets down; This done, he puts the Index again under the Window, and turns it over against the 2d Letter of the Writing, viz. (o), and then (f) appears, which he sets down likewise; And thus he repeats the same thing till the Writing be finished, only between the 3d and 4th Letters he intermingles 3 Nulls, viz. (p w x), and adds 4 Nulls, viz. (n p s o) at the end; And then the Writing stands thus, viz. table of cryptographical transcription Y o u r B r oh t h e r b e t r a y e s y o u b f d p w x y t z d t i h k s q d y m b l n o s l n p s o Here by the way it is observable, that of this Writing, as it is hidden, the Letter (d) is thrice found; in one place it stands for u, in another for o, in a third for t. Thus l, for e and u; and s, for o and b; and t, for b and t. In fine, the nature of this Machina is such, that in long Writing each Letter of the Alphabet may stand both for itself and all the rest, which makes the Intrigue a thousand times more difficult, and leaves the Discoverer in infinite Doubts, and Uncertainties. The Method of Discovering. When B. receives this Writing, he immediately knows where the Nulls are, and cancels them; then placing the Key (m) in the Window of his Machina, he turns it about, till the first Letter of the Writing, as it is hidden, viz. (b) appear through the Window, and look what Capital Letter in the Cover, answers to the small end of his Index (which he is not to take out till he has observed!) That is the first Letter of the given Intelligence. Again, he puts the Point of his Index in the hole under the Window, and turns it about till the 2d Letter of the same Writing, viz. (f) appear, and That is the 2d Letter of the Intelligence; And this B. repeats, till the whole be discovered; and than it stands thus: table of cryptographical transcription b f d * * * y t z d t i h k s q d y m b l n o s l * * * * y o u r b r oh t h e r b e t r a y e s y o u AND THAT this Method may not appear to be less secure than the other, I shall, to satisfy the Reader's curiosity, show him how it may be hidden doubly, trebly, etc. in infinitum. For Example, Let the Writing singly hidden stand as underneath, and a 2d Key being foredetermined between them, suppose (p), A. places it under the Window, and then turns it about till the Point of the Index stand against the first Letter of the simply-hidden Writing, viz. (b), and in the Window appears (g), which he sets down for (b): And thus for (f) he finds (b) and so to the end, putting between the 3d and 4th Letters 3 Nulls, and 4 at the latter end. table of cryptographical transcription b f d y t z d t i h k s q d y m b l n o f l g b c w n o m oh z x a m s z r c k ● a z u g k f b s w x a After this very manner may this also be hidden by a third and different Key, and Alphabet, For so is the Machina contrived, that any Alphabet may be inscribed and shifted, at pleasure, either in the movable Plate, or the Cover, vid. Fig. 2d, 3d and 4th. And for a clearer proof of what has been asserted, The very same Sentence which is here underneath, by the help of that Machina, concealed, is also expressed Word for Word, and Letter for Letter; And which is most of all, without any Nulls or insignificant Characters; To see, if there be any Artist in the World who is able, by any lawful means, or certain Rules, to give the true Genesis, and Analysis of that, or any such Cryptographical Writing; And to discover the Original Alphabet, of each respective Permutation, by determining the several Stations and Aspects of the Literae Exemtiles, and their Nova Clavis; and from what Foramina they are to be turned on and off by the help of the Digital Index, and consequently how each Superior Letter is signified by its Inferior, and no other. diagrams of cryptographical machine Fig: I Fig: TWO Fig: III Fig: IV Fig: V Fig: VI Inde● Digit●lis tables of steganographical transcription Scriptio Steganographica. C A U T È A G E, D U O X l y u t r x i, q b d P R A C I P U I E X A U L A I i mi l b y g h g b r g w p C O N I U R A R U N T C O N T R A T E ● ● w z r g t e q n f b w m n f z x m Soli DEO Gloria