Tabula recta

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The tabula recta in a modern presentation
The Polygraphiae of Johannes Trithemius contains the first representation of the Tabula recta

The tabula recta (from Latin tabula = table, table and rectus = straight, regular, i.e. in German roughly: square table ) is a square representation of the letters of the alphabet , in which the letters are shifted one place to the left in each line. It was given by the German Benedictine abbot Johannes Trithemius (1462-1516) in 1508 in the fifth volume of his six-volume work Polygraphiae libri sex (German: Six books on polygraphy), which was written in Latin . These are the first printed books on cryptography . They did not appear until 1518 after his death.

In the original version (see web links : "Image of the authentic Tabula recta "), one of which is kept in the Bavarian State Library in Munich , contains the table referred to in his book as Recta transpositionis tabula (literally: regularly converted table) based on the archaic Latin alphabet only the 24 letters a, b, c, d, e, f, g, h, i, k, l, m, n, o, p, q, r, s, t, u, x, y , z and w. J and v are missing, because at that time no distinction was made between u and v and i and j.

Recta transpositionis tabula. 

a b c d e f g h i k l m n o p q r s t u x y z w
b c d e f g h i k l m n o p q r s t u x y z w a
c d e f g h i k l m n o p q r s t u x y z w a b
d e f g h i k l m n o p q r s t u x y z w a b c
e f g h i k l m n o p q r s t u x y z w a b c d
f g h i k l m n o p q r s t u x y z w a b c d e
g h i k l m n o p q r s t u x y z w a b c d e f
h i k l m n o p q r s t u x y z w a b c d e f g
i k l m n o p q r s t u x y z w a b c d e f g h
k l m n o p q r s t u x y z w a b c d e f g h i
l m n o p q r s t u x y z w a b c d e f g h i k
m n o p q r s t u x y z w a b c d e f g h i k l
n o p q r s t u x y z w a b c d e f g h i k l m
o p q r s t u x y z w a b c d e f g h i k l m n
p q r s t u x y z w a b c d e f g h i k l m n o
q r s t u x y z w a b c d e f g h i k l m n o p
r s t u x y z w a b c d e f g h i k l m n o p q
s t u x y z w a b c d e f g h i k l m n o p q r
t u x y z w a b c d e f g h i k l m n o p q r s
u x y z w a b c d e f g h i k l m n o p q r s t
x y z w a b c d e f g h i k l m n o p q r s t u
y z w a b c d e f g h i k l m n o p q r s t u x
z w a b c d e f g h i k l m n o p q r s t u x y
w a b c d e f g h i k l m n o p q r s t u x y z
In hac tabula literarum canonica siue recta tot ex uno & usuali nostro latinarum literarum ipsarum per mutationem seu transpositionem habes alphabeta, quot in ea per totum sunt monogrammata, uidelicet quater & uigesies quatuor & uiginti, quae faciunt in numero D.lxxvi. ac per to tidem multiplicata, paulo efficiunt minus quam quatuordecem milia.

German: In this regular or square table of letters you can find the common alphabet of our Latin letters by changing (" per mutationem ") or conversion (" transpositionem "), which in their entirety represent monograms (individual letters), namely 24 by 24, That gives the number of 576 and if you multiply this by that number (24) you get a little less than 14,000.

Trithemius used the two important terms ( permutation and transposition ) in his book as early as 1508 , which are still the basis for modern cryptographic procedures (such as AES ). His tabula recta in its modern version with all 26 capital letters of the Latin alphabet of our time has the appearance shown in the picture (top right).

Trithemius used his blackboard to explain a method of polyalphabetic encryption . He suggested encrypting the first letter of the message to be encrypted using the first line of the tabula recta , the second using the second line, and so on. With this he achieved a leveling of the frequency range of the ciphertext and thus avoided a major weak point of the then still very common variants of the monoalphabetic encryption method, which can be broken (deciphered) relatively easily with the help of statistical methods due to the characteristic frequencies of the individual letters . Today this method proposed by Trithemius with his Tabula recta is called “progressive encryption”, which is still used, for example, in machine encryption . However, there are of course more than two dozen different alphabets in use today .

The tabula recta is also used in the Vigenère encryption proposed by the French cryptographer Blaise de Vigenère in 1585 and is often incorrectly referred to as the “ Vigenère square ” after him .

In general, one speaks of a tabula recta when it is a square arrangement of letters in which they are shifted by one space in each subsequent line, but not in the first (and thus also in all following) arranged in alphabetical order. In such cases, the cryptographer speaks of a “scrambled alphabet” (for more information on creating secret alphabets, see: Creating secret alphabets in monoalphabetic substitution ). Strictly speaking, Trithemius' original tablet is of this type, because in accordance with its time he placed the letter w as the last letter after the z.

literature

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