Polygraphia

The Polygraphia Cipher originates from the work Polygraphia, a 16th-century cryptographic treatise written by the German abbot and polymath Johannes Trithemius and first published in 1518. The book is considered the first printed work devoted entirely to cryptography. Among its many systems, Trithemius introduced a progressive substitution method in which the encryption alphabet changes with each letter of the message.

In its simplest form, the cipher uses a sequence of shifted alphabets derived from a tabula recta (a table of shifted alphabets). The first letter is encrypted with the normal alphabet shifted once, the second with a shift of two, the third with a shift of three, and so on. After reaching the end of the alphabet, the shifts wrap around and continue again from the beginning. Because the substitution changes constantly, the cipher forms an early example of a polyalphabetic encryption method.

Polygraphia Cipher: Encoding

To encode a message, write the plaintext and apply a progressive shift to each letter according to its position in the message. The first letter is shifted by 1, the second by 2, the third by 3, and so on, wrapping around the alphabet when necessary. For example, encoding the message HELLO:

Plaintext:  H  E  L  L  O
Shift:      +1 +2 +3 +4 +5

Alphabet positions:
A=0 B=1 C=2 D=3 E=4 F=5 G=6 H=7 I=8 J=9
K=10 L=11 M=12 N=13 O=14 P=15 Q=16 R=17
S=18 T=19 U=20 V=21 W=22 X=23 Y=24 Z=25

Encoding (plaintext + shift):
H(7) +1 = I(8)
E(4) +2 = G(6)
L(11)+3 = O(14)
L(11)+4 = P(15)
O(14)+5 = T(19)

Ciphertext: IGOPT

Each successive letter is encrypted using a slightly different alphabet, creating a changing substitution pattern throughout the message.

Polygraphia Cipher: Decoding

To decode, subtract the progressive shift values from each ciphertext letter. Using the same sequence of shifts restores the original plaintext:

Ciphertext: I  G  O  P  T
Shift:      -1 -2 -3 -4 -5

Decoding (ciphertext - shift):
I(8)  -1 = H(7)
G(6)  -2 = E(4)
O(14) -3 = L(11)
P(15) -4 = L(11)
T(19) -5 = O(14)

Plaintext: HELLO

Polygraphia Cipher: Notes

The systems described in Polygraphia represent some of the earliest explorations of polyalphabetic cryptography in Europe. Although simple by modern standards, Trithemius’ shifting alphabets introduced the idea that a cipher could change continuously throughout a message. This concept later influenced more sophisticated ciphers such as the Vigenère Cipher and other Renaissance encryption methods.