This was described in "The Gold at Starbow's End" by Frederick Pohl in Analog Science Fiction / Science Fact, April 1972. The example here is mine.
Write out the plain text
message. Encipher each letter with
a prime number in sequence: 1, 2, 3, 5, 7, 11, 13, 17, 19, ... Then, use the alphabet position of the letter as an exponent. A=1, B=2, C=3, D=4, and so on. Raise the prime number to the exponent and you have an integer. Multiply all the integers of the text into one large number.
HIDE A BAD FACE
TEXT
|
H
|
I
|
D
|
E
|
A
|
B
|
A
|
D
|
|||||
PRIME
|
1
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
|||||
POSITION
|
8
|
9
|
4
|
5
|
1
|
2
|
1
|
4
|
|||||
FACTOR
|
1^8
|
2^9
|
3^4
|
5^5
|
7^1
|
11^2
|
13^1
|
17^4
|
|||||
INTEGER
|
1
|
512
|
81
|
3125
|
7
|
121
|
13
|
83521
|
|||||
TEXT
|
F
|
A
|
C
|
E
|
|||||||||
PRIME
|
19
|
23
|
29
|
31
|
|||||||||
POSITION
|
6
|
1
|
3
|
5
|
|||||||||
FACTOR
|
19^6
|
23^1
|
29^3
|
31^5
|
|||||||||
INTEGER
|
47045881
|
23
|
24389
|
28629151
|
|||||||||
4,739,426,072,295,360+ sextillion.
Using the Preamble to the Constitution - "We the people of the United States..." - the H enciphers to 3^20 or 3486784401 and the first P is more than 45949729863572200.
The message conveys meaning only when it is
deciphered. It is easy to see that the longer the message, the harder that
will be. It quickly surpasses any theoretical computing ability and soon
requires more time than is in the universe.
The method was name for Kurt Gödel. “In mathematical logic, a Gödel numbering is a function
that assigns to each symbol and well-formed formula of some formal language a
unique natural number, called its Gödel number. The concept was used by Kurt
Gödel for the proof of his incompleteness theorems. (Gödel 1931).” Wikipedia here.
ALSO ON NECESSARY FACTS
Charles Babbage: Code Breaker
Codes and Coins
U. S. Patent Law Does Not Add Up
Soldiers of Peace
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