Encryption with Irrational Numbers and the One-Time Pad

plain text

Every great advance in science has issued from a new audacity of imagination. — John Dewey

prime 0

5

prime 1

11

length to encode

91

shift digits to left

50

irrational number:

1

1/11

5

pad digits before shift: 0.86388766370259036239...

Cipher Text

{16,56,32,91,61,55,91,124,77,82,57,57,120,124,62,58,123,95,127,58,61,104,0,73,119,110,65,115,44,69,66,73,41,16,1,121,52,127,126,98,77,46,52,111,99,97,39,102,98,61,107,97,35,54,115,83,103,121,44,99,44,22,57,34,49,49,76,111,85,99,74,33,20,104,66,67,17,44,8215,20,112,62,72,37,41,85,44,71,127,111,4571}

Deciphered

Every great advance in science has issued from a new audacity of imagination. — John Deweyᇟ

In this Demonstration, the initial bits of an irrational number

1

p

1

p

0

are used as a one-time pad for the encryption of a sentence. The resulting digits are shifted to the left and XOR-ed with the plain text to the length specified to create the cipher text.

The reverse process is used to decrypt by again generating the irrational number from the two primes, performing the shift left of the number bits, and XOR-ing with the cipher text for the length of that text.

The one-time pad is the shared secret key used to encrypt and decrypt the plain text. If the one-time pad is discovered, the message can be decrypted.