Japanese Cryptology From The 1500s To Meiji - Hara's Pseudo-Random Number Generator

Hara's Pseudo-Random Number Generator

Perhaps realizing the gap between theory and practice, Hara devised a small system for generating pseudo-random numbers that could be used by units whose charts were outdated and which could not be supplied with new ones. This suggests that the cryptographers had real world experience with cryptology under battlefield conditions.

The system is simple, as it no doubt was intended to be. It requires a small chart of random numbers. Instead of using the numbers as additives, the encipherer uses two or more of them to create a much longer number. That number is then used to superencipher the message. The figure below shows how this is done.

Creating a Pseudo-Random Number from Two Other Numbers

831728	8	3	1	7	2	8	8	3	1	7	2	8	8	3	1
96837	9	6	8	3	7	9	6	8	3	7	9	6	8	3	7
Result	7	9	9	0	9	7	4	1	4	4	1	4	6	6	8

When the numbers are added, any tens units are dropped. Thus 8 + 9 = 7. If the encipherer uses a six-digit number and a five-digit number, the resulting pseudo-random number will repeat after 30 digits. Hiyama gives an example of this system using a seven-digit and a five-digit number, which repeats after 35 digits.

This pseudo-random number system is much weaker than the usual system of superencipherment but as an emergency backup system it would have been adequate and certainly better than using a transposition or simple substitution cipher. Like any other cipher system, breaking a pseudo-random number system just requires a sufficient amount of intercepted ciphertext.