The e‐derivative of Boolean functions and its application in the fault detection and cryptographic system

The purpose of this paper is to show that the e‐derivative is of great significance when revealing cryptographic characteristics of Boolean functions and assurance of the safety of the cryptographic system.

A new definition is introduced in this paper.

After introducing the e‐derivative, the authors obtain some relevant cryptographic properties and theorems which can fully reveal the relationships between characteristics and structures of Boolean functions. In logic circuit fields, the authors conduct the test to all the signals with numerical value 1 in the transmission line using the e‐derivative, which improves the ability of the test. In addition, when there is no expression of the transmission line the authors will obtain it through the vector, and then do troubleshooting.

Logic circuit is the main limitation in the fault detection.

A very useful method for assurance of the safety of cryptographic systems.

This paper is the first time, in cryptology fields, that the e‐derivative of Boolean functions as a new definition is introduced to fully reveal the relationships between characteristics and structures of Boolean functions. In addition, they can also be applied to the locating test of the breakdown, which improves the ability of the test.